SHAPE version 2b, with bootstrap Confidence Interval of Hazard Parameters
This commit is contained in:
Konstantinos Leptokaropoulos
parent
1177e49e6d
commit
eab8aa62ef
@ -12,11 +12,15 @@ SHAPE_ver2 - is a Wrapper version (inputs are set in the wrapper script and onc
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REQUIREMENTS: Matlab R2017b or later, with installed Toolboxes:
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REQUIREMENTS: Matlab R2017b or later, with installed Toolboxes:
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- 'Statistics and Machine Learning'
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- 'Statistics and Machine Learning'
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SHAPE_ver2b- is identical to SHAPE_ver2, but also estimates 95% bootstrap confidence interval
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of Hazard Parameters and b-value
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>> Please refer to the "READ_ME_SHAPE_ver*.pdf" file in each directory for further instructions on
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>> Please refer to the "READ_ME_SHAPE_ver*.pdf" file in each directory for further instructions on
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step-by-step implementation of SHAPE as well as for data format specifications and general tips.
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step-by-step implementation of SHAPE as well as for data format specifications and general tips.
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>> Your feedback is welcome! contact Dr K. Leptokaropoulos for questions, suggestions or comments:
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>> Your feedback is welcome! contact Dr Kostas Leptokaropoulos for questions, suggestions or comments:
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- kleptoka@igf.edu.pl
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- yebeneka@gmail.com, kleptoka@igf.edu.pl
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>> Please acknowledge any use of SHAPE in your work, by citing:
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>> Please acknowledge any use of SHAPE in your work, by citing:
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- Leptokaropoulos, K. and S. Lasocki (2020), SHAPE: A MATLAB Software Package for Time-dependent
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- Leptokaropoulos, K. and S. Lasocki (2020), SHAPE: A MATLAB Software Package for Time-dependent
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8
SHAPE_Package/!What's_New!.txt
Executable file
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SHAPE_Package/!What's_New!.txt
Executable file
@ -0,0 +1,8 @@
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>>>> 08 JUNE 2020
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Please find the new version SHAPE_ver2b, which in addition to all functionalities included in SHAPE_ver2
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also estimates the 95% bootstrap confidence interval of Mean Return Period, Exceedance Probability, and
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(for parametric models) b-value.
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The package is available in this repository together with sample data and complete user guide.
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6947
SHAPE_Package/SHAPE_ver2b.0/CATALOGS/ST2_SEIS_Data.txt
Executable file
6947
SHAPE_Package/SHAPE_ver2b.0/CATALOGS/ST2_SEIS_Data.txt
Executable file
File diff suppressed because it is too large
Load Diff
1
SHAPE_Package/SHAPE_ver2b.0/CATALOGS/ST2_SEIS_Fields.txt
Executable file
1
SHAPE_Package/SHAPE_ver2b.0/CATALOGS/ST2_SEIS_Fields.txt
Executable file
@ -0,0 +1 @@
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Time ML Lat Long Depth
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SHAPE_Package/SHAPE_ver2b.0/PRODUCTION_DATA/ST2_PROD_Data.txt
Executable file
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SHAPE_Package/SHAPE_ver2b.0/PRODUCTION_DATA/ST2_PROD_Data.txt
Executable file
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|
2014 07 10 00 00 00 145
|
||||||
|
2014 07 11 00 00 00 144.97
|
||||||
|
2014 07 12 00 00 00 144.6
|
||||||
|
2014 07 13 00 00 00 144.3
|
||||||
|
2014 07 14 00 00 00 144
|
||||||
|
2014 07 15 00 00 00 143.66
|
||||||
|
2014 07 16 00 00 00 143.24
|
||||||
|
2014 07 17 00 00 00 143.02
|
||||||
|
2014 07 18 00 00 00 143.22
|
||||||
|
2014 07 19 00 00 00 143.38
|
||||||
|
2014 07 20 00 00 00 143.47
|
||||||
|
2014 07 21 00 00 00 143.43
|
||||||
|
2014 07 22 00 00 00 143.01
|
||||||
|
2014 07 23 00 00 00 142.84
|
||||||
|
2014 07 24 00 00 00 143.36
|
||||||
|
2014 07 25 00 00 00 142.12
|
||||||
|
2014 07 26 00 00 00 141.72
|
||||||
|
2014 07 27 00 00 00 141.6
|
||||||
|
2014 07 28 00 00 00 141.95
|
||||||
|
2014 07 29 00 00 00 142.23
|
||||||
|
2014 07 30 00 00 00 142.76
|
||||||
|
2014 07 31 00 00 00 142.96
|
||||||
|
2014 08 01 00 00 00 143.06
|
||||||
|
2014 08 02 00 00 00 142.86
|
||||||
|
2014 08 03 00 00 00 142.63
|
||||||
|
2014 08 04 00 00 00 142.37
|
||||||
|
2014 08 05 00 00 00 142.08
|
||||||
|
2014 08 06 00 00 00 141.96
|
||||||
|
2014 08 07 00 00 00 142.19
|
||||||
|
2014 08 08 00 00 00 142.4
|
||||||
|
2014 08 09 00 00 00 142.58
|
||||||
|
2014 08 10 00 00 00 142.57
|
||||||
|
2014 08 11 00 00 00 142.17
|
||||||
|
2014 08 12 00 00 00 141.79
|
||||||
|
2014 08 13 00 00 00 141.43
|
||||||
|
2014 08 14 00 00 00 141.05
|
||||||
|
2014 08 15 00 00 00 140.7
|
||||||
|
2014 08 16 00 00 00 140.68
|
||||||
|
2014 08 17 00 00 00 140.93
|
||||||
|
2014 08 18 00 00 00 141.13
|
||||||
|
2014 08 19 00 00 00 141.1
|
||||||
|
2014 08 20 00 00 00 140.75
|
||||||
|
2014 08 21 00 00 00 140.69
|
||||||
|
2014 08 22 00 00 00 141.01
|
||||||
|
2014 08 23 00 00 00 141.33
|
||||||
|
2014 08 24 00 00 00 141.6
|
||||||
|
2014 08 25 00 00 00 141.8
|
||||||
|
2014 08 26 00 00 00 142.06
|
||||||
|
2014 08 27 00 00 00 142.39
|
||||||
|
2014 08 28 00 00 00 142.75
|
||||||
|
2014 08 29 00 00 00 143.02
|
||||||
|
2014 08 30 00 00 00 143.44
|
||||||
|
2014 08 31 00 00 00 143.87
|
||||||
|
2014 09 01 00 00 00 145.92
|
||||||
|
2014 09 02 00 00 00 146.24
|
||||||
|
2014 09 03 00 00 00 146.81
|
||||||
|
2014 09 04 00 00 00 147.26
|
||||||
|
2014 09 05 00 00 00 147.58
|
||||||
|
2014 09 06 00 00 00 147.71
|
||||||
|
2014 09 07 00 00 00 147.87
|
||||||
|
2014 09 08 00 00 00 148.08
|
||||||
|
2014 09 09 00 00 00 148.46
|
||||||
|
2014 09 10 00 00 00 148.58
|
||||||
|
2014 09 11 00 00 00 148.15
|
||||||
|
2014 09 12 00 00 00 147.39
|
||||||
|
2014 09 13 00 00 00 146.9
|
||||||
|
2014 09 14 00 00 00 146.85
|
||||||
|
2014 09 15 00 00 00 146.66
|
||||||
|
2014 09 16 00 00 00 145.9
|
||||||
|
2014 09 17 00 00 00 145.4
|
||||||
|
2014 09 18 00 00 00 145.19
|
||||||
|
2014 09 19 00 00 00 145.01
|
||||||
|
2014 09 20 00 00 00 145.11
|
||||||
|
2014 09 21 00 00 00 145.44
|
||||||
|
2014 09 22 00 00 00 145.72
|
||||||
|
2014 09 23 00 00 00 145.87
|
||||||
|
2014 09 24 00 00 00 146.57
|
||||||
|
2014 09 25 00 00 00 146.94
|
||||||
|
2014 09 26 00 00 00 147.25
|
||||||
|
2014 09 27 00 00 00 147.61
|
||||||
|
2014 09 28 00 00 00 147.92
|
||||||
|
2014 09 29 00 00 00 148.23
|
||||||
|
2014 09 30 00 00 00 148.53
|
||||||
|
2014 10 01 00 00 00 148.68
|
||||||
|
2014 10 02 00 00 00 148.67
|
||||||
|
2014 10 03 00 00 00 148.35
|
||||||
|
2014 10 04 00 00 00 147.9
|
||||||
|
2014 10 05 00 00 00 147.96
|
||||||
|
2014 10 06 00 00 00 148.34
|
||||||
|
2014 10 07 00 00 00 148.53
|
||||||
|
2014 10 08 00 00 00 149.56
|
||||||
|
2014 10 09 00 00 00 149.92
|
||||||
|
2014 10 10 00 00 00 149.94
|
||||||
|
2014 10 11 00 00 00 149.82
|
||||||
|
2014 10 12 00 00 00 149.55
|
||||||
|
2014 10 13 00 00 00 149.43
|
||||||
|
2014 10 14 00 00 00 148.95
|
||||||
|
2014 10 15 00 00 00 148.6
|
||||||
|
2014 10 16 00 00 00 148.33
|
||||||
|
2014 10 17 00 00 00 148.31
|
||||||
|
2014 10 18 00 00 00 148.4
|
||||||
|
2014 10 19 00 00 00 149.27
|
||||||
|
2014 10 20 00 00 00 149.57
|
||||||
|
2014 10 21 00 00 00 149.02
|
||||||
|
2014 10 22 00 00 00 148.84
|
||||||
|
2014 10 23 00 00 00 149.12
|
||||||
|
2014 10 24 00 00 00 149.12
|
||||||
|
2014 10 25 00 00 00 149.37
|
||||||
|
2014 10 26 00 00 00 150.5
|
||||||
|
2014 10 27 00 00 00 151.23
|
||||||
|
2014 10 28 00 00 00 151.17
|
||||||
|
2014 10 29 00 00 00 150.73
|
||||||
|
2014 10 30 00 00 00 150.42
|
||||||
|
2014 10 31 00 00 00 150.19
|
||||||
|
2014 11 01 00 00 00 150.07
|
||||||
|
2014 11 02 00 00 00 149.75
|
||||||
|
2014 11 03 00 00 00 149.66
|
||||||
|
2014 11 04 00 00 00 149.23
|
||||||
|
2014 11 05 00 00 00 148.96
|
||||||
|
2014 11 06 00 00 00 149.09
|
||||||
|
2014 11 07 00 00 00 149.34
|
||||||
|
2014 11 08 00 00 00 149.84
|
||||||
|
2014 11 09 00 00 00 150.31
|
||||||
|
2014 11 10 00 00 00 150.63
|
||||||
|
2014 11 11 00 00 00 150.76
|
||||||
|
2014 11 12 00 00 00 150.89
|
||||||
|
2014 11 13 00 00 00 151.55
|
||||||
|
2014 11 14 00 00 00 153.94
|
||||||
|
2014 11 15 00 00 00 156.7
|
||||||
|
2014 11 16 00 00 00 158.48
|
||||||
|
2014 11 17 00 00 00 159.22
|
||||||
|
2014 11 18 00 00 00 159.51
|
||||||
|
2014 11 19 00 00 00 159.47
|
||||||
|
2014 11 20 00 00 00 159.62
|
||||||
|
2014 11 21 00 00 00 159.73
|
||||||
|
2014 11 22 00 00 00 159.78
|
||||||
|
2014 11 23 00 00 00 160.01
|
||||||
|
2014 11 24 00 00 00 160.38
|
||||||
|
2014 11 25 00 00 00 160.44
|
||||||
|
2014 11 26 00 00 00 160.52
|
||||||
|
2014 11 27 00 00 00 160.65
|
||||||
|
2014 11 28 00 00 00 160.78
|
||||||
|
2014 11 29 00 00 00 160.98
|
||||||
|
2014 11 30 00 00 00 161.45
|
||||||
|
2014 12 01 00 00 00 162.55
|
||||||
|
2014 12 02 00 00 00 162.91
|
||||||
|
2014 12 03 00 00 00 163.15
|
||||||
|
2014 12 04 00 00 00 163.01
|
||||||
|
2014 12 05 00 00 00 163.36
|
||||||
|
2014 12 06 00 00 00 163.98
|
||||||
|
2014 12 07 00 00 00 164.71
|
||||||
|
2014 12 08 00 00 00 164.92
|
||||||
|
2014 12 09 00 00 00 165.15
|
||||||
|
2014 12 10 00 00 00 165.02
|
||||||
|
2014 12 11 00 00 00 164.78
|
||||||
|
2014 12 12 00 00 00 165.08
|
||||||
|
2014 12 13 00 00 00 165.33
|
||||||
|
2014 12 14 00 00 00 165.39
|
||||||
|
2014 12 15 00 00 00 165.25
|
||||||
|
2014 12 16 00 00 00 165.36
|
||||||
|
2014 12 17 00 00 00 165.8
|
||||||
|
2014 12 18 00 00 00 165.82
|
||||||
|
2014 12 19 00 00 00 165.67
|
||||||
|
2014 12 20 00 00 00 165.41
|
||||||
|
2014 12 21 00 00 00 165.2
|
||||||
|
2014 12 22 00 00 00 165.32
|
||||||
|
2014 12 23 00 00 00 165.57
|
||||||
|
2014 12 24 00 00 00 165.36
|
||||||
|
2014 12 25 00 00 00 165.31
|
||||||
|
2014 12 26 00 00 00 165.42
|
||||||
|
2014 12 27 00 00 00 165.75
|
||||||
|
2014 12 28 00 00 00 165.99
|
||||||
|
2014 12 29 00 00 00 166
|
||||||
|
2014 12 30 00 00 00 166.06
|
||||||
|
2014 12 31 00 00 00 166.79
|
||||||
|
2015 01 01 00 00 00 167.54
|
||||||
|
2015 01 02 00 00 00 168.16
|
||||||
|
2015 01 03 00 00 00 168.72
|
||||||
|
2015 01 04 00 00 00 169.3
|
||||||
|
2015 01 05 00 00 00 169.77
|
||||||
|
2015 01 06 00 00 00 170.17
|
||||||
|
2015 01 07 00 00 00 170.74
|
||||||
|
2015 01 08 00 00 00 171.51
|
||||||
|
2015 01 09 00 00 00 171.91
|
||||||
|
2015 01 10 00 00 00 172
|
||||||
|
2015 01 11 00 00 00 172
|
||||||
|
2015 01 12 00 00 00 171.97
|
||||||
|
2015 01 13 00 00 00 171.77
|
||||||
|
2015 01 14 00 00 00 171.53
|
||||||
|
2015 01 15 00 00 00 171.22
|
||||||
|
2015 01 16 00 00 00 170.97
|
||||||
|
2015 01 17 00 00 00 170.68
|
||||||
|
2015 01 18 00 00 00 170.65
|
||||||
|
2015 01 19 00 00 00 170.78
|
||||||
|
2015 01 20 00 00 00 170.93
|
||||||
|
2015 01 21 00 00 00 171.05
|
||||||
|
2015 01 22 00 00 00 171.07
|
||||||
|
2015 01 23 00 00 00 171.04
|
||||||
|
2015 01 24 00 00 00 170.99
|
||||||
|
2015 01 25 00 00 00 170.94
|
||||||
|
2015 01 26 00 00 00 170.91
|
||||||
|
2015 01 27 00 00 00 170.95
|
||||||
|
2015 01 28 00 00 00 170.93
|
||||||
|
2015 01 29 00 00 00 171.02
|
||||||
|
2015 01 30 00 00 00 171.05
|
||||||
|
2015 01 31 00 00 00 171.1
|
||||||
|
2015 02 01 00 00 00 171.28
|
||||||
|
2015 02 02 00 00 00 171.57
|
||||||
|
2015 02 03 00 00 00 171.29
|
||||||
|
2015 02 04 00 00 00 170.9
|
||||||
|
2015 02 05 00 00 00 170.82
|
||||||
|
2015 02 06 00 00 00 170.77
|
||||||
|
2015 02 07 00 00 00 170.73
|
||||||
|
2015 02 08 00 00 00 170.66
|
||||||
|
2015 02 09 00 00 00 170.6
|
||||||
|
2015 02 10 00 00 00 170.53
|
||||||
|
2015 02 11 00 00 00 170.4
|
||||||
|
2015 02 12 00 00 00 170.37
|
||||||
|
2015 02 13 00 00 00 170.34
|
||||||
|
2015 02 14 00 00 00 170.4
|
||||||
|
2015 02 15 00 00 00 170.58
|
||||||
|
2015 02 16 00 00 00 170.63
|
||||||
|
2015 02 17 00 00 00 170.64
|
||||||
|
2015 02 18 00 00 00 170.8
|
||||||
|
2015 02 19 00 00 00 170.88
|
||||||
|
2015 02 20 00 00 00 171.11
|
||||||
|
2015 02 21 00 00 00 171.33
|
||||||
|
2015 02 22 00 00 00 171.59
|
||||||
|
2015 02 23 00 00 00 171.72
|
||||||
|
2015 02 24 00 00 00 171.69
|
||||||
|
2015 02 25 00 00 00 171.53
|
||||||
|
2015 02 26 00 00 00 171.47
|
||||||
|
2015 02 27 00 00 00 171.46
|
||||||
|
2015 02 28 00 00 00 171.38
|
||||||
|
2015 03 01 00 00 00 171.37
|
||||||
|
2015 03 02 00 00 00 171.35
|
||||||
|
2015 03 03 00 00 00 171.27
|
||||||
|
2015 03 04 00 00 00 171.15
|
||||||
|
2015 03 05 00 00 00 171.04
|
||||||
|
2015 03 06 00 00 00 170.9
|
||||||
|
2015 03 07 00 00 00 170.82
|
||||||
|
2015 03 08 00 00 00 170.7
|
||||||
|
2015 03 09 00 00 00 170.57
|
||||||
|
2015 03 10 00 00 00 170.55
|
||||||
|
2015 03 11 00 00 00 170.69
|
||||||
|
2015 03 12 00 00 00 170.86
|
||||||
|
2015 03 13 00 00 00 170.95
|
||||||
|
2015 03 14 00 00 00 170.88
|
||||||
|
2015 03 15 00 00 00 170.76
|
||||||
|
2015 03 16 00 00 00 170.5
|
||||||
|
2015 03 17 00 00 00 170.29
|
||||||
|
2015 03 18 00 00 00 170.17
|
||||||
|
2015 03 19 00 00 00 169.91
|
||||||
|
2015 03 20 00 00 00 169.5
|
||||||
|
2015 03 21 00 00 00 169.28
|
||||||
|
2015 04 01 00 00 00 170.68
|
||||||
|
2015 04 02 00 00 00 170.36
|
||||||
|
2015 04 03 00 00 00 170.02
|
||||||
|
2015 04 04 00 00 00 169.7
|
||||||
|
2015 04 05 00 00 00 169.55
|
||||||
|
2015 04 06 00 00 00 169.41
|
||||||
|
2015 04 07 00 00 00 169.04
|
||||||
|
2015 04 08 00 00 00 168.37
|
||||||
|
2015 04 09 00 00 00 167.64
|
||||||
|
2015 04 10 00 00 00 167.32
|
||||||
|
2015 04 11 00 00 00 167.49
|
||||||
|
2015 04 12 00 00 00 167.63
|
||||||
|
2015 04 13 00 00 00 167.87
|
||||||
|
2015 04 14 00 00 00 168.05
|
||||||
|
2015 04 15 00 00 00 168.21
|
||||||
|
2015 04 16 00 00 00 168.34
|
||||||
|
2015 04 17 00 00 00 168.48
|
||||||
|
2015 04 18 00 00 00 168.61
|
||||||
|
2015 04 19 00 00 00 168.75
|
||||||
|
2015 04 20 00 00 00 168.89
|
||||||
|
2015 04 21 00 00 00 169.01
|
||||||
|
2015 04 22 00 00 00 169.18
|
||||||
|
2015 04 23 00 00 00 169.09
|
||||||
|
2015 04 24 00 00 00 168.78
|
||||||
|
2015 04 25 00 00 00 168.29
|
||||||
|
2015 04 26 00 00 00 167.85
|
||||||
|
2015 04 27 00 00 00 167.34
|
||||||
|
2015 04 28 00 00 00 167.01
|
||||||
|
2015 04 29 00 00 00 166.79
|
||||||
|
2015 04 30 00 00 00 166.7
|
||||||
|
2015 05 01 00 00 00 166.83
|
||||||
|
2015 05 02 00 00 00 166.65
|
||||||
|
2015 05 03 00 00 00 166.01
|
||||||
|
2015 05 04 00 00 00 165.45
|
||||||
|
2015 05 05 00 00 00 164.61
|
||||||
|
2015 05 06 00 00 00 163.86
|
||||||
|
2015 05 07 00 00 00 163.36
|
||||||
|
2015 05 08 00 00 00 163.02
|
||||||
|
2015 05 09 00 00 00 162.73
|
||||||
|
2015 05 10 00 00 00 162.81
|
||||||
|
2015 05 11 00 00 00 162.93
|
||||||
|
2015 05 12 00 00 00 162.76
|
||||||
|
2015 05 13 00 00 00 162.54
|
||||||
|
2015 05 14 00 00 00 162.36
|
||||||
|
2015 05 15 00 00 00 162.19
|
||||||
|
2015 05 16 00 00 00 162.03
|
||||||
|
2015 05 17 00 00 00 161.93
|
||||||
|
2015 05 18 00 00 00 161.79
|
||||||
|
2015 05 19 00 00 00 161.38
|
||||||
|
2015 05 20 00 00 00 160.79
|
||||||
|
2015 05 21 00 00 00 160.15
|
||||||
|
2015 05 22 00 00 00 159.43
|
||||||
|
2015 05 23 00 00 00 158.84
|
||||||
|
2015 05 24 00 00 00 158.38
|
||||||
|
2015 05 25 00 00 00 158
|
||||||
|
2015 05 26 00 00 00 157.48
|
||||||
|
2015 05 27 00 00 00 157.09
|
||||||
|
2015 05 28 00 00 00 156.77
|
||||||
|
2015 05 29 00 00 00 156.41
|
||||||
|
2015 05 30 00 00 00 156.06
|
||||||
|
2015 05 31 00 00 00 155.75
|
||||||
|
2015 06 01 00 00 00 155.45
|
||||||
|
2015 06 02 00 00 00 155.02
|
||||||
|
2015 06 03 00 00 00 154.79
|
||||||
|
2015 06 04 00 00 00 154.45
|
||||||
|
2015 06 05 00 00 00 154.18
|
||||||
|
2015 06 06 00 00 00 153.97
|
||||||
|
2015 06 07 00 00 00 153.78
|
||||||
|
2015 06 08 00 00 00 153.53
|
||||||
|
2015 06 09 00 00 00 153.28
|
||||||
|
2015 06 10 00 00 00 153.1
|
||||||
|
2015 06 11 00 00 00 152.48
|
||||||
|
2015 06 12 00 00 00 152.02
|
||||||
|
2015 06 13 00 00 00 152.06
|
||||||
|
2015 06 14 00 00 00 151.98
|
||||||
|
2015 06 15 00 00 00 152.06
|
||||||
|
2015 06 16 00 00 00 151.69
|
||||||
|
2015 06 17 00 00 00 151.11
|
||||||
|
2015 06 18 00 00 00 150.89
|
||||||
|
2015 06 19 00 00 00 150.73
|
||||||
|
2015 06 20 00 00 00 150.5
|
||||||
|
2015 06 21 00 00 00 150.41
|
||||||
|
2015 06 22 00 00 00 150.56
|
||||||
|
2015 06 23 00 00 00 150.56
|
||||||
|
2015 06 24 00 00 00 150.44
|
||||||
|
2015 06 25 00 00 00 150.18
|
||||||
|
2015 06 26 00 00 00 149.74
|
||||||
|
2015 06 28 00 00 00 149.24
|
||||||
|
2015 06 29 00 00 00 148.92
|
||||||
|
2015 06 30 00 00 00 148.5
|
||||||
|
2015 07 01 00 00 00 148.19
|
||||||
|
2015 07 02 00 00 00 148.16
|
||||||
|
2015 07 03 00 00 00 147.92
|
||||||
|
2015 07 04 00 00 00 147.4
|
||||||
|
2015 07 05 00 00 00 147.07
|
||||||
|
2015 07 06 00 00 00 146.79
|
||||||
|
2015 07 07 00 00 00 146.46
|
||||||
|
2015 07 08 00 00 00 146.11
|
||||||
|
2015 07 09 00 00 00 145.9
|
||||||
|
2015 07 10 00 00 00 146.13
|
||||||
|
2015 07 11 00 00 00 146.38
|
||||||
|
2015 07 12 00 00 00 146.58
|
||||||
|
2015 07 13 00 00 00 146.57
|
||||||
|
2015 07 14 00 00 00 146.36
|
||||||
|
2015 07 15 00 00 00 146.08
|
||||||
|
2015 07 16 00 00 00 145.89
|
||||||
|
2015 07 17 00 00 00 146.06
|
||||||
|
2015 07 18 00 00 00 146.2
|
||||||
|
2015 07 19 00 00 00 146.45
|
||||||
|
2015 07 21 00 00 00 146.53
|
||||||
|
2015 07 22 00 00 00 146.16
|
||||||
|
2015 07 23 00 00 00 145.81
|
||||||
|
2015 07 24 00 00 00 145.4
|
||||||
|
2015 07 25 00 00 00 145.02
|
||||||
|
2015 07 26 00 00 00 144.61
|
||||||
|
2015 07 27 00 00 00 144.41
|
||||||
|
2015 07 28 00 00 00 144.51
|
||||||
|
2015 07 29 00 00 00 144.65
|
||||||
|
2015 07 30 00 00 00 144.82
|
||||||
|
2015 07 31 00 00 00 144.75
|
||||||
|
2015 08 01 00 00 00 144.38
|
||||||
|
2015 08 02 00 00 00 144.01
|
||||||
|
2015 08 03 00 00 00 143.67
|
||||||
|
2015 08 04 00 00 00 143.49
|
||||||
|
2015 08 05 00 00 00 143.19
|
||||||
|
2015 08 06 00 00 00 143.28
|
||||||
|
2015 08 07 00 00 00 144.03
|
||||||
|
2015 08 08 00 00 00 144.44
|
||||||
|
2015 08 09 00 00 00 144.81
|
||||||
|
2015 08 10 00 00 00 145.19
|
||||||
|
2015 08 11 00 00 00 145.23
|
||||||
|
2015 08 12 00 00 00 145.14
|
||||||
|
2015 08 13 00 00 00 144.96
|
||||||
|
2015 08 14 00 00 00 144.69
|
||||||
|
2015 08 15 00 00 00 144.43
|
||||||
|
2015 08 16 00 00 00 144.29
|
||||||
|
2015 08 17 00 00 00 144.5
|
||||||
|
2015 08 18 00 00 00 144.68
|
||||||
|
2015 08 19 00 00 00 144.82
|
||||||
|
2015 08 20 00 00 00 144.8
|
||||||
|
2015 08 21 00 00 00 144.59
|
||||||
|
2015 08 22 00 00 00 144.34
|
||||||
|
2015 08 23 00 00 00 144.07
|
||||||
|
2015 08 24 00 00 00 143.76
|
||||||
1
SHAPE_Package/SHAPE_ver2b.0/PRODUCTION_DATA/ST2_PROD_Fields.txt
Executable file
1
SHAPE_Package/SHAPE_ver2b.0/PRODUCTION_DATA/ST2_PROD_Fields.txt
Executable file
@ -0,0 +1 @@
|
|||||||
|
Date Water_Level
|
||||||
BIN
SHAPE_Package/SHAPE_ver2b.0/READ_ME_SHAPE_ver2b.pdf
Executable file
BIN
SHAPE_Package/SHAPE_ver2b.0/READ_ME_SHAPE_ver2b.pdf
Executable file
Binary file not shown.
529
SHAPE_Package/SHAPE_ver2b.0/SHAPE_ver2b_1.m
Executable file
529
SHAPE_Package/SHAPE_ver2b.0/SHAPE_ver2b_1.m
Executable file
@ -0,0 +1,529 @@
|
|||||||
|
% PROGRAM : SHAPE [Seismic HAzard Parameters Evaluation]
|
||||||
|
% VERSION : V_2b.1 [Wrapper (fast) Standalone Version]
|
||||||
|
% LAST UPDATED: June 2020
|
||||||
|
% COMPATIBLE : Matlab version 2017b or later
|
||||||
|
% REQUIREMENTS: "Statistics and Machine Learning" Matlab Toolbox installed
|
||||||
|
% TOOLBOX : "Hazard Analysis Toolbox" developed within SERA Project
|
||||||
|
% USER GUIDE : "READ_ME_SHAPE_ver2b.pdf"
|
||||||
|
% CITE AS : Leptokaropoulos K. and S. Lasocki (2020), Seismol. Res. Lett., doi: 10.1785/0220190319
|
||||||
|
% CONTACT : kleptoka@igf.edu.pl (Dr. Kostas Leptokaropoulos)
|
||||||
|
% --------------------------------------------------------------------------------------------------------------------
|
||||||
|
% Time-and-Technology Dependent Seismic Hazard Assessment (SHA)
|
||||||
|
% --------------------------------------------------------------------------------------------------------------------
|
||||||
|
% INPUT:
|
||||||
|
% !!! ---------------------------- INPUT DATA REQUIREMENTS ----------------------------- !!!
|
||||||
|
% the program works with ASCII input data files (e.g. *.txt). The files needed are:
|
||||||
|
% > File with the parameters of seismic data [mandatory]
|
||||||
|
% > File with the parameters of production data [optional]
|
||||||
|
% > File specifying time windows for SHA analysis [optional]
|
||||||
|
% > File with the fields description of the corresponding parameters in the seismic data file
|
||||||
|
% > File with the fields description of the corresponding parameters in the production data files
|
||||||
|
% FOR DETAILS on data requirements please refer to the document:
|
||||||
|
% "READ_ME_SHAPE_ver2b.pdf"
|
||||||
|
% --------------------------------------------------------------------------------------------------------------------
|
||||||
|
% OVERVIEW: THE PROGRAM takes as input a Seismic and optionally, a Production data parameter file to provide Seismic
|
||||||
|
% Hazard Assessment for specified time-windows, following User's specifications.
|
||||||
|
% --------------------------------------------------------------------------------------------------------------------
|
||||||
|
% AUTHORS: K. Leptokaropoulos and S. Lasocki
|
||||||
|
% Based on magnitude distribution/stationary hazard parameters estimation functions originally developed by S. Lasocki
|
||||||
|
% Last Updated: 06/2020, within SERA PROJECT, EU Horizon 2020 R&I programme under grant agreement No.730900
|
||||||
|
% CURRENT VERSION: v2b.1 **** [WRAPPER (fast) STANDALONE VERSION!!]
|
||||||
|
%% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
|
||||||
|
% PLEASE refer to the accompanying document:
|
||||||
|
% "READ_ME_SHAPE_ver2b.pdf"
|
||||||
|
% for description of the Application and its requirements.
|
||||||
|
%% -----------------------------------------------------------------------------------------------------------------------
|
||||||
|
% DESCRIPTION: The Application performs time-dependent Seismic Hazard Analysis (SHA),
|
||||||
|
% taking into account the activity rate and the magnitude distribution of seismicity
|
||||||
|
% for selected time windows. The hazard parameters estimated are:
|
||||||
|
% 1) The Mean Return Period (MRP) of a given magnitude, M, which is defined as the
|
||||||
|
% average elapsed time between the occurrence of consecutive events of M and
|
||||||
|
% 2) The Exceedance Probability (EPR) of a given magnitude, M, within a given time
|
||||||
|
% period of length, T, which is defined as the probability of an earthquake of
|
||||||
|
% M to occur during T.
|
||||||
|
% These hazard parameters together with the 95% confidence interval are estimated for
|
||||||
|
% different time windows which are constructe upon User’s particular specifications.
|
||||||
|
% 4 different magnitude distribution models can be chosen. The input files must be in
|
||||||
|
% ASCII format (e.g. *.txt). A brief description of the preparation process is given here:
|
||||||
|
% !!! THE USER SETS THE PARAMETERS IN LINES 125-143 !!! then the following steps are executed
|
||||||
|
% (please see in the script for more comments and details for each STEP)
|
||||||
|
% STEP_1. Upload Data
|
||||||
|
% STEP_2. Select Magnidue Scale
|
||||||
|
% STEP_3. Filter Data for Mc
|
||||||
|
% STEP_4. TIME WINDOWS GENERATION
|
||||||
|
% STEP_5. SHA PARAMETERS ESTIMATION
|
||||||
|
% STEP_6. Plotting (optional)
|
||||||
|
% STEP_7. save OUTPUTS
|
||||||
|
% ---------------------------------------------------------------------------------------------------------------------
|
||||||
|
%% INPUT: All input data are sufficiently explained in the script as well as while running the code
|
||||||
|
% (interaction with the user). NOTE that all input files (seismic catalog, production data,
|
||||||
|
% time windows) must be in ASCII format (i.e. *.txt). Please refer to the APPLICATION DOCUMENTATION
|
||||||
|
% for further instructions and input data requirement specifications: "READ_ME_SHAPE_ver2b.pdf"
|
||||||
|
% ----------------------------------------------------------------------------------------------------------------------
|
||||||
|
%% OUTPUT:
|
||||||
|
% <> Output Report with summary of the Results as well as data and parameters used
|
||||||
|
% <> Output Figure with the results in *.mat and *.jpeg formats (optional)
|
||||||
|
% <> Output Matlab Structure with input parameter values and output results, having
|
||||||
|
% as many cells as the number of time windows generated.
|
||||||
|
% Structure fields are:
|
||||||
|
% - Time : vector with origin times of the events included in each time window
|
||||||
|
% - M : vector with events magnitudes
|
||||||
|
% - Mmin : Completeness magnitude
|
||||||
|
% - eps : Magnitude round-off interval
|
||||||
|
% - lambd : mean activity rate
|
||||||
|
% - lambd_err : events number sufficiency (0-all parametes estiamated, 1-all parameters set as NaNs)
|
||||||
|
% - unit : Time Unit
|
||||||
|
% - method : Magnitude Distribution Model
|
||||||
|
% - b : b-value of GR law
|
||||||
|
% [applies only when "method" is set to 'GRU' or 'GRT']
|
||||||
|
% - b_0025 : these two parameters define the b-value 95% bootstrap Confidence interval
|
||||||
|
% - b_0075 : -//-
|
||||||
|
% - h : Kernel smoothing factor
|
||||||
|
% [applies only when "method" is set to 'NPU' or 'NPT']
|
||||||
|
% - xx : Background sample for kernel magnitude estimate
|
||||||
|
% [applies only when "method" is set to 'NPU' or 'NPT']
|
||||||
|
% - ambd : weigthing factors for the adaptive kernel
|
||||||
|
% [applies only when "method" is set to 'NPU' or 'NPT']
|
||||||
|
% - ierr : h convergence indicator (0-converges,1-multiple zeros, 2-no zeros)
|
||||||
|
% [applies only when "method" is set to 'NPU' or 'NPT']
|
||||||
|
% - Mmax : Upper limit of magnitude distribution (truncated)
|
||||||
|
% [applies only when "method" is set to 'GRT' or 'NPT']
|
||||||
|
% - err : Mmax convergence indicator (0-converge, 1-no converge)
|
||||||
|
% [applies only when "method" is set to 'GRT' or 'NPT']
|
||||||
|
% - PDF : 2 columns, first representing magnitudes and second the Probability Density Function of those magnitudes
|
||||||
|
% - CDF : 2 columns, first representing magnitudes and second the Cumulative Distribution Function of those magnitudes
|
||||||
|
% - MRP : Mean Return Period
|
||||||
|
% - MRP_0.025 : these two parameters define the MRP 95% bootstrap Confidence interval
|
||||||
|
% - MRP_0.975 : -//-
|
||||||
|
% - EP : Exceedance Probability
|
||||||
|
% - EP_0.025 : these two parameters define the EP 95% bootstrap Confidence interval
|
||||||
|
% - EP_0.975 : -//-
|
||||||
|
% -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
|
||||||
|
% REFERENCES:
|
||||||
|
% Kijko A, Lasocki S, Graham G (2001), Pure Appl. Geophys. 158:1655–1676
|
||||||
|
% Kijko A, Sellevoll MA (1989), Bull Seismol. Soc. Am. 79:645–654
|
||||||
|
% Lasocki S (2017), Chapter 11.3 in Rockburst Mechanisms, Oxford, pp 366-380
|
||||||
|
% Lasocki S, Urban P (2011), Acta Geophys. 59:659–673
|
||||||
|
% Lasocki S, Orlecka-Sikora B (2008), Tectonophysics 456:28–37
|
||||||
|
% Leptokaropoulos K, Staszek M, Cielesta S, Urban P, Olszewska D, Lizurek G (2017), Acta Geophys. 65:493-505
|
||||||
|
% Leptokaropoulos K, Lasocki S (2020), Seismol. Res. Lett., doi: 10.1785/0220190319.
|
||||||
|
% ---------------------------------------------------------------------------------------------------------------------
|
||||||
|
% LICENSE
|
||||||
|
% This is free software: you can redistribute it and/or modify it under the terms of the
|
||||||
|
% GNU General Public License as published by the Free Software Foundation, either version
|
||||||
|
% 3 of the License, or (at your option) any later version.
|
||||||
|
% This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
|
||||||
|
% without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
|
||||||
|
% See the GNU General Public License for more details.
|
||||||
|
% -------------------------------------------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
clc;clear;
|
||||||
|
close all;mkdir Outputs_SHA
|
||||||
|
|
||||||
|
% PLEASE SET INPUT ARGUMENTS [LINES 125-143]
|
||||||
|
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||||
|
SEIS_DATA='ST2_SEIS_Data.txt'; % Seismic Data File - NOTE: SEIS_DATA=[] is valid as well
|
||||||
|
SEIS_FIELDS='ST2_SEIS_Fields.txt'; % Seismic Data Fields File
|
||||||
|
PROD_DATA='ST2_PROD_Data.txt'; % Production Data (non-seismic) File - NOTE: PROD_DATA=[] is valid as well
|
||||||
|
PROD_FIELDS='ST2_PROD_Fields.txt'; % Production Data (non-seismic) Fields File
|
||||||
|
PROD_FIELD=2; % field (column) corresponding to a selected Production Parameter
|
||||||
|
MScale='ML'; % Magnitude Scale (e.g. 'ML', 'Mw' etc). NOTE: MScale=[] is also valid
|
||||||
|
Mc=1.0; % Select Mc
|
||||||
|
Mmax=[]; % Valid for GRT and NPT/ if Mmax=[], it is calculated internally
|
||||||
|
Nsynth=1000; % number of trials to estimated Mmax bias/ if Nsynth=[], no bias is estimated
|
||||||
|
winmode='Time'; % Select MODE for windows creation: 'Time' or 'Events' or 'File'
|
||||||
|
file_n='ST2_test_timewindows.txt'; % Select file name with starting and ending time of time windows, applicable only for winmode='File'
|
||||||
|
window_size=50; % time window span (days or events, depending on "winmode")
|
||||||
|
dt=50; % time step (days)
|
||||||
|
method='GRT'; % Select M distribution model among 'GRU','GRT','NPU','NPT'
|
||||||
|
Tunit='day'; % Select time unit among 'day', 'month', 'year'
|
||||||
|
MaG=3.0; % set target Magnitude for EPR and MRP calculation
|
||||||
|
Plength=1; % set target time Period (days) for EPR calculation
|
||||||
|
Nbst=100; % number of bootstrap iterations to determine Hazard Parameters confidence interval
|
||||||
|
Plotopt='ON'; % To enable ('ON') or disable ('OFF') plotting
|
||||||
|
%% -------------------------------------------------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
if method=='GRT' & isempty(Mmax)==0 & MaG>Mmax | method=='NPT' & isempty(Mmax)==0 & MaG>Mmax
|
||||||
|
error('Mmax is smaller than the target magnitude (MaG), please change input')
|
||||||
|
end
|
||||||
|
|
||||||
|
%% STEP 1: Load data
|
||||||
|
[Catalog,PROD_Data,s1]=Data_Hand_A2M_ver2...
|
||||||
|
(SEIS_DATA,SEIS_FIELDS,PROD_DATA,PROD_FIELDS,PROD_FIELD);
|
||||||
|
|
||||||
|
%% STEP 2: Select Magnitude Scale
|
||||||
|
[Ctime,Cmag]=Select_Magnitude_Scale_ver2(Catalog,MScale);
|
||||||
|
|
||||||
|
%% STEP 3: Filter data for Mc
|
||||||
|
[Ctime,Cmag,Catalog]=FiltMc_ver2(Ctime,Cmag,Catalog,s1,Mc);
|
||||||
|
|
||||||
|
%% STEP 3b: Estimate Mmax for Truncated Distributions (GRT and NPT)
|
||||||
|
cd SSH/
|
||||||
|
if strcmp(method,'GRT')==1 & isempty(Mmax)==1;
|
||||||
|
[p1,p2,p3,p4,p5,pb,Mmax,err,BIAS,SD]=TruncGR_O(Ctime,Cmag,0,Mc,Mmax,Nsynth);
|
||||||
|
Mmax=Mmax+BIAS;
|
||||||
|
elseif strcmp(method,'NPT')==1 & isempty(Mmax)==1;
|
||||||
|
[p1,p2,p3,p4,p5,p6,p7,p8,p9,Mmax,err,BIAS,SD]=Nonpar_tr_O(Ctime,Cmag,0,Mc,Mmax,Nsynth);
|
||||||
|
Mmax=Mmax+BIAS;
|
||||||
|
end
|
||||||
|
|
||||||
|
cd ../
|
||||||
|
|
||||||
|
%% STEP 4: Create Time Windows
|
||||||
|
time_windows=struct;time_windows.Time=[];
|
||||||
|
to=Ctime-Ctime(1);tmin=min(to);tmax=max(to);
|
||||||
|
|
||||||
|
switch winmode
|
||||||
|
%% TIME
|
||||||
|
case 'Time'
|
||||||
|
if window_size>tmax;n=1;warning('time window is set larger than data time span');end
|
||||||
|
n=ceil((tmax-window_size)/dt);
|
||||||
|
for i=1:n
|
||||||
|
time_windows(i).Time=Ctime(to>=(i-1)*dt & to<(i-1)*dt+window_size);
|
||||||
|
time_windows(i).M=Cmag(to>=(i-1)*dt & to<(i-1)*dt+window_size);
|
||||||
|
time_windows(i).Tstart=Ctime(1)+(i-1)*dt;
|
||||||
|
time_windows(i).Tend=Ctime(1)+(i-1)*dt+window_size;
|
||||||
|
end
|
||||||
|
%% EVENTS
|
||||||
|
case 'Events'
|
||||||
|
if window_size>numel(to);window_size=numel(to);warning('events window is set larger than given data');end
|
||||||
|
n=ceil(tmax/dt);
|
||||||
|
for i=1:n
|
||||||
|
To=find(to>=(i-1)*dt);To=To(1);
|
||||||
|
if To<=length(Ctime)-window_size+1;
|
||||||
|
time_windows(i).Time=Ctime(To:To+window_size-1);
|
||||||
|
time_windows(i).M=Cmag(To:To+window_size-1);
|
||||||
|
time_windows(i).Tstart=Ctime(1)+(i-1)*dt;
|
||||||
|
time_windows(i).Tend=max(time_windows(i).Time);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
%% FILE
|
||||||
|
case 'File'
|
||||||
|
cd TIME_WINDOWS
|
||||||
|
Twindows=dlmread(file_n);
|
||||||
|
T1=Twindows(:,1);T2=Twindows(:,2);n=numel(T1);
|
||||||
|
for i=1:n
|
||||||
|
time_windows(i).Time=Ctime(Ctime>=T1(i) & Ctime<T2(i));
|
||||||
|
time_windows(i).M=Cmag(Ctime>=T1(i) & Ctime<T2(i));
|
||||||
|
time_windows(i).Tstart=T1(i);
|
||||||
|
time_windows(i).Tend=T2(i);
|
||||||
|
end
|
||||||
|
cd ../
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
%% STEP 5: ESTIMATE HAZARD PARAMETERS
|
||||||
|
if strcmp(Tunit,'day');iop=0;elseif strcmp(Tunit,'month');iop=1;elseif strcmp(Tunit,'year');iop=2;
|
||||||
|
else; error('Please set "Tunit" Parameter as "day", "month" or "year"');end
|
||||||
|
|
||||||
|
%% RUN MAGDIST
|
||||||
|
[HP] = TDHMagDistWrapper(method, time_windows, Mc, iop,Mmax,Nbst);
|
||||||
|
|
||||||
|
%% Harzard Parameters Estimate
|
||||||
|
%[MRPer,ExPr,MRPer_low,MRPer_high,ExPr_low,ExPr_high]=TDHRetPeriodExcProbWrapper(method,MaG,Plength,Mc,HP,Plength)
|
||||||
|
for i=1:length(HP)
|
||||||
|
if isnan(HP(i).CDF)
|
||||||
|
lambda(i)=HP(i).lamb;MRPer(i)=NaN;ExPr(i)=NaN;MRPer_low(i)=NaN;MRPer_high(i)=NaN;ExPr_low(i)=NaN;ExPr_high(i)=NaN;
|
||||||
|
else
|
||||||
|
[MRPer1,ExPr1,MRPer_low1,MRPer_high1,ExPr_low1,ExPr_high1]=RetPeriodExcProbWrapper(HP(i).lamb,HP(i).CDF,Plength,MaG);
|
||||||
|
lambda(i)=HP(i).lamb;
|
||||||
|
MRPer(i)=MRPer1;ExPr(i)=ExPr1;
|
||||||
|
MRPer_low(i)=MRPer_low1;MRPer_high(i)=MRPer_high1;
|
||||||
|
ExPr_low(i)=ExPr_low1;ExPr_high(i)=ExPr_high1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
%%
|
||||||
|
%% STEP 7: Ploting (optional)
|
||||||
|
Zplo_ver2b_1
|
||||||
|
|
||||||
|
%% STEP 6: Save outputs
|
||||||
|
Zsave_output_ver2b_1
|
||||||
|
|
||||||
|
|
||||||
|
%% -*-*-*-*-*-*-*-*-*-*-*-*-*- F U N C T I O N S -*-*-*-*-*-*-*-*-*-*-*-*-*-
|
||||||
|
|
||||||
|
%% ------------------------- DATA HANDLING FUNCTION --------------------------
|
||||||
|
|
||||||
|
function [Catalog,PROD_data,ss1]=Data_Hand_A2M_ver2...
|
||||||
|
(SEIS_DATA,SEIS_FIELDS,PROD_DATA,PROD_FIELDS,PROD_FIELD)
|
||||||
|
|
||||||
|
if isempty(PROD_DATA)
|
||||||
|
%% SEISMIC DATA
|
||||||
|
cd CATALOGS
|
||||||
|
SData=load(SEIS_DATA);
|
||||||
|
SFields=fileread(SEIS_FIELDS);
|
||||||
|
cd ../
|
||||||
|
|
||||||
|
Na=length(SFields);if SFields(Na)~=' ';SFields(Na+1)=' ';end
|
||||||
|
[cou,c,Datime,Catalog]=Fields_dat(SData,SFields,1);
|
||||||
|
ss1=1:length(Catalog);% ss1=SetParams(Catalog);%Catalog=Catalog(ss1);
|
||||||
|
PROD_data=[];ss=[];s2=[];ss2=[];dstr2=[];
|
||||||
|
|
||||||
|
else
|
||||||
|
%% ------------------------------------------------------------------------------------------------------------------------------------
|
||||||
|
% BOTH -SEISMIC and PRODUCTION DATA
|
||||||
|
|
||||||
|
cd CATALOGS %Seismic Data
|
||||||
|
SData=load(SEIS_DATA);
|
||||||
|
SFields=fileread(SEIS_FIELDS);
|
||||||
|
cd ../
|
||||||
|
|
||||||
|
Na=length(SFields);if SFields(Na)~=' ';SFields(Na+1)=' ';end
|
||||||
|
[cou,c,Datime,Catalog]=Fields_dat(SData,SFields,1);
|
||||||
|
ss1=1:length(Catalog);
|
||||||
|
% ss1=SetParams(Catalog);%Catalog=Catalog(ss1);
|
||||||
|
|
||||||
|
cd PRODUCTION_DATA % Production (non-Seismic) Data
|
||||||
|
OData=load(PROD_DATA);
|
||||||
|
OFields=fileread(PROD_FIELDS);
|
||||||
|
cd ../
|
||||||
|
|
||||||
|
Na1=length(OFields);if OFields(Na1)~=' ';OFields(Na1+1)=' ';end
|
||||||
|
[cou1,c1,Datime1,PROD_data]=Fields_dat(OData,OFields,2);
|
||||||
|
|
||||||
|
end
|
||||||
|
% save('Catalog_ST2_Test','Catalog')
|
||||||
|
% save('Catalog_ST2_Test','Catalog')
|
||||||
|
|
||||||
|
|
||||||
|
%% ----------------------------------------- F U N C T I O N S -----------------------------------------
|
||||||
|
function [cou,c,Datime,OUT]=Fields_dat(indata,infields,iop)
|
||||||
|
|
||||||
|
Datime=datenum(indata(:,1),indata(:,2),indata(:,3),indata(:,4),indata(:,5),indata(:,6)); % Convert time to matlab format
|
||||||
|
|
||||||
|
% Define Fields
|
||||||
|
c=1;
|
||||||
|
for i=1:length(infields)-1
|
||||||
|
if strcmp(infields(i),' ')==1;cou(i)=0;
|
||||||
|
else cou(i)=c;end
|
||||||
|
if strcmp(infields(i),' ')==0 & strcmp(infields(i+1),' ')==1;c=c+1;end
|
||||||
|
end
|
||||||
|
|
||||||
|
if iop==1
|
||||||
|
OUT(1).field='Occurrence_Time';OUT(1).val=Datime;
|
||||||
|
elseif iop==2
|
||||||
|
OUT(1).field='Production_Time';OUT(1).val=Datime;
|
||||||
|
end
|
||||||
|
|
||||||
|
for i=2:c-1
|
||||||
|
OUT(i).field=infields(cou==i);
|
||||||
|
OUT(i).val=indata(:,i+5);
|
||||||
|
end
|
||||||
|
|
||||||
|
%Set Field Type for Magnitude Recognition
|
||||||
|
for i=1:size(OUT,2)
|
||||||
|
if strcmp(OUT(i).field,'ML') || strcmp(OUT(i).field,'Mw') || strcmp(OUT(i).field,'M') ...
|
||||||
|
|| strcmp(OUT(i).field,'Ms') || strcmp(OUT(i).field,'mb') || strcmp(OUT(i).field,'Md')
|
||||||
|
OUT(i).fieldType='Magnitude';
|
||||||
|
else
|
||||||
|
OUT(i).fieldType=[];
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
%% -----------------------------------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
% ----------------------------------------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
%%
|
||||||
|
function [Ctime,Cmag,Data]=FiltMc_ver2(Ctime,Cmag,Catalog,s1,Mc)
|
||||||
|
clc
|
||||||
|
id_time=findfield(Catalog,'Occurrence_Time');
|
||||||
|
%opts.Interpreter='tex';opts.Default='Yes';
|
||||||
|
%quest='Do you wish to filter Data for Mc?';
|
||||||
|
%answer=questdlg(quest,'Data Completenes','Yes','No',opts);
|
||||||
|
%if strcmp(answer,'Yes')
|
||||||
|
|
||||||
|
%% THIS HAS MOVED TO A SEPARATE FUNCTION IN THE BEGINNING OF THE APPLICATION
|
||||||
|
% cou=1;
|
||||||
|
% for i=1:length(Catalog)
|
||||||
|
% if strcmp(Catalog(i).fieldType,'Magnitude')==1
|
||||||
|
% C(cou).field=Catalog(i).field;cou=cou+1;
|
||||||
|
% end
|
||||||
|
% end
|
||||||
|
%
|
||||||
|
% % Check for no magnitude
|
||||||
|
% if cou==1;error('MyComponent:incorrectType',...
|
||||||
|
% 'No magnitude column detected!! Please check: Magnitude fields must be noted as one of the following:\nM , Mw , ML , Ms , mb , Md\n or select the entire sample for analysis');end
|
||||||
|
%
|
||||||
|
% %Select Parameters from Seismic Catalog -
|
||||||
|
% [ss1,ok]=listdlg('PromptString','Please Select M scale:',...
|
||||||
|
% 'ListString',{C.field}, 'SelectionMode','single');
|
||||||
|
%
|
||||||
|
% id=findfield(Catalog,C(ss1).field);
|
||||||
|
% Mtype=Catalog(id).field;
|
||||||
|
% Ctime=Catalog(id_time).val;
|
||||||
|
% id_M=findfield(Catalog,Mtype);
|
||||||
|
% Cmag=Catalog(id_M).val;
|
||||||
|
|
||||||
|
%%
|
||||||
|
|
||||||
|
cou=1;
|
||||||
|
|
||||||
|
|
||||||
|
for i=1:length(s1)
|
||||||
|
x=Catalog(s1(i)).val;x=x(Cmag>=Mc);
|
||||||
|
index=isnan(x)==0;
|
||||||
|
x=x(isnan(x)==0);
|
||||||
|
Data(cou).field=Catalog(s1(i)).field;
|
||||||
|
Data(cou).fieldType=Catalog(s1(i)).fieldType;
|
||||||
|
Data(cou).val=nan(size(index)); Data(cou).val(index)=x;
|
||||||
|
cou=cou+1;
|
||||||
|
end
|
||||||
|
|
||||||
|
Ctime=Ctime(Cmag>=Mc);Cmag=Cmag(Cmag>=Mc);
|
||||||
|
|
||||||
|
n=length(Ctime);
|
||||||
|
disp(['number of events: ',num2str(n)])
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
%% --------------------------------------------------------------------------------------
|
||||||
|
% finds a field defined by a certain (string) name
|
||||||
|
function [id] = findfield( catalog,field )
|
||||||
|
id=0;
|
||||||
|
j=1;
|
||||||
|
while j <= size(catalog,2) && id==0
|
||||||
|
if (strcmp(catalog(j).field,field)==1)
|
||||||
|
id=j;
|
||||||
|
end
|
||||||
|
j=j+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
%%
|
||||||
|
function [Ctime,Cmag]=Select_Magnitude_Scale_ver2(Catalog,MType)
|
||||||
|
|
||||||
|
cou=1;
|
||||||
|
for i=1:length(Catalog)
|
||||||
|
if strcmp(Catalog(i).fieldType,'Magnitude')==1
|
||||||
|
C(cou).field=Catalog(i).field;cou=cou+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% Check for no magnitude
|
||||||
|
if cou==1;error('MyComponent:incorrectType',...
|
||||||
|
'No magnitude column detected!! Please check: Magnitude fields must be noted as one of the following:\nM , Mw , ML , Ms , mb , Md\n or select the entire sample for analysis');end
|
||||||
|
|
||||||
|
|
||||||
|
id=findfield(Catalog,MType);
|
||||||
|
id_time=findfield(Catalog,'Occurrence_Time');
|
||||||
|
Cmag=Catalog(id).val;Ctime=Catalog(id_time).val;
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
%% -----------!!!!!!!!!!! HAZARD PARAMETERS ESTIMATE FUNCTIONS !!!!!!!!!!!-----------
|
||||||
|
|
||||||
|
function [HP] = TDHMagDistWrapper(method, time_win_data, mmin, iop,Mmax,Nbst)
|
||||||
|
cd SSH
|
||||||
|
for j=1:size(time_win_data,2);if isempty(time_win_data(j).Time);M1(j)=NaN;else;M1(j)=max(time_win_data(j).M);end;end
|
||||||
|
Mmaxcat=max(M1);Mmax=max([Mmaxcat Mmax])
|
||||||
|
|
||||||
|
for i=1:size(time_win_data,2)
|
||||||
|
mags_vec = time_win_data(i).M;
|
||||||
|
time_vec = time_win_data(i).Time;
|
||||||
|
HP(i).mmin = mmin;
|
||||||
|
HP(i).iop = iop;
|
||||||
|
HP(i).method = method;
|
||||||
|
switch method
|
||||||
|
case 'GRU'
|
||||||
|
try
|
||||||
|
[HP(i).lamb_all, HP(i).lamb, HP(i).lamb_err, HP(i).unit, HP(i).eps, HP(i).b, HP(i).bCI]=UnlimitGR(time_vec, mags_vec, iop, mmin,Nbst);
|
||||||
|
HP(i).Mmax=NaN;eps=HP(i).eps;
|
||||||
|
[m, PDF_GRU, CDF_GRU]=dist_GRU_CI(mmin,Mmax+eps,eps,mmin,eps,HP(i).b,HP(i).bCI); %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
HP(i).PDF=[m PDF_GRU];HP(i).CDF=[m CDF_GRU]; %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
catch err
|
||||||
|
HP(i).lamb_all=NaN; HP(i).lamb=NaN; HP(i).lamb_err=2; HP(i).unit=''; HP(i).eps=NaN; HP(i).b=NaN;HP(i).Mmax=NaN;HP(i).PDF=NaN;HP(i).CDF=NaN;
|
||||||
|
HP(i).bCI(1)=NaN;HP(i).bCI(2)=NaN;warning('%s: %s', err.identifier, err.message);
|
||||||
|
end
|
||||||
|
case 'GRT'
|
||||||
|
try
|
||||||
|
[HP(i).lamb_all, HP(i).lamb, HP(i).lamb_err, HP(i).unit, HP(i).eps, HP(i).b, HP(i).Mmax, HP(i).err]=TruncGR_O(time_vec, mags_vec, iop, mmin,Mmax);
|
||||||
|
eps=HP(i).eps;[m, PDF_GRT, CDF_GRT]=dist_GRT(mmin,Mmax+eps,eps,mmin,eps,HP(i).b,Mmax); %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
funct=@(mags_vec)TruncGR_O_CI(time_vec,mags_vec,iop,mmin,Mmax,[]); % K04JUN2020 GRT
|
||||||
|
HP(i).bCI=bootci(Nbst,{funct,mags_vec},'alpha',0.05); % K04JUN2020 GRT
|
||||||
|
[m, PDF_GRT, CDF_GRT]=dist_GRT_CI(mmin,Mmax+eps,eps,mmin,eps,HP(i).b,Mmax,HP(i).bCI); % K04JUN2020 GRT
|
||||||
|
HP(i).PDF=[m PDF_GRT];HP(i).CDF=[m CDF_GRT]; %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
catch err
|
||||||
|
HP(i).lamb_all=NaN; HP(i).lamb=NaN; HP(i).lamb_err=2; HP(i).unit=''; HP(i).eps=NaN; HP(i).b=NaN; HP(i).Mmax=NaN; HP(i).err=NaN;HP(i).PDF=NaN;HP(i).CDF=NaN;
|
||||||
|
HP(i).bCI(1)=NaN;HP(i).bCI(2)=NaN;warning('%s: %s', err.identifier, err.message);
|
||||||
|
end
|
||||||
|
case 'NPU'
|
||||||
|
try
|
||||||
|
[HP(i).lamb_all, HP(i).lamb, HP(i).lamb_err, HP(i).unit, HP(i).eps, HP(i).ierr, HP(i).h, HP(i).xx, HP(i).ambd]=Nonpar_O(time_vec, mags_vec, iop, mmin);
|
||||||
|
HP(i).Mmax=NaN;eps=HP(i).eps;
|
||||||
|
[m, PDF_NPU, CDF_NPU]=dist_NPU(mmin,Mmax+eps,eps,mmin,eps,HP(i).h,HP(i).xx,HP(i).ambd); %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
HP(i).PDF=[m PDF_NPU];HP(i).CDF=[m CDF_NPU]; %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
data=[HP(i).xx,HP(i).ambd']; % K04JUN2020 NPU
|
||||||
|
[CDF_NP]=dist_NPU_CI(mmin,Mmax+eps,eps,mmin,eps,HP(i).h,data); % K04JUN2020 NPU
|
||||||
|
funct=@(data)dist_NPU_CI(mmin,Mmax+eps,eps,mmin,eps,HP(i).h,data); % K04JUN2020 NPU
|
||||||
|
[CDF_CI]=bootci(Nbst,{funct,data},'alpha',0.05)'; % K04JUN2020 NPU
|
||||||
|
HP(i).CDF=[HP(i).CDF CDF_CI]; % K04JUN2020 NPU
|
||||||
|
catch err
|
||||||
|
HP(i).lamb_all=NaN; HP(i).lamb=NaN;HP(i).lamb_err=2; HP(i).unit=''; HP(i).eps=NaN; HP(i).ierr=NaN; HP(i).h=NaN; HP(i).xx=[]; HP(i).ambd=[];HP(i).Mmax=NaN;HP(i).PDF=NaN;HP(i).CDF=NaN;
|
||||||
|
warning('%s: %s', err.identifier, err.message);
|
||||||
|
end
|
||||||
|
case 'NPT'
|
||||||
|
try
|
||||||
|
[HP(i).lamb_all, HP(i).lamb, HP(i).lamb_err, HP(i).unit, HP(i).eps, HP(i).ierr, HP(i).h, HP(i).xx, HP(i).ambd, HP(i).Mmax, HP(i).err]=Nonpar_tr_O(time_vec, mags_vec, iop, mmin,Mmax);
|
||||||
|
eps=HP(i).eps;
|
||||||
|
[m, PDF_NPT, CDF_NPT]=dist_NPT(mmin,Mmax+eps,eps,mmin,eps,HP(i).h,HP(i).xx,HP(i).ambd,Mmax); %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
HP(i).PDF=[m PDF_NPT];HP(i).CDF=[m CDF_NPT]; %K29JAN2020 - magnitude PDF/CDF
|
||||||
|
data=[HP(i).xx,HP(i).ambd']; % K04JUN2020 NPT
|
||||||
|
[CDF_NP]=dist_NPT_CI(mmin,Mmax+eps,eps,mmin,eps,HP(i).h,data,Mmax); % K04JUN2020 NPT
|
||||||
|
funct=@(data)dist_NPT_CI(mmin,Mmax+eps,eps,mmin,eps,HP(i).h,data,Mmax); % K04JUN2020 NPT
|
||||||
|
[CDF_CI]=bootci(Nbst,{funct,data},'alpha',0.05)'; % K04JUN2020 NPT
|
||||||
|
HP(i).CDF=[HP(i).CDF CDF_CI]; % K04JUN2020 NPU
|
||||||
|
catch err
|
||||||
|
HP(i).lamb_all=NaN; HP(i).lamb=NaN; HP(i).lamb_err=2; HP(i).unit=''; HP(i).eps=NaN; HP(i).ierr=NaN; HP(i).h=NaN; HP(i).xx=[]; HP(i).ambd=[]; HP(i).Mmax=NaN; HP(i).err=NaN;HP(i).PDF=NaN;HP(i).CDF=NaN;
|
||||||
|
warning('%s: %s', err.identifier, err.message);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% K12NOV2015
|
||||||
|
% Calculate lamb and lamb_all in case of 0, 1, or 2 events.
|
||||||
|
% It may be generalized in all cases. Rate is now calculated
|
||||||
|
% by division of the event number by the duration of the set
|
||||||
|
% - not the time difference between the first and last events.
|
||||||
|
if numel(mags_vec(mags_vec>=mmin))<3
|
||||||
|
HP(i).lamb_all=NaN; % numel(mags_vec)/(time_win_data(i).Tend-time_win_data(i).Tstart);
|
||||||
|
HP(i).lamb=NaN; % numel(mags_vec(mags_vec>=mmin))/(time_win_data(i).Tend-time_win_data(i).Tstart);
|
||||||
|
switch iop
|
||||||
|
case 0
|
||||||
|
%OK
|
||||||
|
case 1
|
||||||
|
HP(i).lamb_all=HP(i).lamb_all*30;
|
||||||
|
HP(i).lamb=HP(i).lamb*30;
|
||||||
|
case 2
|
||||||
|
HP(i).lamb_all=HP(i).lamb_all*365;
|
||||||
|
HP(i).lamb=HP(i).lamb*365;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
% K12NOV2015
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
cd ../
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
%%
|
||||||
|
function [MRPer,ExPr,MRPer_low,MRPer_high,ExPr_low,ExPr_high]=RetPeriodExcProbWrapper(lamb,CDF,DT,MaG)
|
||||||
|
DM=abs(CDF(:,1)-MaG);ind=find(DM==min(DM));
|
||||||
|
CDF1=CDF(ind,2);CDF_CI=[CDF(ind,3) CDF(ind,4)];
|
||||||
|
|
||||||
|
% Exceedance probability
|
||||||
|
EP=1-exp(-lamb*DT.*(1-CDF1));
|
||||||
|
EP_CI=1-exp(-lamb*DT.*(1-CDF_CI));
|
||||||
|
ExPr=EP;ExPr_low=EP_CI(:,2);ExPr_high=EP_CI(:,1);
|
||||||
|
% Mean Return Period
|
||||||
|
MRP=1/lamb./(1-CDF1);
|
||||||
|
MRP_CI=1/lamb./(1-CDF_CI);
|
||||||
|
MRPer=MRP;MRPer_low=MRP_CI(:,1);MRPer_high=MRP_CI(:,2);
|
||||||
|
|
||||||
|
end
|
||||||
99
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbGRT.m
Executable file
99
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbGRT.m
Executable file
@ -0,0 +1,99 @@
|
|||||||
|
% [x,z]=ExcProbGRT(opt,xd,xu,dx,y,Mmin,lamb,eps,b,Mmax)
|
||||||
|
%
|
||||||
|
%EVALUATES THE EXCEEDANCE PROBABILITY VALUES USING THE UPPER-BOUNDED G-R
|
||||||
|
% LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution, consequently the G-R
|
||||||
|
% b-value and the end-point of the distriobution Mmax as well as the
|
||||||
|
% activity rate of M>=Mmin events are calculated at start-up of the
|
||||||
|
% stationary hazard assessment services in the upper-bounded
|
||||||
|
% Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The exceedance probability of magnitude M' in the time period of
|
||||||
|
% length T' is the probability of an earthquake of magnitude M' or greater
|
||||||
|
% to occur in T'. Depending on the value of the parameter opt the
|
||||||
|
% exceedance probability values are calculated for a fixed time period T'
|
||||||
|
% and different magnitude values or for a fixed magnitude M' and different
|
||||||
|
% time period length values. In either case the independent variable vector
|
||||||
|
% starts from xd, up to xu with step dx. In either case the result is
|
||||||
|
% returned in the vector z.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% opt - determines the mode of calculations. opt=0 - fixed time period
|
||||||
|
% length (y), different magnitude values (x), opt=1 - fixed magnitude
|
||||||
|
% (y), different time period lengths (x)
|
||||||
|
% xd - starting value of the changeable independent variable
|
||||||
|
% xu - ending value of the changeable independent variable
|
||||||
|
% dx - step change of the changeable independent variable
|
||||||
|
% y - fixed independent variable value: time period length T' if opt=0,
|
||||||
|
% magnitude M' if opt=1
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
|
||||||
|
|
||||||
|
%OUTPUT:
|
||||||
|
% x - vector of changeable independent variable: magnitudes if opt=0,
|
||||||
|
% time period lengths if opt=1,
|
||||||
|
% x=(xd:dx:xu)
|
||||||
|
% z - vector of exceedance probability values of the same length as x
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [x,z]=ExcProbGRT(opt,xd,xu,dx,y,Mmin,lamb,eps,b,Mmax)
|
||||||
|
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dx<=0;error('Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
beta=b*log(10);
|
||||||
|
if opt==0
|
||||||
|
if xd<Mmin; xd=Mmin;end
|
||||||
|
if xu>Mmax; xu=Mmax;end
|
||||||
|
end
|
||||||
|
x=(xd:dx:xu)';
|
||||||
|
if opt==0
|
||||||
|
z=1-exp(-lamb*y.*(1-Cdfgr(x,beta,Mmin-eps/2,Mmax)));
|
||||||
|
else
|
||||||
|
z=1-exp(-lamb*(1-Cdfgr(y,beta,Mmin-eps/2,Mmax)).*x);
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=Cdfgr(t,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
%CDF of the truncated upper-bounded exponential distribution (truncated G-R
|
||||||
|
% model
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% t - vector of magnitudes (independent variable)
|
||||||
|
% y - CDF vector
|
||||||
|
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin)));
|
||||||
|
y=(1-exp(-beta*(t-Mmin)))/mian;
|
||||||
|
idx=find(y>1);
|
||||||
|
y(idx)=ones(size(idx));
|
||||||
|
end
|
||||||
|
|
||||||
78
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbGRU.m
Executable file
78
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbGRU.m
Executable file
@ -0,0 +1,78 @@
|
|||||||
|
% [x,z]=ExcProbGRU(opt,xd,xu,dx,y,Mmin,lamb,eps,b)
|
||||||
|
%
|
||||||
|
%EVALUATES THE EXCEEDANCE PROBABILITY VALUES USING THE UNLIMITED G-R
|
||||||
|
% LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the unlimited Gutenberg-Richter relation
|
||||||
|
% leads to the exponential distribution model of magnitude distribution
|
||||||
|
% from and above the catalog completness level Mmin. The shape parameter of
|
||||||
|
% this distribution and consequently the G-R b-value are calculated at
|
||||||
|
% start-up of the stationary hazard assessment services in the
|
||||||
|
% unlimited Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The exceedance probability of magnitude M' in the time period of
|
||||||
|
% length T' is the probability of an earthquake of magnitude M' or greater
|
||||||
|
% to occur in T'. Depending on the value of the parameter opt the
|
||||||
|
% exceedance probability values are calculated for a fixed time period T'
|
||||||
|
% and different magnitude values or for a fixed magnitude M' and different
|
||||||
|
% time period length values. In either case the independent variable vector
|
||||||
|
% starts from xd, up to xu with step dx. In either case the result is
|
||||||
|
% returned in the vector z.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% opt - determines the mode of calculations. opt=0 - fixed time period
|
||||||
|
% length (y), different magnitude values (x), opt=1 - fixed magnitude
|
||||||
|
% (y), different time period lengths (x)
|
||||||
|
% xd - starting value of the changeable independent variable
|
||||||
|
% xu - ending value of the changeable independent variable
|
||||||
|
% dx - step change of the changeable independent variable
|
||||||
|
% y - fixed independent variable value: time period length T' if opt=0,
|
||||||
|
% magnitude M' if opt=1
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
|
||||||
|
|
||||||
|
%OUTPUT
|
||||||
|
% x - vector of changeable independent variable: magnitudes if opt=0,
|
||||||
|
% time period lengths if opt=1,
|
||||||
|
% x=(xd:dx:xu)
|
||||||
|
% z - vector of exceedance probability values of the same length as x
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [x,z]=ExcProbGRU(opt,xd,xu,dx,y,Mmin,lamb,eps,b)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dx<=0;error('Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
beta=b*log(10);
|
||||||
|
|
||||||
|
if opt==0
|
||||||
|
if xd<Mmin; xd=Mmin;end
|
||||||
|
end
|
||||||
|
x=(xd:dx:xu)';
|
||||||
|
if opt==0
|
||||||
|
z=1-exp(-lamb*y.*exp(-beta*(x-Mmin+eps/2)));
|
||||||
|
else
|
||||||
|
z=1-exp(-lamb*exp(-beta*(y-Mmin+eps/2)).*x);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
116
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbNPT.m
Executable file
116
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbNPT.m
Executable file
@ -0,0 +1,116 @@
|
|||||||
|
% [x,z]=ExcProbNPT(opt,xd,xu,dx,y,Mmin,lamb,eps,h,xx,ambd,Mmax)
|
||||||
|
%
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES THE
|
||||||
|
% EXCEEDANCE PROBABILITY VALUES FOR THE UPPER-BOUNDED NONPARAMETRIC
|
||||||
|
% DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution has a hard end point Mmax from the right hand
|
||||||
|
% side.The estimation makes use of the previously estimated parameters
|
||||||
|
% namely the mean activity rate lamb, the length of magnitude round-off
|
||||||
|
% interval, eps, the smoothing factor, h, the background sample, xx, the
|
||||||
|
% scaling factors for the background sample, ambd, and the end-point of
|
||||||
|
% magnitude distribution Mmax. The background sample,xx, comprises the
|
||||||
|
% randomized values of observed magnitude doubled symmetrically with
|
||||||
|
% respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% The exceedance probability of magnitude M' in the time
|
||||||
|
% period of length T' is the probability of an earthquake of magnitude M'
|
||||||
|
% or greater to occur in T'.
|
||||||
|
%
|
||||||
|
% Depending on the value of the parameter opt the exceedance probability
|
||||||
|
% values are calculated for a fixed time period T' and different magnitude
|
||||||
|
% values or for a fixed magnitude M' and different time period length
|
||||||
|
% values. In either case the independent variable vector starts from
|
||||||
|
% xd, up to xu with step dx. In either case the result is returned in the
|
||||||
|
% vector z.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
% Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
% Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
% Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% opt - determines the mode of calculations. opt=0 - fixed time period
|
||||||
|
% length (y), different magnitude values (x), opt=1 - fixed magnitude
|
||||||
|
% (y), different time period lengths (x)
|
||||||
|
% xd - starting value of the changeable independent variable
|
||||||
|
% xu - ending value of the changeable independent variable
|
||||||
|
% dx - step change of the changeable independent variable
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% x - vector of changeable independent variable x=(xd:dx:xu)
|
||||||
|
% z - vector of exceedance probability values
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [x,z]=...
|
||||||
|
ExcProbNPT(opt,xd,xu,dx,y,Mmin,lamb,eps,h,xx,ambd,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dx<=0;error('Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
if opt==0
|
||||||
|
if xd<Mmin; xd=Mmin;end
|
||||||
|
if xu>Mmax; xu=Mmax;end
|
||||||
|
end
|
||||||
|
x=(xd:dx:xu)';
|
||||||
|
n=length(x);
|
||||||
|
mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
|
||||||
|
if opt==0
|
||||||
|
for i=1:n
|
||||||
|
CDF_NPT=2*(Dystr_npr(x(i),xx,ambd,h)...
|
||||||
|
-Dystr_npr(Mmin-eps/2,xx,ambd,h))./mian;
|
||||||
|
z(i)=1-exp(-lamb*y.*(1-CDF_NPT));
|
||||||
|
end
|
||||||
|
else
|
||||||
|
CDF_NPT=2*(Dystr_npr(y,xx,ambd,h)...
|
||||||
|
-Dystr_npr(Mmin-eps/2,xx,ambd,h))./mian;
|
||||||
|
z=1-exp(-lamb*(1-CDF_NPT).*x);
|
||||||
|
if y>Mmax;z=zeros(size(x));end %K15DEC2015
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
105
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbNPU.m
Executable file
105
SHAPE_Package/SHAPE_ver2b.0/SSH/ExcProbNPU.m
Executable file
@ -0,0 +1,105 @@
|
|||||||
|
% [x,z]=ExcProbNPU(opt,xd,xu,dx,y,Mmin,lamb,eps,h,xx,ambd)
|
||||||
|
%
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES THE
|
||||||
|
% EXCEEDANCE PROBABILITY VALUES FOR THE UNBOUNDED NONPARAMETRIC
|
||||||
|
% DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution is unlimited from the right hand side.
|
||||||
|
% The estimation makes use of the previously estimated parameters of kernel
|
||||||
|
% estimation, namely the smoothing factor, the background sample and the
|
||||||
|
% scaling factors for the background sample. The background sample
|
||||||
|
% - xx comprises the randomized values of observed magnitude doubled
|
||||||
|
% symmetrically with respect to the value Mmin-eps/2.
|
||||||
|
% The exceedance probability of magnitude M' in the time period of length
|
||||||
|
% T' is the probability of an earthquake of magnitude M' or greater to
|
||||||
|
% occur in T'.
|
||||||
|
% Depending on the value of the parameter opt the exceedance probability
|
||||||
|
% values are calculated for a fixed time period T' and different magnitude
|
||||||
|
% values or for a fixed magnitude M' and different time period length
|
||||||
|
% values. In either case the independent variable vector starts from
|
||||||
|
% xd, up to xu with step dx. In either case the result is returned in the
|
||||||
|
% vector z.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation fro Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% opt - determines the mode of calculations. opt=0 - fixed time period
|
||||||
|
% length (y), different magnitude values (x), opt=1 - fixed magnitude
|
||||||
|
% (y), different time period lengths (x)
|
||||||
|
% xd - starting value of the changeable independent variable
|
||||||
|
% xu - ending value of the changeable independent variable
|
||||||
|
% dx - step change of the changeable independent variable
|
||||||
|
% y - fixed independent variable value: time period length T' if opt=0,
|
||||||
|
% magnitude M' if opt=1
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% x - vector of changeable independent variable: magnitudes if opt=0,
|
||||||
|
% time period lengths if opt=1,
|
||||||
|
% x=(xd:dx:xu)
|
||||||
|
% z - vector of exceedance probability values of the same length as x
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [x,z]=ExcProbNPU(opt,xd,xu,dx,y,Mmin,lamb,eps,h,xx,ambd)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dx<=0;error('Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
x=(xd:dx:xu)';
|
||||||
|
n=length(x);
|
||||||
|
|
||||||
|
if opt==0
|
||||||
|
for i=1:n
|
||||||
|
CDF_NPU=2*(Dystr_npr(x(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
z(i)=1-exp(-lamb*y.*(1-CDF_NPU));
|
||||||
|
end
|
||||||
|
else
|
||||||
|
CDF_NPU=2*(Dystr_npr(y,xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
z=1-exp(-lamb*(1-CDF_NPU).*x);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
59
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_GRT.m
Executable file
59
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_GRT.m
Executable file
@ -0,0 +1,59 @@
|
|||||||
|
% [T,m]=Max_credM_GRT(Td,Tu,dT,Mmin,lamb,eps,b,Mmax)
|
||||||
|
|
||||||
|
%EVALUATES THE MAXIMUM CREDIBLE MAGNITUDE VALUES USING THE UPPER-BOUNDED
|
||||||
|
% G-R LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution, consequently the G-R
|
||||||
|
% b-value and the end-point of the distriobution Mmax as well as the
|
||||||
|
% activity rate of M>=Mmin events are calculated at start-up of the
|
||||||
|
% stationary hazard assessment services in the upper-bounded
|
||||||
|
% Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The maximum credible magnitude values are calculated for periods of
|
||||||
|
% length starting from Td up to Tu with step dT.
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% Td - starting period length for maximum credible magnitude calculations
|
||||||
|
% Tu - ending period length for maximum credible magnitude calculations
|
||||||
|
% dT - period length step for maximum credible magnitude calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% T - vector of independent variable (period lengths) T=(Td:dT:Tu)
|
||||||
|
% m - vector of maximum credible magnitudes of the same length as T
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [T,m]=Max_credM_GRT(Td,Tu,dT,Mmin,lamb,eps,b,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dT<=0;error('Time Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
T=(Td:dT:Tu)';
|
||||||
|
beta=b*log(10);
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin+eps/2)));
|
||||||
|
m=Mmin-eps/2-1/beta*log((1-(1-1./(lamb*T))*mian));
|
||||||
|
end
|
||||||
|
|
||||||
63
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_GRU.m
Executable file
63
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_GRU.m
Executable file
@ -0,0 +1,63 @@
|
|||||||
|
% [T,m]=Max_credM_GRU(Td,Tu,dT,Mmin,lamb,eps,b)
|
||||||
|
%
|
||||||
|
%EVALUATES THE MAXIMUM CREDIBLE MAGNITUDE VALUES USING THE UNLIMITED
|
||||||
|
% G-R LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the unlimited Gutenberg-Richter relation
|
||||||
|
% leads to the exponential distribution model of magnitude distribution
|
||||||
|
% from and above the catalog completness level Mmin. The shape parameter of
|
||||||
|
% this distribution and consequently the G-R b-value are calculated at
|
||||||
|
% start-up of the stationary hazard assessment services in the
|
||||||
|
% unlimited Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The maximum credible magnitude for the period of length T
|
||||||
|
% is the magnitude value whose mean return period is T.
|
||||||
|
%
|
||||||
|
% The maximum credible magnitude values are calculated for periods of
|
||||||
|
% length starting from Td up to Tu with step dT.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Td - starting period length for maximum credible magnitude calculations
|
||||||
|
% Tu - ending period length for maximum credible magnitude calculations
|
||||||
|
% dT - period length step for maximum credible magnitude calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% T - vector of independent variable (period lengths) T=(Td:dT:Tu)
|
||||||
|
% m - vector of maximum credible magnitudes of the same length as T
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [T,m]=Max_credM_GRU(Td,Tu,dT,Mmin,lamb,eps,b)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dT<=0;error('Time Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
T=(Td:dT:Tu)';
|
||||||
|
beta=b*log(10);
|
||||||
|
m=Mmin-eps/2+1/beta.*log(lamb*T);
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
98
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPT.m
Executable file
98
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPT.m
Executable file
@ -0,0 +1,98 @@
|
|||||||
|
% [T,m]=Max_credM_NPT(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd,Mmax)
|
||||||
|
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES THE MAXIMUM
|
||||||
|
% CREDIBLE MAGNITUDE VALUES FOR THE UPPER-BOUNDED NONPARAMETRIC
|
||||||
|
% DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution has a hard end point Mmax from the right hand
|
||||||
|
% side.The estimation makes use of the previously estimated parameters
|
||||||
|
% namely the mean activity rate lamb, the length of magnitude round-off
|
||||||
|
% interval, eps, the smoothing factor, h, the background sample, xx, the
|
||||||
|
% scaling factors for the background sample, ambd, and the end-point of
|
||||||
|
% magnitude distribution Mmax. The background sample,xx, comprises the
|
||||||
|
% randomized values of observed magnitude doubled symmetrically with
|
||||||
|
% respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% The maximum credible magnitude for the period of length T
|
||||||
|
% is the magnitude value whose mean return period is T.
|
||||||
|
% The maximum credible magnitude values are calculated for periods of
|
||||||
|
% length starting from Td up to Tu with step dT.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
% Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
% Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
% Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% Td - starting period length for maximum credible magnitude calculations
|
||||||
|
% Tu - ending period length for maximum credible magnitude calculations
|
||||||
|
% dT - period length step for maximum credible magnitude calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% T - vector of independent variable (period lengths) T=(Td:dT:Tu)
|
||||||
|
% m - vector of maximum credible magnitudes of the same length as T
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [T,m]=Max_credM_NPT(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dT<=0;error('Time Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
T=(Td:dT:Tu)';
|
||||||
|
n=length(T);
|
||||||
|
interval=[Mmin-eps/2 Mmax-0.001];
|
||||||
|
for i=1:n
|
||||||
|
m(i)=fzero(@F_maxmagn,interval,[],xx,h,ambd,Mmin-eps/2,Mmax,lamb,T(i));
|
||||||
|
end
|
||||||
|
m=m';
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [y]=F_maxmagn(t,xx,h,ambd,xmin,Mmax,lamb,D)
|
||||||
|
mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(xmin,xx,ambd,h));
|
||||||
|
CDF_NPT=2*(Dystr_npr(t,xx,ambd,h)-Dystr_npr(xmin,xx,ambd,h))/mian;
|
||||||
|
y=CDF_NPT-1+1/(lamb*D);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
98
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPT_O.m
Executable file
98
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPT_O.m
Executable file
@ -0,0 +1,98 @@
|
|||||||
|
% [T,m]=Max_credM_NPT_O(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd,Mmax) ---- (Octave Compatible Version)
|
||||||
|
%
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES THE MAXIMUM
|
||||||
|
% CREDIBLE MAGNITUDE VALUES FOR THE UPPER-BOUNDED NONPARAMETRIC
|
||||||
|
% DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution has a hard end point Mmax from the right hand
|
||||||
|
% side.The estimation makes use of the previously estimated parameters
|
||||||
|
% namely the mean activity rate lamb, the length of magnitude round-off
|
||||||
|
% interval, eps, the smoothing factor, h, the background sample, xx, the
|
||||||
|
% scaling factors for the background sample, ambd, and the end-point of
|
||||||
|
% magnitude distribution Mmax. The background sample,xx, comprises the
|
||||||
|
% randomized values of observed magnitude doubled symmetrically with
|
||||||
|
% respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% The maximum credible magnitude for the period of length T
|
||||||
|
% is the magnitude value whose mean return period is T.
|
||||||
|
% The maximum credible magnitude values are calculated for periods of
|
||||||
|
% length starting from Td up to Tu with step dT.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
% Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
% Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
% Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% Td - starting period length for maximum credible magnitude calculations
|
||||||
|
% Tu - ending period length for maximum credible magnitude calculations
|
||||||
|
% dT - period length step for maximum credible magnitude calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% T - vector of independent variable (period lengths) T=(Td:dT:Tu)
|
||||||
|
% m - vector of maximum credible magnitudes of the same length as T
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [T,m]=Max_credM_NPT_O(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dT<=0;error('Time Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
T=(Td:dT:Tu)';
|
||||||
|
n=length(T);
|
||||||
|
interval=[Mmin-eps/2 Mmax-0.001];
|
||||||
|
for i=1:n
|
||||||
|
m(i)=fzero(@(t) F_maxmagn(t,xx,h,ambd,Mmin-eps/2,Mmax,lamb,T(i)),interval);
|
||||||
|
end
|
||||||
|
m=m';
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [y]=F_maxmagn(t,xx,h,ambd,xmin,Mmax,lamb,D)
|
||||||
|
mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(xmin,xx,ambd,h));
|
||||||
|
CDF_NPT=2*(Dystr_npr(t,xx,ambd,h)-Dystr_npr(xmin,xx,ambd,h))/mian;
|
||||||
|
y=CDF_NPT-1+1/(lamb*D);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
98
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPU.m
Executable file
98
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPU.m
Executable file
@ -0,0 +1,98 @@
|
|||||||
|
% [T,m]=Max_credM_NPU(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd)
|
||||||
|
%
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES
|
||||||
|
% THE MAXIMUM CREDIBLE MAGNITUDE VALUES FOR THE UNBOUNDED
|
||||||
|
% NONPARAMETRIC DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution is unlimited from the right hand side.
|
||||||
|
% The estimation makes use of the previously estimated parameters of kernel
|
||||||
|
% estimation, namely the smoothing factor, the background sample and the
|
||||||
|
% scaling factors for the background sample. The background sample
|
||||||
|
% - xx comprises the randomized values of observed magnitude doubled
|
||||||
|
% symmetrically with respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% The maximum credible magnitude for the period of length T
|
||||||
|
% is the magnitude value whose mean return period is T.
|
||||||
|
% The maximum credible magnitude values are calculated for periods of
|
||||||
|
% length starting from Td up to Tu with step dT.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation fro Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% opt - determines the mode of calculations. opt=0 - fixed time period
|
||||||
|
% length (y), different magnitude values (x), opt=1 - fixed magnitude
|
||||||
|
% (y), different time period lengths (x)
|
||||||
|
% xd - starting value of the changeable independent variable
|
||||||
|
% xu - ending value of the changeable independent variable
|
||||||
|
% dx - step change of the changeable independent variable
|
||||||
|
% y - fixed independent variable value: time period length T' if opt=0,
|
||||||
|
% magnitude M' if opt=1
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% T - vector of independent variable (period lengths) T=(Td:dT:Tu)
|
||||||
|
% m - vector of maximum credible magnitudes of the same length as T
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [T,m]=Max_credM_NPU(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dT<=0;error('Time Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
T=(Td:dT:Tu)';
|
||||||
|
n=length(T);
|
||||||
|
interval=[Mmin-eps/2 10.0];
|
||||||
|
for i=1:n
|
||||||
|
m(i)=fzero(@F_maxmagn_NPU,interval,[],xx,h,ambd,Mmin-eps/2,lamb,T(i));
|
||||||
|
end
|
||||||
|
m=m';
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=F_maxmagn_NPU(t,xx,h,ambd,xmin,lamb,D)
|
||||||
|
CDF_NPU=2*(Dystr_npr(t,xx,ambd,h)-Dystr_npr(xmin,xx,ambd,h));
|
||||||
|
y=CDF_NPU-1+1/(lamb*D);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
99
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPU_O.m
Executable file
99
SHAPE_Package/SHAPE_ver2b.0/SSH/Max_credM_NPU_O.m
Executable file
@ -0,0 +1,99 @@
|
|||||||
|
% [T,m]=Max_credM_NPU_O(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd) ---- (Octave Comlatible Version)
|
||||||
|
%
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES
|
||||||
|
% THE MAXIMUM CREDIBLE MAGNITUDE VALUES FOR THE UNBOUNDED
|
||||||
|
% NONPARAMETRIC DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution is unlimited from the right hand side.
|
||||||
|
% The estimation makes use of the previously estimated parameters of kernel
|
||||||
|
% estimation, namely the smoothing factor, the background sample and the
|
||||||
|
% scaling factors for the background sample. The background sample
|
||||||
|
% - xx comprises the randomized values of observed magnitude doubled
|
||||||
|
% symmetrically with respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% The maximum credible magnitude for the period of length T
|
||||||
|
% is the magnitude value whose mean return period is T.
|
||||||
|
% The maximum credible magnitude values are calculated for periods of
|
||||||
|
% length starting from Td up to Tu with step dT.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation fro Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% opt - determines the mode of calculations. opt=0 - fixed time period
|
||||||
|
% length (y), different magnitude values (x), opt=1 - fixed magnitude
|
||||||
|
% (y), different time period lengths (x)
|
||||||
|
% xd - starting value of the changeable independent variable
|
||||||
|
% xu - ending value of the changeable independent variable
|
||||||
|
% dx - step change of the changeable independent variable
|
||||||
|
% y - fixed independent variable value: time period length T' if opt=0,
|
||||||
|
% magnitude M' if opt=1
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% T - vector of independent variable (period lengths) T=(Td:dT:Tu)
|
||||||
|
% m - vector of maximum credible magnitudes of the same length as T
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [T,m]=Max_credM_NPU_O(Td,Tu,dT,Mmin,lamb,eps,h,xx,ambd)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dT<=0;error('Time Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
T=(Td:dT:Tu)';
|
||||||
|
n=length(T);
|
||||||
|
interval=[Mmin-eps/2 10.0];
|
||||||
|
for i=1:n
|
||||||
|
% m(i)=fzero(@F_maxmagn_NPU,interval,[],xx,h,ambd,Mmin-eps/2,lamb,T(i));
|
||||||
|
m(i)=fzero(@(t) F_maxmagn_NPU(t,xx,h,ambd,Mmin-eps/2,lamb,T(i)),interval);
|
||||||
|
end
|
||||||
|
m=m';
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=F_maxmagn_NPU(t,xx,h,ambd,xmin,lamb,D)
|
||||||
|
CDF_NPU=2*(Dystr_npr(t,xx,ambd,h)-Dystr_npr(xmin,xx,ambd,h));
|
||||||
|
y=CDF_NPU-1+1/(lamb*D);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
259
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar.m
Executable file
259
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar.m
Executable file
@ -0,0 +1,259 @@
|
|||||||
|
% [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd]=Nonpar(t,M,iop,Mmin)
|
||||||
|
%
|
||||||
|
% BASED ON MAGNITUDE SAMPLE DATA M DETERMINES THE ROUND-OFF INTERVAL LENGTH
|
||||||
|
% OF THE MAGNITUDE DATA - eps, THE SMOOTHING FACTOR - h, CONSTRUCTS
|
||||||
|
% THE BACKGROUND SAMPLE - xx AND CALCULATES THE WEIGHTING FACTORS - ambd
|
||||||
|
% FOR A USE OF THE NONPARAMETRIC ADAPTATIVE KERNEL ESTIMATORS OF MAGNITUDE
|
||||||
|
% DISTRIBUTION.
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UNBOUNDED
|
||||||
|
% NON-PARAMETRIC HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. The smoothing factor
|
||||||
|
% h, is estimated using the least-squares cross-validation for the Gaussian
|
||||||
|
% kernel function. The final form of the kernel is the adaptive kernel.
|
||||||
|
% In order to avoid repetitions, which cannot appear in a sample when the
|
||||||
|
% kernel estimators are used, the magnitude sample data are randomized
|
||||||
|
% within the magnitude round-off interval. The round-off interval length -
|
||||||
|
% eps is the least non-zero difference between sample data or 0.1 is the
|
||||||
|
% least difference if greater than 0.1. The randomization is done
|
||||||
|
% assuming exponential distribution of m in [m0-eps/2, m0+eps/2], where m0
|
||||||
|
% is the sample data point and eps is the length of roud-off inteval. The
|
||||||
|
% shape parameter of the exponential distribution is estimated from the whole
|
||||||
|
% data sample assuming the exponential distribution. The background sample
|
||||||
|
% - xx comprises the randomized values of magnitude doubled symmetrically
|
||||||
|
% with respect to the value Mmin-eps/2: length(xx)=2*length(M). Weigthing
|
||||||
|
% factors row vector for the adaptive kernel is of the same size as xx.
|
||||||
|
% See: the references below for a more comprehensive description.
|
||||||
|
%
|
||||||
|
% This is a beta version of the program. Further developments are foreseen.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of earthquake magnitudes (sample data)
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
%
|
||||||
|
% OUTPUT
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 50 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% ierr - h-convergence indicator. ierr=0 if the estimation procedure of
|
||||||
|
% the optimal smoothing factor has converged (the zero of the h functional
|
||||||
|
% has been found, ierr=1 when multiple zeros of h functional were
|
||||||
|
% encountered - the largest h is accepted, ierr = 2 when h functional did
|
||||||
|
% not zeroe - the approximate h value is taken.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample for the nonparametric estimators of magnitude
|
||||||
|
% distribution
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd]=...
|
||||||
|
Nonpar(t,M,iop,Mmin)
|
||||||
|
|
||||||
|
lamb_err=0;
|
||||||
|
n=length(M);
|
||||||
|
t1=t(1);
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
lamb_all=n/round(t(n)-t(1));
|
||||||
|
lamb=nn/round(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
lamb_all=30*n/(t(n)-t(1)); % K20OCT2014
|
||||||
|
lamb=30*nn/(t2-t1); % K20OCT2014
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
lamb_all=365*n/(t(n)-t(1)); % K20OCT2014
|
||||||
|
lamb=365*nn/(t2-t1); % K20OCT2014
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
|
||||||
|
if nn<50
|
||||||
|
eps=0;ierr=0;h=0;
|
||||||
|
lamb_err=1;
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
n=0;
|
||||||
|
for i=1:length(M)
|
||||||
|
if M(i)>=Mmin;
|
||||||
|
n=n+1;
|
||||||
|
x(n)=M(i);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
x=sort(x)';
|
||||||
|
beta=1/(mean(x)-Mmin+eps/2);
|
||||||
|
[xx]=korekta(x,Mmin,eps,beta);
|
||||||
|
xx=sort(xx);
|
||||||
|
clear x;
|
||||||
|
xx = podwajanie(xx,Mmin-eps/2);
|
||||||
|
[h,ierr]=hopt(xx);
|
||||||
|
[ambd]=scaling(xx,h);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [m_corr]=korekta(m,Mmin,eps,beta)
|
||||||
|
|
||||||
|
% RANDOMIZATION OF MAGNITUDE WITHIN THE ACCURACY INTERVAL
|
||||||
|
%
|
||||||
|
% m - input vector of magnitudes
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% eps - accuracy of magnitude
|
||||||
|
% beta - the parameter of the unbounded exponential distribution
|
||||||
|
%
|
||||||
|
% m_corr - vector of randomized magnitudes
|
||||||
|
%
|
||||||
|
F1=1-exp(-beta*(m-Mmin-0.5*eps));
|
||||||
|
F2=1-exp(-beta*(m-Mmin+0.5*eps));
|
||||||
|
u=rand(size(m));
|
||||||
|
w=u.*(F2-F1)+F1;
|
||||||
|
m_corr=Mmin-log(1-w)./beta;
|
||||||
|
end
|
||||||
|
|
||||||
|
function x2 = podwajanie(x,x0)
|
||||||
|
|
||||||
|
% DOUBLES THE SAMPLE
|
||||||
|
|
||||||
|
% If the sample x(i) is is truncated from the left hand side and belongs
|
||||||
|
% to the interval [x0,inf) or it is truncated from the right hand side and
|
||||||
|
% belongs to the interval (-inf,x0]
|
||||||
|
% then the doubled sample is [-x(i)+2x0,x(i)]
|
||||||
|
% x - is the column data vector
|
||||||
|
% x2 - is the column vector of data doubled and sorted in the ascending
|
||||||
|
% order
|
||||||
|
|
||||||
|
x2=[-x+2*x0
|
||||||
|
x];
|
||||||
|
x2=sort(x2);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [h,ierr]=hopt(x)
|
||||||
|
|
||||||
|
%Estimation of the optimal smoothing factor by means of the least squares
|
||||||
|
%method
|
||||||
|
% x - column data vector
|
||||||
|
% The result is an optimal smoothing factor
|
||||||
|
% ierr=0 - convergence, ierr=1 - multiple h, ierr=2 - approximate h is used
|
||||||
|
% The function calls the procedure FZERO for the function 'funct'
|
||||||
|
% NEW VERSION 2 - without a square matrix. Also equipped with extra zeros
|
||||||
|
% search
|
||||||
|
|
||||||
|
% MODIFIED JUNE 2014
|
||||||
|
|
||||||
|
ierr=0;
|
||||||
|
n=length(x);
|
||||||
|
x=sort(x);
|
||||||
|
interval=[0.000001 2*std(x)/n^0.2];
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
[hh(1),fval,exitflag]=fzero(@funct,interval,[],x);
|
||||||
|
|
||||||
|
% Extra zeros search
|
||||||
|
jj=1;
|
||||||
|
for kk=2:7
|
||||||
|
interval(1)=1.1*hh(jj);
|
||||||
|
interval(2)=interval(1)+(kk-1)*hh(jj);
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
jj=jj+1;
|
||||||
|
[hh(jj),fval,exitflag]=fzero(@funct,interval,[],x);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
if jj>1;ierr=1;end
|
||||||
|
h=max(hh);
|
||||||
|
|
||||||
|
if exitflag==1;return;end
|
||||||
|
|
||||||
|
end
|
||||||
|
h=0.891836*(mean(x)-x(1))/(n^0.2);
|
||||||
|
ierr=2;
|
||||||
|
end
|
||||||
|
|
||||||
|
function [fct]=funct(t,x)
|
||||||
|
p2=1.41421356;
|
||||||
|
n=length(x);
|
||||||
|
yy=zeros(size(x));
|
||||||
|
for i=1:n,
|
||||||
|
xij=(x-x(i)).^2/t^2;
|
||||||
|
y=exp(-xij/4).*((xij/2-1)/p2)-2*exp(-xij/2).*(xij-1);
|
||||||
|
yy(i)=sum(y);
|
||||||
|
end;
|
||||||
|
fct=sum(yy)-2*n;
|
||||||
|
clear xij y yy;
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [ambd]=scaling(x,h)
|
||||||
|
|
||||||
|
% EVALUATES A VECTOR OF SCALING FACTORS FOR THE NONPARAMETRIC ADAPTATIVE
|
||||||
|
% ESTIMATION
|
||||||
|
|
||||||
|
% x - the n dimensional column vector of data values sorted in the ascending
|
||||||
|
% order
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% ambd - the resultant n dimensional row vector of local scaling factors
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
gau=zeros(1,n);
|
||||||
|
for i=1:n,
|
||||||
|
gau(i)=sum(exp(-0.5*((x(i)-x)/h).^2))/c/n/h;
|
||||||
|
end
|
||||||
|
g=exp(mean(log(gau)));
|
||||||
|
ambd=sqrt(g./gau);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
310
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar_O.m
Executable file
310
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar_O.m
Executable file
@ -0,0 +1,310 @@
|
|||||||
|
% [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd]=Nonpar(t,M,iop,Mmin)
|
||||||
|
%
|
||||||
|
% BASED ON MAGNITUDE SAMPLE DATA M DETERMINES THE ROUND-OFF INTERVAL LENGTH
|
||||||
|
% OF THE MAGNITUDE DATA - eps, THE SMOOTHING FACTOR - h, CONSTRUCTS
|
||||||
|
% THE BACKGROUND SAMPLE - xx AND CALCULATES THE WEIGHTING FACTORS - ambd
|
||||||
|
% FOR A USE OF THE NONPARAMETRIC ADAPTATIVE KERNEL ESTIMATORS OF MAGNITUDE
|
||||||
|
% DISTRIBUTION.
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UNBOUNDED
|
||||||
|
% NON-PARAMETRIC HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki ver 2 01/2015 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. The smoothing factor
|
||||||
|
% h, is estimated using the least-squares cross-validation for the Gaussian
|
||||||
|
% kernel function. The final form of the kernel is the adaptive kernel.
|
||||||
|
% In order to avoid repetitions, which cannot appear in a sample when the
|
||||||
|
% kernel estimators are used, the magnitude sample data are randomized
|
||||||
|
% within the magnitude round-off interval. The round-off interval length -
|
||||||
|
% eps is the least non-zero difference between sample data or 0.1 is the
|
||||||
|
% least difference if greater than 0.1. The randomization is done
|
||||||
|
% assuming exponential distribution of m in [m0-eps/2, m0+eps/2], where m0
|
||||||
|
% is the sample data point and eps is the length of roud-off inteval. The
|
||||||
|
% shape parameter of the exponential distribution is estimated from the whole
|
||||||
|
% data sample assuming the exponential distribution. The background sample
|
||||||
|
% - xx comprises the randomized values of magnitude doubled symmetrically
|
||||||
|
% with respect to the value Mmin-eps/2: length(xx)=2*length(M). Weigthing
|
||||||
|
% factors row vector for the adaptive kernel is of the same size as xx.
|
||||||
|
% See: the references below for a more comprehensive description.
|
||||||
|
%
|
||||||
|
% This is a beta version of the program. Further developments are foreseen.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of earthquake magnitudes (sample data)
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
%
|
||||||
|
% OUTPUT
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 50 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% ierr - h-convergence indicator. ierr=0 if the estimation procedure of
|
||||||
|
% the optimal smoothing factor has converged (the zero of the h functional
|
||||||
|
% has been found, ierr=1 when multiple zeros of h functional were
|
||||||
|
% encountered - the largest h is accepted, ierr = 2 when h functional did
|
||||||
|
% not zeroe - the approximate h value is taken.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample for the nonparametric estimators of magnitude
|
||||||
|
% distribution
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd]=...
|
||||||
|
Nonpar_O(t,M,iop,Mmin)
|
||||||
|
if isempty(t) || numel(t)<3 ,isempty(M(M>=Mmin)) %K03OCT
|
||||||
|
t=[1 2];M=[1 2]; end %K30SEP
|
||||||
|
|
||||||
|
|
||||||
|
lamb_err=0;
|
||||||
|
%%% %%%%%%%%%%%%%MICHAL
|
||||||
|
xx=NaN;
|
||||||
|
ambd=NaN;
|
||||||
|
%%% %%%%%%%%%%%%%MICHAL
|
||||||
|
n=length(M);
|
||||||
|
t1=t(1);
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
[NM,unit]=time_diff(t(1),t(n),iop);
|
||||||
|
lamb_all=n/NM;
|
||||||
|
[NM,unit]=time_diff(t1,t2,iop);
|
||||||
|
lamb=nn/NM;
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
if nn<50
|
||||||
|
eps=0;ierr=0;h=0;
|
||||||
|
lamb_err=1;
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
n=0;
|
||||||
|
for i=1:length(M)
|
||||||
|
if M(i)>=Mmin;
|
||||||
|
n=n+1;
|
||||||
|
x(n)=M(i);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
x=sort(x)';
|
||||||
|
beta=1/(mean(x)-Mmin+eps/2);
|
||||||
|
[xx]=korekta(x,Mmin,eps,beta);
|
||||||
|
xx=sort(xx);
|
||||||
|
clear x;
|
||||||
|
xx = podwajanie(xx,Mmin-eps/2);
|
||||||
|
[h,ierr]=hopt(xx);
|
||||||
|
[ambd]=scaling(xx,h);
|
||||||
|
% enai=dlmread('para.txt'); %for fixed xx,ambd to test in different platforms
|
||||||
|
% [ambd]=enai(:,1);
|
||||||
|
% xx=enai(:,2)';
|
||||||
|
% [h,ierr]=hopt(xx);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [NM,unit]=time_diff(t1,t2,iop) % SL 03MAR2015
|
||||||
|
|
||||||
|
% TIME DIFFERENCE BETWEEEN t1,t2 EXPRESSED IN DAY, MONTH OR YEAR UNIT
|
||||||
|
%
|
||||||
|
% t1 - start time (in MATLAB numerical format)
|
||||||
|
% t2 - end time (in MATLAB numerical format) t2>=t1
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
%
|
||||||
|
% NM - number of time units from t1 to t2
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
NM=(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM=V2(3)/eomday(V2(1),V2(2))+V2(2)+12-V1(2)-V1(3)/eomday(V1(1),V1(2))...
|
||||||
|
+(V2(1)-V1(1)-1)*12;
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM2=V2(3);
|
||||||
|
if V2(2)>1
|
||||||
|
for k=1:V2(2)-1
|
||||||
|
NM2=NM2+eomday(V2(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day2=365; if eomday(V2(1),2)==29; day2=366; end;
|
||||||
|
NM2=NM2/day2;
|
||||||
|
NM1=V1(3);
|
||||||
|
if V1(2)>1
|
||||||
|
for k=1:V1(2)-1
|
||||||
|
NM1=NM1+eomday(V1(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day1=365; if eomday(V1(1),2)==29; day1=366; end;
|
||||||
|
NM1=(day1-NM1)/day1;
|
||||||
|
NM=NM2+NM1+V2(1)-V1(1)-1;
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [m_corr]=korekta(m,Mmin,eps,beta)
|
||||||
|
|
||||||
|
% RANDOMIZATION OF MAGNITUDE WITHIN THE ACCURACY INTERVAL
|
||||||
|
%
|
||||||
|
% m - input vector of magnitudes
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% eps - accuracy of magnitude
|
||||||
|
% beta - the parameter of the unbounded exponential distribution
|
||||||
|
%
|
||||||
|
% m_corr - vector of randomized magnitudes
|
||||||
|
%
|
||||||
|
F1=1-exp(-beta*(m-Mmin-0.5*eps));
|
||||||
|
F2=1-exp(-beta*(m-Mmin+0.5*eps));
|
||||||
|
u=rand(size(m));
|
||||||
|
w=u.*(F2-F1)+F1;
|
||||||
|
m_corr=Mmin-log(1-w)./beta;
|
||||||
|
end
|
||||||
|
|
||||||
|
function x2 = podwajanie(x,x0)
|
||||||
|
|
||||||
|
% DOUBLES THE SAMPLE
|
||||||
|
|
||||||
|
% If the sample x(i) is is truncated from the left hand side and belongs
|
||||||
|
% to the interval [x0,inf) or it is truncated from the right hand side and
|
||||||
|
% belongs to the interval (-inf,x0]
|
||||||
|
% then the doubled sample is [-x(i)+2x0,x(i)]
|
||||||
|
% x - is the column data vector
|
||||||
|
% x2 - is the column vector of data doubled and sorted in the ascending
|
||||||
|
% order
|
||||||
|
|
||||||
|
x2=[-x+2*x0
|
||||||
|
x];
|
||||||
|
x2=sort(x2);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [h,ierr]=hopt(x)
|
||||||
|
|
||||||
|
%Estimation of the optimal smoothing factor by means of the least squares
|
||||||
|
%method
|
||||||
|
% x - column data vector
|
||||||
|
% The result is an optimal smoothing factor
|
||||||
|
% ierr=0 - convergence, ierr=1 - multiple h, ierr=2 - approximate h is used
|
||||||
|
% The function calls the procedure FZERO for the function 'funct'
|
||||||
|
% NEW VERSION 2 - without a square matrix. Also equipped with extra zeros
|
||||||
|
% search
|
||||||
|
|
||||||
|
% MODIFIED JUNE 2014
|
||||||
|
|
||||||
|
ierr=0;
|
||||||
|
n=length(x);
|
||||||
|
x=sort(x);
|
||||||
|
interval=[0.000001 2*std(x)/n^0.2];
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
fun = @(t) funct(t,x); % FOR OCTAVE
|
||||||
|
x0 =interval; % FOR OCTAVE
|
||||||
|
[hh(1),fval,exitflag] = fzero(fun,x0); % FOR OCTAVE
|
||||||
|
|
||||||
|
% Extra zeros search
|
||||||
|
jj=1;
|
||||||
|
for kk=2:7
|
||||||
|
interval(1)=1.1*hh(jj);
|
||||||
|
interval(2)=interval(1)+(kk-1)*hh(jj);
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
jj=jj+1;
|
||||||
|
fun = @(t) funct(t,x); % FOR OCTAVE
|
||||||
|
x0 =interval; % FOR OCTAVE
|
||||||
|
[hh(jj),fval,exitflag] = fzero(fun,x0); % FOR OCTAVE
|
||||||
|
end
|
||||||
|
end
|
||||||
|
if jj>1;ierr=1;end
|
||||||
|
h=max(hh);
|
||||||
|
|
||||||
|
if exitflag==1;return;end
|
||||||
|
|
||||||
|
end
|
||||||
|
h=0.891836*(mean(x)-x(1))/(n^0.2);
|
||||||
|
ierr=2;
|
||||||
|
end
|
||||||
|
|
||||||
|
function [fct]=funct(t,x)
|
||||||
|
p2=1.41421356;
|
||||||
|
n=length(x);
|
||||||
|
yy=zeros(size(x));
|
||||||
|
for i=1:n,
|
||||||
|
xij=(x-x(i)).^2/t^2;
|
||||||
|
y=exp(-xij/4).*((xij/2-1)/p2)-2*exp(-xij/2).*(xij-1);
|
||||||
|
yy(i)=sum(y);
|
||||||
|
end;
|
||||||
|
fct=sum(yy)-2*n;
|
||||||
|
clear xij y yy;
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [ambd]=scaling(x,h)
|
||||||
|
|
||||||
|
% EVALUATES A VECTOR OF SCALING FACTORS FOR THE NONPARAMETRIC ADAPTATIVE
|
||||||
|
% ESTIMATION
|
||||||
|
|
||||||
|
% x - the n dimensional column vector of data values sorted in the ascending
|
||||||
|
% order
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% ambd - the resultant n dimensional row vector of local scaling factors
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
gau=zeros(1,n);
|
||||||
|
for i=1:n,
|
||||||
|
gau(i)=sum(exp(-0.5*((x(i)-x)/h).^2))/c/n/h;
|
||||||
|
end
|
||||||
|
g=exp(mean(log(gau)));
|
||||||
|
ambd=sqrt(g./gau);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
373
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar_tr.m
Executable file
373
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar_tr.m
Executable file
@ -0,0 +1,373 @@
|
|||||||
|
% [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd,Mmax,err]=
|
||||||
|
% Nonpar(t,M,iop,Mmin)
|
||||||
|
%
|
||||||
|
% BASED ON MAGNITUDE SAMPLE DATA M DETERMINES THE ROUND-OFF INTERVAL LENGTH
|
||||||
|
% OF THE MAGNITUDE DATA - eps, THE SMOOTHING FACTOR - h, CONSTRUCTS
|
||||||
|
% THE BACKGROUND SAMPLE - xx, CALCULATES THE WEIGHTING FACTORS - amb, AND
|
||||||
|
% THE END-POINT OF MAGNITUDE DISTRIBUTION Mmax FOR A USE OF THE NONPARAMETRIC
|
||||||
|
% ADAPTATIVE KERNEL ESTIMATORS OF MAGNITUDE DISTRIBUTION UNDER THE
|
||||||
|
% ASSUMPTION OF THE EXISTENCE OF THE UPPER LIMIT OF MAGNITUDE DISTRIBUTION.
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UPPER-BOUNDED
|
||||||
|
% NON-PARAMETRIC HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. The smoothing factor
|
||||||
|
% h, is estimated using the least-squares cross-validation for the Gaussian
|
||||||
|
% kernel function. The final form of the kernel is the adaptive kernel.
|
||||||
|
% In order to avoid repetitions, which cannot appear in a sample when the
|
||||||
|
% kernel estimators are used, the magnitude sample data are randomized
|
||||||
|
% within the magnitude round-off interval. The round-off interval length -
|
||||||
|
% eps is the least non-zero difference between sample data or 0.1 is the
|
||||||
|
% least difference if greater than 0.1. The randomization is done
|
||||||
|
% assuming exponential distribution of m in [m0-eps/2, m0+eps/2], where m0
|
||||||
|
% is the sample data point and eps is the length of roud-off inteval. The
|
||||||
|
% shape parameter of the exponential distribution is estimated from the whole
|
||||||
|
% data sample assuming the exponential distribution. The background sample
|
||||||
|
% - xx comprises the randomized values of magnitude doubled symmetrically
|
||||||
|
% with respect to the value Mmin-eps/2: length(xx)=2*length(M). Weigthing
|
||||||
|
% factors row vector for the adaptive kernel is of the same size as xx.
|
||||||
|
% The mean activity rate, lamb, is the number of events >=Mmin into the
|
||||||
|
% length of the period in which they occurred.
|
||||||
|
% The upper limit of the distribution Mmax is evaluated using
|
||||||
|
% the Kijko-Sellevol generic formula. If convergence is not reached the
|
||||||
|
% Whitlock @ Robson simplified formula is used:
|
||||||
|
% Mmaxest= 2(max obs M) - (second max obs M)).
|
||||||
|
%
|
||||||
|
% See: the references below for a more comprehensive description.
|
||||||
|
%
|
||||||
|
% This is a beta version of the program. Further developments are foreseen.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%Kijko, A., and M.A. Sellevoll (1989) Bull. Seismol. Soc. Am. 79, 3,645-654
|
||||||
|
%Lasocki, S., Urban, P. (2011) Acta Geophys 59, 659-673,
|
||||||
|
% doi: 10.2478/s11600-010-0049-y
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of earthquake magnitudes (sample data)
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
%
|
||||||
|
% OUTPUT
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 50 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% ierr - h-convergence indicator. ierr=0 if the estimation procedure of
|
||||||
|
% the optimal smoothing factor has converged (a zero of the h functional
|
||||||
|
% has been found), ierr=1 when multiple zeros of h functional were
|
||||||
|
% encountered - the largest h is accepted, ierr = 2 when h functional did
|
||||||
|
% not zeroe - the approximate h value is taken.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample for the nonparametric estimators of magnitude
|
||||||
|
% distribution
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
% err - error parameter on Mmax estimation, err=0 - convergence, err=1 -
|
||||||
|
% no converegence of Kijko-Sellevol estimator, Robinson @ Whitlock
|
||||||
|
% method used.
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd,Mmax,err]=...
|
||||||
|
Nonpar_tr(t,M,iop,Mmin)
|
||||||
|
|
||||||
|
lamb_err=0;
|
||||||
|
n=length(M);
|
||||||
|
t1=t(1);
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
lamb_all=n/round(t(n)-t(1));
|
||||||
|
lamb=nn/round(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
lamb_all=30*n/(t(n)-t(1)); % K20OCT2014
|
||||||
|
lamb=30*nn/(t2-t1); % K20OCT2014
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
lamb_all=365*n/(t(n)-t(1)); % K20OCT2014
|
||||||
|
lamb=365*nn/(t2-t1); % K20OCT2014
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
|
||||||
|
if nn<50
|
||||||
|
eps=0;ierr=0;h=0;Mmax=0;err=0;
|
||||||
|
lamb_err=1;
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
n=0;
|
||||||
|
for i=1:length(M)
|
||||||
|
if M(i)>=Mmin;
|
||||||
|
n=n+1;
|
||||||
|
x(n)=M(i);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
x=sort(x)';
|
||||||
|
beta=1/(mean(x)-Mmin+eps/2);
|
||||||
|
[xx]=korekta(x,Mmin,eps,beta);
|
||||||
|
xx=sort(xx);
|
||||||
|
clear x;
|
||||||
|
xx = podwajanie(xx,Mmin-eps/2);
|
||||||
|
[h,ierr]=hopt(xx);
|
||||||
|
[ambd]=scaling(xx,h);
|
||||||
|
[Mmax,err]=Mmaxest(xx,h,Mmin-eps/2);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [m_corr]=korekta(m,Mmin,eps,beta)
|
||||||
|
|
||||||
|
% RANDOMIZATION OF MAGNITUDE WITHIN THE ACCURACY INTERVAL
|
||||||
|
%
|
||||||
|
% m - input vector of magnitudes
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% eps - accuracy of magnitude
|
||||||
|
% beta - the parameter of the unbounded exponential distribution
|
||||||
|
%
|
||||||
|
% m_corr - vector of randomized magnitudes
|
||||||
|
%
|
||||||
|
F1=1-exp(-beta*(m-Mmin-0.5*eps));
|
||||||
|
F2=1-exp(-beta*(m-Mmin+0.5*eps));
|
||||||
|
u=rand(size(m));
|
||||||
|
w=u.*(F2-F1)+F1;
|
||||||
|
m_corr=Mmin-log(1-w)./beta;
|
||||||
|
end
|
||||||
|
|
||||||
|
function x2 = podwajanie(x,x0)
|
||||||
|
|
||||||
|
% DOUBLES THE SAMPLE
|
||||||
|
|
||||||
|
% If the sample x(i) is is truncated from the left hand side and belongs
|
||||||
|
% to the interval [x0,inf) or it is truncated from the right hand side and
|
||||||
|
% belongs to the interval (-inf,x0]
|
||||||
|
% then the doubled sample is [-x(i)+2x0,x(i)]
|
||||||
|
% x - is the column data vector
|
||||||
|
% x2 - is the column vector of data doubled and sorted in the ascending
|
||||||
|
% order
|
||||||
|
|
||||||
|
x2=[-x+2*x0
|
||||||
|
x];
|
||||||
|
x2=sort(x2);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [h,ierr]=hopt(x)
|
||||||
|
|
||||||
|
%Estimation of the optimal smoothing factor by means of the least squares
|
||||||
|
%method
|
||||||
|
% x - column data vector
|
||||||
|
% The result is an optimal smoothing factor
|
||||||
|
% ierr=0 - convergence, ierr=1 - multiple h, ierr=2 - approximate h is used
|
||||||
|
% The function calls the procedure FZERO for the function 'funct'
|
||||||
|
% NEW VERSION 2 - without a square matrix. Also equipped with extra zeros
|
||||||
|
% search
|
||||||
|
|
||||||
|
% MODIFIED JUNE 2014
|
||||||
|
|
||||||
|
ierr=0;
|
||||||
|
n=length(x);
|
||||||
|
x=sort(x);
|
||||||
|
interval=[0.000001 2*std(x)/n^0.2];
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
[hh(1),fval,exitflag]=fzero(@funct,interval,[],x);
|
||||||
|
|
||||||
|
% Extra zeros search
|
||||||
|
jj=1;
|
||||||
|
for kk=2:7
|
||||||
|
interval(1)=1.1*hh(jj);
|
||||||
|
interval(2)=interval(1)+(kk-1)*hh(jj);
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
jj=jj+1;
|
||||||
|
[hh(jj),fval,exitflag]=fzero(@funct,interval,[],x);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
if jj>1;ierr=1;end
|
||||||
|
h=max(hh);
|
||||||
|
|
||||||
|
if exitflag==1;return;end
|
||||||
|
|
||||||
|
end
|
||||||
|
h=0.891836*(mean(x)-x(1))/(n^0.2);
|
||||||
|
ierr=2;
|
||||||
|
end
|
||||||
|
|
||||||
|
function [fct]=funct(t,x)
|
||||||
|
p2=1.41421356;
|
||||||
|
n=length(x);
|
||||||
|
yy=zeros(size(x));
|
||||||
|
for i=1:n,
|
||||||
|
xij=(x-x(i)).^2/t^2;
|
||||||
|
y=exp(-xij/4).*((xij/2-1)/p2)-2*exp(-xij/2).*(xij-1);
|
||||||
|
yy(i)=sum(y);
|
||||||
|
end;
|
||||||
|
fct=sum(yy)-2*n;
|
||||||
|
clear xij y yy;
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [ambd]=scaling(x,h)
|
||||||
|
|
||||||
|
% EVALUATES A VECTOR OF SCALING FACTORS FOR THE NONPARAMETRIC ADAPTATIVE
|
||||||
|
% ESTIMATION
|
||||||
|
|
||||||
|
% x - the n dimensional column vector of data values sorted in the ascending
|
||||||
|
% order
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% ambd - the resultant n dimensional row vector of local scaling factors
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
gau=zeros(1,n);
|
||||||
|
for i=1:n,
|
||||||
|
gau(i)=sum(exp(-0.5*((x(i)-x)/h).^2))/c/n/h;
|
||||||
|
end
|
||||||
|
g=exp(mean(log(gau)));
|
||||||
|
ambd=sqrt(g./gau);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [Mmax,ierr]=Mmaxest(x,h,Mmin)
|
||||||
|
|
||||||
|
% ESTIMATION OF UPPER BOUND USING NONPARAMETRIC DISTRIBUTION FUNCTIONS
|
||||||
|
% x - row vector of magnitudes (basic sample).
|
||||||
|
% h - optimal smoothing factor
|
||||||
|
% Mmax - upper bound
|
||||||
|
% ierr=0 if basic procedure converges, ierr=1 when Robsen & Whitlock Mmas
|
||||||
|
% estimation
|
||||||
|
|
||||||
|
% Uses function 'dystryb'
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
ierr=1;
|
||||||
|
x=sort(x);
|
||||||
|
Mmax1=x(n);
|
||||||
|
for i=1:50,
|
||||||
|
d=normcdf((Mmin-x)./h);
|
||||||
|
mian=sum(normcdf((Mmax1-x)./h)-d);
|
||||||
|
Mmax=x(n)+moja_calka(@dystryb,x(1),Mmax1,0.00001,h,mian,x,d);
|
||||||
|
if abs(Mmax-Mmax1)<0.01
|
||||||
|
ierr=0;break;
|
||||||
|
end
|
||||||
|
Mmax1=Mmax;
|
||||||
|
end
|
||||||
|
if (ierr==1 || Mmax>9)
|
||||||
|
Mmax=2*x(n)-x(n-1);
|
||||||
|
ierr=1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=dystryb(z,h,mian,x,d)
|
||||||
|
n=length(x);
|
||||||
|
m=length(z);
|
||||||
|
for i=1:m,
|
||||||
|
t=(z(i)-x)./h;
|
||||||
|
t=normcdf(t);
|
||||||
|
yy=sum(t-d);
|
||||||
|
y(i)=(yy/mian)^n;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [calka,ier]=moja_calka(funfc,a,b,eps,varargin)
|
||||||
|
|
||||||
|
% Integration by means of 16th poit Gauss method. Adopted from CERNLIBRARY
|
||||||
|
|
||||||
|
% funfc - string with the name of function to be integrated
|
||||||
|
% a,b - integration limits
|
||||||
|
% eps - accurracy
|
||||||
|
% varargin - other parameters of function to be integrated
|
||||||
|
% calka - integral
|
||||||
|
% ier=0 - convergence, ier=1 - no conbergence
|
||||||
|
|
||||||
|
persistent W X CONST
|
||||||
|
W=[0.101228536290376 0.222381034453374 0.313706645877887 ...
|
||||||
|
0.362683783378362 0.027152459411754 0.062253523938648 ...
|
||||||
|
0.095158511682493 0.124628971255534 0.149595988816577 ...
|
||||||
|
0.169156519395003 0.182603415044924 0.189450610455069];
|
||||||
|
X=[0.960289856497536 0.796666477413627 0.525532409916329 ...
|
||||||
|
0.183434642495650 0.989400934991650 0.944575023073233 ...
|
||||||
|
0.865631202387832 0.755404408355003 0.617876244402644 ...
|
||||||
|
0.458016777657227 0.281603550779259 0.095012509837637];
|
||||||
|
CONST=1E-12;
|
||||||
|
delta=CONST*abs(a-b);
|
||||||
|
calka=0.;
|
||||||
|
aa=a;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
while abs(y)>delta,
|
||||||
|
bb=aa+y;
|
||||||
|
c1=0.5*(aa+bb);
|
||||||
|
c2=c1-aa;
|
||||||
|
s8=0.;
|
||||||
|
s16=0.;
|
||||||
|
for i=1:4,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s8=s8+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
for i=5:12,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s16=s16+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
s8=s8*c2;
|
||||||
|
s16=s16*c2;
|
||||||
|
if abs(s16-s8)>eps*(1+abs(s16))
|
||||||
|
y=0.5*y;
|
||||||
|
calka=0.;
|
||||||
|
ier=1;
|
||||||
|
else
|
||||||
|
calka=calka+s16;
|
||||||
|
aa=bb;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
506
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar_tr_O.m
Executable file
506
SHAPE_Package/SHAPE_ver2b.0/SSH/Nonpar_tr_O.m
Executable file
@ -0,0 +1,506 @@
|
|||||||
|
% [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd,Mmax,err,BIAS,SD]=
|
||||||
|
% Nonpar_tr(t,M,iop,Mmin,Mmax,Nsynth)
|
||||||
|
%
|
||||||
|
% BASED ON MAGNITUDE SAMPLE DATA M DETERMINES THE ROUND-OFF INTERVAL LENGTH
|
||||||
|
% OF THE MAGNITUDE DATA - eps, THE SMOOTHING FACTOR - h, CONSTRUCTS
|
||||||
|
% THE BACKGROUND SAMPLE - xx, CALCULATES THE WEIGHTING FACTORS - amb, AND
|
||||||
|
% THE END-POINT OF MAGNITUDE DISTRIBUTION Mmax FOR A USE OF THE NONPARAMETRIC
|
||||||
|
% ADAPTATIVE KERNEL ESTIMATORS OF MAGNITUDE DISTRIBUTION UNDER THE
|
||||||
|
% ASSUMPTION OF THE EXISTENCE OF THE UPPER LIMIT OF MAGNITUDE DISTRIBUTION.
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UPPER-BOUNDED
|
||||||
|
% NON-PARAMETRIC HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki ver 2 01/2015 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. The smoothing factor
|
||||||
|
% h, is estimated using the least-squares cross-validation for the Gaussian
|
||||||
|
% kernel function. The final form of the kernel is the adaptive kernel.
|
||||||
|
% In order to avoid repetitions, which cannot appear in a sample when the
|
||||||
|
% kernel estimators are used, the magnitude sample data are randomized
|
||||||
|
% within the magnitude round-off interval. The round-off interval length -
|
||||||
|
% eps is the least non-zero difference between sample data or 0.1 is the
|
||||||
|
% least difference if greater than 0.1. The randomization is done
|
||||||
|
% assuming exponential distribution of m in [m0-eps/2, m0+eps/2], where m0
|
||||||
|
% is the sample data point and eps is the length of roud-off inteval. The
|
||||||
|
% shape parameter of the exponential distribution is estimated from the whole
|
||||||
|
% data sample assuming the exponential distribution. The background sample
|
||||||
|
% - xx comprises the randomized values of magnitude doubled symmetrically
|
||||||
|
% with respect to the value Mmin-eps/2: length(xx)=2*length(M). Weigthing
|
||||||
|
% factors row vector for the adaptive kernel is of the same size as xx.
|
||||||
|
% The mean activity rate, lamb, is the number of events >=Mmin into the
|
||||||
|
% length of the period in which they occurred.
|
||||||
|
% The upper limit of the distribution Mmax is evaluated using
|
||||||
|
% the Kijko-Sellevol generic formula. If convergence is not reached the
|
||||||
|
% Whitlock @ Robson simplified formula is used:
|
||||||
|
% Mmaxest= 2(max obs M) - (second max obs M)).
|
||||||
|
%
|
||||||
|
% See: the references below for a more comprehensive description.
|
||||||
|
%
|
||||||
|
% This is a beta version of the program. Further developments are foreseen.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%Kijko, A., and M.A. Sellevoll (1989) Bull. Seismol. Soc. Am. 79, 3,645-654
|
||||||
|
%Lasocki, S., Urban, P. (2011) Acta Geophys 59, 659-673,
|
||||||
|
% doi: 10.2478/s11600-010-0049-y
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of earthquake magnitudes (sample data)
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% Mmax - upper limit of Magnitude Distribution. Can be set by user, or
|
||||||
|
% estimate within the program - it then should be set as Mmax=[].
|
||||||
|
%
|
||||||
|
% OUTPUT
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 50 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% ierr - h-convergence indicator. ierr=0 if the estimation procedure of
|
||||||
|
% the optimal smoothing factor has converged (a zero of the h functional
|
||||||
|
% has been found), ierr=1 when multiple zeros of h functional were
|
||||||
|
% encountered - the largest h is accepted, ierr = 2 when h functional did
|
||||||
|
% not zeroe - the approximate h value is taken.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample for the nonparametric estimators of magnitude
|
||||||
|
% distribution
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
% err - error parameter on Mmax estimation, err=0 - convergence, err=1 -
|
||||||
|
% no converegence of Kijko-Sellevol estimator, Robinson @ Whitlock
|
||||||
|
% method used.
|
||||||
|
% BIAS - Mmax estimation Bias (Lasocki and Urban, 2011)
|
||||||
|
% SD - Mmax standard deviation (Lasocki ands Urban, 2011)
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [lamb_all,lamb,lamb_err,unit,eps,ierr,h,xx,ambd,Mmax,err,BIAS,SD]=...
|
||||||
|
Nonpar_tr_Ob(t,M,iop,Mmin,Mmax,Nsynth)
|
||||||
|
if nargin==5;Nsynth=[];end % K08DEC2019
|
||||||
|
if isempty(t) || numel(t)<3 isempty(M(M>=Mmin)) %K03OCT
|
||||||
|
t=[1 2];M=[1 2]; end %K30SEP
|
||||||
|
|
||||||
|
lamb_err=0;
|
||||||
|
n=length(M);
|
||||||
|
t1=t(1);
|
||||||
|
%%% %%%%%%%%%%%%%MICHAL
|
||||||
|
xx=NaN;
|
||||||
|
ambd=NaN;
|
||||||
|
%%% %%%%%%%%%%%%%MICHAL
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
[NM,unit]=time_diff(t(1),t(n),iop);
|
||||||
|
lamb_all=n/NM;
|
||||||
|
[NM,unit]=time_diff(t1,t2,iop);
|
||||||
|
lamb=nn/NM;
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
if nn<50
|
||||||
|
eps=0;ierr=0;h=0;Mmax=0;err=0;
|
||||||
|
lamb_err=1;
|
||||||
|
BIAS=NaN;SD=NaN; %%% K 08NOV2019
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
n=0;
|
||||||
|
for i=1:length(M)
|
||||||
|
if M(i)>=Mmin;
|
||||||
|
n=n+1;
|
||||||
|
x(n)=M(i);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
x=sort(x)';
|
||||||
|
beta=1/(mean(x)-Mmin+eps/2);
|
||||||
|
[xx]=korekta(x,Mmin,eps,beta);
|
||||||
|
xx=sort(xx);
|
||||||
|
clear x;
|
||||||
|
xx = podwajanie(xx,Mmin-eps/2);
|
||||||
|
[h,ierr]=hopt(xx);
|
||||||
|
[ambd]=scaling(xx,h);
|
||||||
|
|
||||||
|
if isempty(Mmax) %K30AUG2019 - Allow for manually set Mmax
|
||||||
|
err_Mmax=1;[Mmax,err]=Mmaxest(xx,h,Mmin-eps/2); % err_Mmax added 04DEC2019
|
||||||
|
else
|
||||||
|
err_Mmax=0;err=0; %K30AUG2019
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% Estimation of Mmax Bias %%% K 04DEC2019
|
||||||
|
% (Lasocki and Urban, 2011, doi:10.2478/s11600-010-0049-y)
|
||||||
|
if isempty(Nsynth)==0 && err_Mmax==1 % set number of synthetic datasets, e.g. 10000
|
||||||
|
[BIAS,SD]=Mmax_Bias_GR(t,M,Mmin,Mmax,err,h,xx,ambd,Nsynth);
|
||||||
|
elseif isempty(Nsynth)==0 && err_Mmax==0;
|
||||||
|
warning('Mmax must be empty for BIAS calculation');BIAS=[];SD=[];
|
||||||
|
else; BIAS=0;SD=0;
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
function [NM,unit]=time_diff(t1,t2,iop) % SL 03MAR2015 ----------------------------------
|
||||||
|
|
||||||
|
% TIME DIFFERENCE BETWEEEN t1,t2 EXPRESSED IN DAY, MONTH OR YEAR UNIT
|
||||||
|
%
|
||||||
|
% t1 - start time (in MATLAB numerical format)
|
||||||
|
% t2 - end time (in MATLAB numerical format) t2>=t1
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
%
|
||||||
|
% NM - number of time units from t1 to t2
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
NM=(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM=V2(3)/eomday(V2(1),V2(2))+V2(2)+12-V1(2)-V1(3)/eomday(V1(1),V1(2))...
|
||||||
|
+(V2(1)-V1(1)-1)*12;
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM2=V2(3);
|
||||||
|
if V2(2)>1
|
||||||
|
for k=1:V2(2)-1
|
||||||
|
NM2=NM2+eomday(V2(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day2=365; if eomday(V2(1),2)==29; day2=366; end;
|
||||||
|
NM2=NM2/day2;
|
||||||
|
NM1=V1(3);
|
||||||
|
if V1(2)>1
|
||||||
|
for k=1:V1(2)-1
|
||||||
|
NM1=NM1+eomday(V1(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day1=365; if eomday(V1(1),2)==29; day1=366; end;
|
||||||
|
NM1=(day1-NM1)/day1;
|
||||||
|
NM=NM2+NM1+V2(1)-V1(1)-1;
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [m_corr]=korekta(m,Mmin,eps,beta)
|
||||||
|
|
||||||
|
% RANDOMIZATION OF MAGNITUDE WITHIN THE ACCURACY INTERVAL
|
||||||
|
%
|
||||||
|
% m - input vector of magnitudes
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% eps - accuracy of magnitude
|
||||||
|
% beta - the parameter of the unbounded exponential distribution
|
||||||
|
%
|
||||||
|
% m_corr - vector of randomized magnitudes
|
||||||
|
%
|
||||||
|
F1=1-exp(-beta*(m-Mmin-0.5*eps));
|
||||||
|
F2=1-exp(-beta*(m-Mmin+0.5*eps));
|
||||||
|
u=rand(size(m));
|
||||||
|
w=u.*(F2-F1)+F1;
|
||||||
|
m_corr=Mmin-log(1-w)./beta;
|
||||||
|
end
|
||||||
|
|
||||||
|
function x2 = podwajanie(x,x0)
|
||||||
|
|
||||||
|
% DOUBLES THE SAMPLE
|
||||||
|
|
||||||
|
% If the sample x(i) is is truncated from the left hand side and belongs
|
||||||
|
% to the interval [x0,inf) or it is truncated from the right hand side and
|
||||||
|
% belongs to the interval (-inf,x0]
|
||||||
|
% then the doubled sample is [-x(i)+2x0,x(i)]
|
||||||
|
% x - is the column data vector
|
||||||
|
% x2 - is the column vector of data doubled and sorted in the ascending
|
||||||
|
% order
|
||||||
|
|
||||||
|
x2=[-x+2*x0
|
||||||
|
x];
|
||||||
|
x2=sort(x2);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [h,ierr]=hopt(x)
|
||||||
|
|
||||||
|
%Estimation of the optimal smoothing factor by means of the least squares
|
||||||
|
%method
|
||||||
|
% x - column data vector
|
||||||
|
% The result is an optimal smoothing factor
|
||||||
|
% ierr=0 - convergence, ierr=1 - multiple h, ierr=2 - approximate h is used
|
||||||
|
% The function calls the procedure FZERO for the function 'funct'
|
||||||
|
% NEW VERSION 2 - without a square matrix. Also equipped with extra zeros
|
||||||
|
% search
|
||||||
|
|
||||||
|
% MODIFIED JUNE 2014
|
||||||
|
|
||||||
|
ierr=0;
|
||||||
|
n=length(x);
|
||||||
|
x=sort(x);
|
||||||
|
interval=[0.000001 2*std(x)/n^0.2];
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
fun = @(t) funct(t,x); % for octave
|
||||||
|
x0 =interval; % for octave
|
||||||
|
[hh(1),fval,exitflag] = fzero(fun,x0); % for octave
|
||||||
|
|
||||||
|
% Extra zeros search
|
||||||
|
jj=1;
|
||||||
|
for kk=2:7
|
||||||
|
interval(1)=1.1*hh(jj);
|
||||||
|
interval(2)=interval(1)+(kk-1)*hh(jj);
|
||||||
|
x1=funct(interval(1),x);
|
||||||
|
x2=funct(interval(2),x);
|
||||||
|
if x1*x2<0
|
||||||
|
jj=jj+1;
|
||||||
|
fun = @(t) funct(t,x); % for octave
|
||||||
|
x0 =interval; % for octave
|
||||||
|
[hh(jj),fval,exitflag] = fzero(fun,x0); % for octave
|
||||||
|
end
|
||||||
|
end
|
||||||
|
if jj>1;ierr=1;end
|
||||||
|
h=max(hh);
|
||||||
|
|
||||||
|
if exitflag==1;return;end
|
||||||
|
|
||||||
|
end
|
||||||
|
h=0.891836*(mean(x)-x(1))/(n^0.2);
|
||||||
|
ierr=2;
|
||||||
|
end
|
||||||
|
|
||||||
|
function [fct]=funct(t,x)
|
||||||
|
p2=1.41421356;
|
||||||
|
n=length(x);
|
||||||
|
yy=zeros(size(x));
|
||||||
|
for i=1:n,
|
||||||
|
xij=(x-x(i)).^2/t^2;
|
||||||
|
y=exp(-xij/4).*((xij/2-1)/p2)-2*exp(-xij/2).*(xij-1);
|
||||||
|
yy(i)=sum(y);
|
||||||
|
end;
|
||||||
|
fct=sum(yy)-2*n;
|
||||||
|
clear xij y yy;
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [ambd]=scaling(x,h)
|
||||||
|
|
||||||
|
% EVALUATES A VECTOR OF SCALING FACTORS FOR THE NONPARAMETRIC ADAPTATIVE
|
||||||
|
% ESTIMATION
|
||||||
|
|
||||||
|
% x - the n dimensional column vector of data values sorted in the ascending
|
||||||
|
% order
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% ambd - the resultant n dimensional row vector of local scaling factors
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
gau=zeros(1,n);
|
||||||
|
for i=1:n,
|
||||||
|
gau(i)=sum(exp(-0.5*((x(i)-x)/h).^2))/c/n/h;
|
||||||
|
end
|
||||||
|
g=exp(mean(log(gau)));
|
||||||
|
ambd=sqrt(g./gau);
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [Mmax,ierr]=Mmaxest(x,h,Mmin)
|
||||||
|
|
||||||
|
% ESTIMATION OF UPPER BOUND USING NONPARAMETRIC DISTRIBUTION FUNCTIONS
|
||||||
|
% x - row vector of magnitudes (basic sample).
|
||||||
|
% h - optimal smoothing factor
|
||||||
|
% Mmax - upper bound
|
||||||
|
% ierr=0 if basic procedure converges, ierr=1 when Robsen & Whitlock Mmas
|
||||||
|
% estimation
|
||||||
|
|
||||||
|
% Uses function 'dystryb'
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
ierr=1;
|
||||||
|
x=sort(x);
|
||||||
|
Mmax1=x(n);
|
||||||
|
for i=1:50,
|
||||||
|
d=normcdf((Mmin-x)./h);
|
||||||
|
mian=sum(normcdf((Mmax1-x)./h)-d);
|
||||||
|
Mmax=x(n)+moja_calka(@dystryb,x(1),Mmax1,0.00001,h,mian,x,d);
|
||||||
|
if abs(Mmax-Mmax1)<0.01
|
||||||
|
ierr=0;break;
|
||||||
|
end
|
||||||
|
Mmax1=Mmax;
|
||||||
|
end
|
||||||
|
if (ierr==1 || Mmax>9)
|
||||||
|
Mmax=2*x(n)-x(n-1);
|
||||||
|
ierr=1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=dystryb(z,h,mian,x,d)
|
||||||
|
n=length(x);
|
||||||
|
m=length(z);
|
||||||
|
for i=1:m,
|
||||||
|
t=(z(i)-x)./h;
|
||||||
|
t=normcdf(t);
|
||||||
|
yy=sum(t-d);
|
||||||
|
y(i)=(yy/mian)^n;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [calka,ier]=moja_calka(funfc,a,b,eps,varargin)
|
||||||
|
|
||||||
|
% Integration by means of 16th poit Gauss method. Adopted from CERNLIBRARY
|
||||||
|
|
||||||
|
% funfc - string with the name of function to be integrated
|
||||||
|
% a,b - integration limits
|
||||||
|
% eps - accurracy
|
||||||
|
% varargin - other parameters of function to be integrated
|
||||||
|
% calka - integral
|
||||||
|
% ier=0 - convergence, ier=1 - no conbergence
|
||||||
|
|
||||||
|
persistent W X CONST
|
||||||
|
W=[0.101228536290376 0.222381034453374 0.313706645877887 ...
|
||||||
|
0.362683783378362 0.027152459411754 0.062253523938648 ...
|
||||||
|
0.095158511682493 0.124628971255534 0.149595988816577 ...
|
||||||
|
0.169156519395003 0.182603415044924 0.189450610455069];
|
||||||
|
X=[0.960289856497536 0.796666477413627 0.525532409916329 ...
|
||||||
|
0.183434642495650 0.989400934991650 0.944575023073233 ...
|
||||||
|
0.865631202387832 0.755404408355003 0.617876244402644 ...
|
||||||
|
0.458016777657227 0.281603550779259 0.095012509837637];
|
||||||
|
CONST=1E-12;
|
||||||
|
delta=CONST*abs(a-b);
|
||||||
|
calka=0.;
|
||||||
|
aa=a;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
while abs(y)>delta,
|
||||||
|
bb=aa+y;
|
||||||
|
c1=0.5*(aa+bb);
|
||||||
|
c2=c1-aa;
|
||||||
|
s8=0.;
|
||||||
|
s16=0.;
|
||||||
|
for i=1:4,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s8=s8+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
for i=5:12,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s16=s16+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
s8=s8*c2;
|
||||||
|
s16=s16*c2;
|
||||||
|
if abs(s16-s8)>eps*(1+abs(s16))
|
||||||
|
y=0.5*y;
|
||||||
|
calka=0.;
|
||||||
|
ier=1;
|
||||||
|
else
|
||||||
|
calka=calka+s16;
|
||||||
|
aa=bb;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% --------------------- Mmax BIAS estimation routine ---------------------- K 08NOV2019
|
||||||
|
|
||||||
|
function [BIAS,SD]=Mmax_Bias_GR(t,m,Mc,Mmax1,err,h,xx,ambd,synth)
|
||||||
|
|
||||||
|
s1=sort(unique(m));s2=s1(2:length(s1))-s1(1:length(s1)-1);EPS=min(s2);
|
||||||
|
|
||||||
|
if err~=0
|
||||||
|
warning('process did not converge!!')
|
||||||
|
end
|
||||||
|
|
||||||
|
MAXm=max(m);N=numel(m(m>=Mc));DeltaM=MAXm-Mc; %beta=b*log(10);
|
||||||
|
[mag,PDF_NPT,CDF_NPT]=dist_NPT(Mc-EPS,Mmax1+EPS,0.01,Mc,EPS,h,xx,ambd,Mmax1);
|
||||||
|
|
||||||
|
for j=1:synth %set number of synthetic datasets, default is 10000
|
||||||
|
% % CDF:
|
||||||
|
|
||||||
|
% j
|
||||||
|
|
||||||
|
% linear interpolation to assign magnitude values from a uniform distribution sample
|
||||||
|
iM=rand(1,N);M1=interp1q(CDF_NPT,mag,iM');
|
||||||
|
br(j)=1/(log(10)*(mean(M1)-min(M1)+EPS/2));DM=range(M1);
|
||||||
|
Mmax=max(M1);
|
||||||
|
|
||||||
|
% Iteration Process to estimate b and Mmax
|
||||||
|
b1=10;best=[1.0 10.0];i=1;
|
||||||
|
while min(abs(diff(best)))>0.00001
|
||||||
|
w=exp(b1*(Mmax-Mc));E1=expint(N/(w-1));E2=expint(N*w/(w-1));
|
||||||
|
%E=expint(w);
|
||||||
|
Mme=Mmax+(E1-E2)/(b1*exp(-N/(w-1)))+(Mc)*exp(-N); %Mme=round(Mme/EPS)*EPS;
|
||||||
|
|
||||||
|
if isnan(Mme)
|
||||||
|
KM=sort(unique(M1),'descend');
|
||||||
|
Mme=2*KM(1)-KM(2);
|
||||||
|
end
|
||||||
|
|
||||||
|
fun=@(bb) 1/bb+(Mme-Mc)/(1-exp(bb*(Mme-Mc)))-mean(M1)+Mc-EPS/2; %consider th5 last 0.05 term
|
||||||
|
b1=fzero(fun,1);best(i)=b1;i=i+1;
|
||||||
|
|
||||||
|
if i==50
|
||||||
|
warning('process did not converge!!');break
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
be(j)=b1/log(10);
|
||||||
|
Me(j)=Mme;dm(j)=DM;Mm(j)=Mmax;
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
BIAS=mean(MAXm-Me);
|
||||||
|
SD=std(MAXm-Me);
|
||||||
|
|
||||||
|
%b-mean(be) %check b-value difference
|
||||||
|
%histogram(be)
|
||||||
|
|
||||||
|
% MAXm: maximum magnitude in the real catalog
|
||||||
|
% Mmax: maximum magnitudes observed in the synthetic catalogs (rounded)
|
||||||
|
% Me: maximum magnitude estimates for the synthetic catalogs
|
||||||
|
% Mmax1: maximum magnitude estimated by GRT
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
83
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodGRT.m
Executable file
83
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodGRT.m
Executable file
@ -0,0 +1,83 @@
|
|||||||
|
% [m,T]=Ret_periodGRT(Md,Mu,dM,Mmin,lamb,eps,b,Mmax)
|
||||||
|
%
|
||||||
|
% EVALUATES THE MEAN RETURN PERIOD VALUES USING THE UPPER-BOUNDED G-R LED
|
||||||
|
% MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution, consequently the G-R
|
||||||
|
% b-value and the end-point of the distriobution Mmax as well as the
|
||||||
|
% activity rate of M>=Mmin events are calculated at start-up of the
|
||||||
|
% stationary hazard assessment services in the upper-bounded
|
||||||
|
% Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The mean return period of magnitude M is the average elapsed time between
|
||||||
|
% the consecutive earthquakes of magnitude M.
|
||||||
|
% The mean return periods are calculated for magnitude starting from Md up
|
||||||
|
% to Mu with step dM.
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of earthquake magnitudes
|
||||||
|
% Md - starting magnitude for return period calculations
|
||||||
|
% Mu - ending magnitude for return period calculations
|
||||||
|
% dM - magnitude step for return period calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
|
||||||
|
% OUTPUT:
|
||||||
|
% m - vector of independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% T - vector od mean return periods of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
function [m,T]=Ret_periodGRT(Md,Mu,dM,Mmin,lamb,eps,b,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
if Md<Mmin; Md=Mmin;end
|
||||||
|
if Mu>Mmax; Mu=Mmax;end
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
beta=b*log(10);
|
||||||
|
T=1/lamb./(1-Cdfgr(m,beta,Mmin-eps/2,Mmax));
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [y]=Cdfgr(t,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
%CDF of the truncated upper-bounded exponential distribution (truncated G-R
|
||||||
|
% model
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% t - vector of magnitudes (independent variable)
|
||||||
|
% y - CDF vector
|
||||||
|
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin)));
|
||||||
|
y=(1-exp(-beta*(t-Mmin)))/mian;
|
||||||
|
idx=find(y>1);
|
||||||
|
y(idx)=ones(size(idx));
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
59
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodGRU.m
Executable file
59
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodGRU.m
Executable file
@ -0,0 +1,59 @@
|
|||||||
|
% [m,T]=Ret_periodGRU(Md,Mu,dM,Mmin,lamb,eps,b)
|
||||||
|
%
|
||||||
|
% EVALUATES THE MEAN RETURN PERIOD VALUES USING THE UNLIMITED G-R LED
|
||||||
|
% MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the unlimited Gutenberg-Richter relation
|
||||||
|
% leads to the exponential distribution model of magnitude distribution
|
||||||
|
% from and above the catalog completness level Mmin. The shape parameter of
|
||||||
|
% this distribution and consequently the G-R b-value are calculated at
|
||||||
|
% start-up of the stationary hazard assessment services in the
|
||||||
|
% unlimited Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The mean return period of magnitude M is the average elapsed time between
|
||||||
|
% the consecutive earthquakes of magnitude M.
|
||||||
|
% The mean return periods are calculated for magnitude starting from Md up
|
||||||
|
% to Mu with step dM.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for return period calculations
|
||||||
|
% Mu - ending magnitude for return period calculations
|
||||||
|
% dM - magnitude step for return period calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% m - vector of independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% T - vector od mean return periods of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [m,T]=Ret_periodGRU(Md,Mu,dM,Mmin,lamb,eps,b)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
if Md<Mmin; Md=Mmin;end
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
beta=b*log(10);
|
||||||
|
T=1/lamb./exp(-beta*(m-Mmin+eps/2));
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
94
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodNPT.m
Executable file
94
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodNPT.m
Executable file
@ -0,0 +1,94 @@
|
|||||||
|
% [m,T]=Ret_periodNPT(Md,Mu,dM,Mmin,lamb,eps,h,xx,ambd,Mmax)
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES THE MEAN
|
||||||
|
% RETURN PERIOD VALUES FOR THE UPPER-BOUNDED NONPARAMETRIC
|
||||||
|
% DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution has a hard end point Mmax from the right hand
|
||||||
|
% side.The estimation makes use of the previously estimated parameters
|
||||||
|
% namely the mean activity rate lamb, the length of magnitude round-off
|
||||||
|
% interval, eps, the smoothing factor, h, the background sample, xx, the
|
||||||
|
% scaling factors for the background sample, ambd, and the end-point of
|
||||||
|
% magnitude distribution Mmax. The background sample,xx, comprises the
|
||||||
|
% randomized values of observed magnitude doubled symmetrically with
|
||||||
|
% respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% The mean return periods are calculated for magnitude starting from Md up
|
||||||
|
% to Mu with step dM.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
% Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
% Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
% Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% Md - starting magnitude for return period calculations
|
||||||
|
% Mu - ending magnitude for return period calculations
|
||||||
|
% dM - magnitude step for return period calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% m - vector of independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% T - vector od mean return periods of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [m,T]=Ret_periodNPT(Md,Mu,dM,Mmin,lamb,eps,h,xx,ambd,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
if Md<Mmin; Md=Mmin;end
|
||||||
|
if Mu>Mmax; Mu=Mmax;end
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
n=length(m);
|
||||||
|
mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
for i=1:n
|
||||||
|
CDF_NPT=2*(Dystr_npr(m(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h))/mian;
|
||||||
|
T(i)=1/lamb./(1-CDF_NPT);
|
||||||
|
end
|
||||||
|
T=T';
|
||||||
|
end
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
91
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodNPU.m
Executable file
91
SHAPE_Package/SHAPE_ver2b.0/SSH/Ret_periodNPU.m
Executable file
@ -0,0 +1,91 @@
|
|||||||
|
% [m,T]=Ret_periodNPU(Md,Mu,dM,Mmin,lamb,eps,h,xx,ambd)
|
||||||
|
%
|
||||||
|
%USING THE NONPARAMETRIC ADAPTATIVE KERNEL APPROACH EVALUATES
|
||||||
|
% THE MEAN RETURN PERIOD VALUES FOR THE UNBOUNDED
|
||||||
|
% NONPARAMETRIC DISTRIBUTION FOR MAGNITUDE.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution is unlimited from the right hand side.
|
||||||
|
% The estimation makes use of the previously estimated parameters of kernel
|
||||||
|
% estimation, namely the smoothing factor, the background sample and the
|
||||||
|
% scaling factors for the background sample. The background sample
|
||||||
|
% - xx comprises the randomized values of observed magnitude doubled
|
||||||
|
% symmetrically with respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% The mean return period of magnitude M is the average
|
||||||
|
% elapsed time between the consecutive earthquakes of magnitude M.
|
||||||
|
% The mean return periods are calculated for magnitude starting from Md up
|
||||||
|
% to Mu with step dM.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation fro Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% Md - starting magnitude for return period calculations
|
||||||
|
% Mu - ending magnitude for return period calculations
|
||||||
|
% dM - magnitude step for return period calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% lamb - mean activity rate for events M>=Mmin
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% m - vector of independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% T - vector od mean return periods of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [m,T]=Ret_periodNPU(Md,Mu,dM,Mmin,lamb,eps,h,xx,ambd)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
if Md<Mmin; Md=Mmin;end
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
n=length(m);
|
||||||
|
|
||||||
|
for i=1:n
|
||||||
|
CDF_NPU=2*(Dystr_npr(m(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
T(i)=1/lamb./(1-CDF_NPU);
|
||||||
|
end
|
||||||
|
T=T';
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
250
SHAPE_Package/SHAPE_ver2b.0/SSH/TruncGR.m
Executable file
250
SHAPE_Package/SHAPE_ver2b.0/SSH/TruncGR.m
Executable file
@ -0,0 +1,250 @@
|
|||||||
|
%
|
||||||
|
% [lamb_all,lamb,lmab_err,unit,eps,b,Mmax,err]=TruncGR(t,M,iop,Mmin)
|
||||||
|
%
|
||||||
|
% ESTIMATES THE MEAN ACTIVITY RATE WITHIN THE WHOLE SAMPLE AND WITHIN THE
|
||||||
|
% COMPLETE PART OF THE SAMPLE, THE ROUND-OFF ERROR OF MAGNITUDE,
|
||||||
|
% THE GUTENBERG-RICHTER B-VALUE AND THE UPPER BOUND OF MAGNITUDE
|
||||||
|
% DISTRIBUTION USING THE UPPER-BOUNDED G-R LED MAGNITUDE DISTRIBUTION MODEL
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UPPER-BOUNDED
|
||||||
|
% GUTENBERG-RICHETR HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution and consequently the G-R
|
||||||
|
% b-value is estimated by maximum likelihood method (Aki-Utsu procedure).
|
||||||
|
% The upper limit of the distribution Mmax is evaluated using
|
||||||
|
% the Kijko-Sellevol generic formula. If convergence is not reached the
|
||||||
|
% Whitlock @ Robson simplified formula is used:
|
||||||
|
% Mmaxest= 2(max obs M) - (second max obs M)).
|
||||||
|
% The mean activity rate, lamb, is the number of events >=Mmin into the
|
||||||
|
% length of the period in which they occurred. Upon the value of the input
|
||||||
|
% parameter, iop, the used unit of time can be either day ot month or year.
|
||||||
|
% The round-off interval length - eps is the least non-zero difference
|
||||||
|
% between sample data or 0.1 if the least difference is greater than 0.1.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Kijko, A., and M.A. Sellevoll (1989) Bull. Seismol. Soc. Am. 79, 3,645-654
|
||||||
|
%Lasocki, S., Urban, P. (2011) Acta Geophys 59, 659-673,
|
||||||
|
% doi: 10.2478/s11600-010-0049-y
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of magnitudes from a user selected catalog
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - catalog completeness level. Must be determined externally.
|
||||||
|
% Can take any value from [min(M), max(M)].
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
%
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 15 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
% err - error parameter on Mmax estimation, err=0 - convergence, err=1 -
|
||||||
|
% no converegence of Kijko-Sellevol estimator, Robinson @ Whitlock
|
||||||
|
% method used.
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [lamb_all,lamb,lamb_err,unit,eps,b,Mmax,err]=TruncGR(t,M,iop,Mmin)
|
||||||
|
n=length(M);
|
||||||
|
lamb_err=0;
|
||||||
|
t1=t(1);
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
lamb_all=n/round(t(n)-t(1));
|
||||||
|
lamb=nn/round(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
lamb_all=30*n/(t(n)-t(1)); % K20OCT2014
|
||||||
|
lamb=30*nn/(t2-t1); % K20OCT2014
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
lamb_all=365*n/(t(n)-t(1)); % K20OCT2014
|
||||||
|
lamb=365*nn/(t2-t1); % K20OCT2014
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
|
||||||
|
if nn<15
|
||||||
|
eps=0;b=0;Mmax=0;err=0;
|
||||||
|
lamb_err=1;
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
xx=M(M>=Mmin); %K21OCT2014
|
||||||
|
% x=sort(M,'descend');
|
||||||
|
% for i=1:n
|
||||||
|
% if x(i)<Mmin; break; end
|
||||||
|
% xx(i)=x(i); %
|
||||||
|
% end
|
||||||
|
|
||||||
|
clear x;
|
||||||
|
nn=length(xx);
|
||||||
|
|
||||||
|
Max_obs=max(xx);
|
||||||
|
beta0=0;
|
||||||
|
Mmax1=Max_obs;
|
||||||
|
for i=1:50,
|
||||||
|
beta=fzero(@bet_est,[0.05,4.0],[],mean(xx),Mmin-eps/2,Mmax1);
|
||||||
|
Mmax=Max_obs+moja_calka('f_podc',Mmin,Max_obs,1e-5,nn,beta,Mmin-eps/2,Mmax1);
|
||||||
|
if ((abs(Mmax-Mmax1)<0.01)&&(abs(beta-beta0)<0.0001))
|
||||||
|
err=0;
|
||||||
|
break;
|
||||||
|
end
|
||||||
|
Mmax1=Mmax;
|
||||||
|
beta0=beta;
|
||||||
|
end
|
||||||
|
if i==50;
|
||||||
|
err=1.0;
|
||||||
|
Mmax=2*xx(1)-xx(2);
|
||||||
|
beta=fzero(@bet_est,1.0,[],mean(xx),Mmin-eps/2,Mmax);
|
||||||
|
end
|
||||||
|
b=beta/log(10);
|
||||||
|
clear xx
|
||||||
|
end
|
||||||
|
|
||||||
|
function [zero]=bet_est(b,ms,Mmin,Mmax)
|
||||||
|
|
||||||
|
%First derivative of the log likelihood function of the upper-bounded
|
||||||
|
% exponential distribution (truncated GR model)
|
||||||
|
% b - parameter of the distribution 'beta'
|
||||||
|
% ms - mean of the observed magnitudes
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
|
||||||
|
M_max_min=Mmax-Mmin;
|
||||||
|
e_m=exp(-b*M_max_min);
|
||||||
|
zero=1/b-ms+Mmin-M_max_min*e_m/(1-e_m);
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [calka,ier]=moja_calka(funfc,a,b,eps,varargin)
|
||||||
|
|
||||||
|
% Integration by means of 16th poit Gauss method. Adopted from CERNLIBRARY
|
||||||
|
|
||||||
|
% funfc - string with the name of function to be integrated
|
||||||
|
% a,b - integration limits
|
||||||
|
% eps - accurracy
|
||||||
|
% varargin - other parameters of function to be integrated
|
||||||
|
% calka - integral
|
||||||
|
% ier=0 - convergence, ier=1 - no conbergence
|
||||||
|
|
||||||
|
persistent W X CONST
|
||||||
|
W=[0.101228536290376 0.222381034453374 0.313706645877887 ...
|
||||||
|
0.362683783378362 0.027152459411754 0.062253523938648 ...
|
||||||
|
0.095158511682493 0.124628971255534 0.149595988816577 ...
|
||||||
|
0.169156519395003 0.182603415044924 0.189450610455069];
|
||||||
|
X=[0.960289856497536 0.796666477413627 0.525532409916329 ...
|
||||||
|
0.183434642495650 0.989400934991650 0.944575023073233 ...
|
||||||
|
0.865631202387832 0.755404408355003 0.617876244402644 ...
|
||||||
|
0.458016777657227 0.281603550779259 0.095012509837637];
|
||||||
|
CONST=1E-12;
|
||||||
|
delta=CONST*abs(a-b);
|
||||||
|
calka=0.;
|
||||||
|
aa=a;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
while abs(y)>delta,
|
||||||
|
bb=aa+y;
|
||||||
|
c1=0.5*(aa+bb);
|
||||||
|
c2=c1-aa;
|
||||||
|
s8=0.;
|
||||||
|
s16=0.;
|
||||||
|
for i=1:4,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s8=s8+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
for i=5:12,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s16=s16+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
s8=s8*c2;
|
||||||
|
s16=s16*c2;
|
||||||
|
if abs(s16-s8)>eps*(1+abs(s16))
|
||||||
|
y=0.5*y;
|
||||||
|
calka=0.;
|
||||||
|
ier=1;
|
||||||
|
else
|
||||||
|
calka=calka+s16;
|
||||||
|
aa=bb;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=f_podc(z,n,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
% Integrated function for Mmax estimation. Truncated GR model
|
||||||
|
% z - column vector of independent variable
|
||||||
|
% n - the size of 'z'
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% Mmin - the catalog completeness level
|
||||||
|
% Mmax - the upper limit of the distribution
|
||||||
|
|
||||||
|
y=Cdfgr(z,beta,Mmin,Mmax).^n;
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=Cdfgr(t,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
%CDF of the truncated upper-bounded exponential distribution (truncated G-R
|
||||||
|
% model
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% t - vector of magnitudes (independent variable)
|
||||||
|
% y - CDF vector
|
||||||
|
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin)));
|
||||||
|
y=(1-exp(-beta*(t-Mmin)))/mian;
|
||||||
|
idx=find(y>1);
|
||||||
|
y(idx)=ones(size(idx));
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
387
SHAPE_Package/SHAPE_ver2b.0/SSH/TruncGR_O.m
Executable file
387
SHAPE_Package/SHAPE_ver2b.0/SSH/TruncGR_O.m
Executable file
@ -0,0 +1,387 @@
|
|||||||
|
%
|
||||||
|
%[lamb_all,lamb,lamb_err,unit,eps,b,Mmax,err,BIAS,SD]=TruncGR_Ob(t,M,iop,Mmin,Mmax,Nsynth)
|
||||||
|
%
|
||||||
|
% ESTIMATES THE MEAN ACTIVITY RATE WITHIN THE WHOLE SAMPLE AND WITHIN THE
|
||||||
|
% COMPLETE PART OF THE SAMPLE, THE ROUND-OFF ERROR OF MAGNITUDE,
|
||||||
|
% THE GUTENBERG-RICHTER B-VALUE AND THE UPPER BOUND OF MAGNITUDE
|
||||||
|
% DISTRIBUTION USING THE UPPER-BOUNDED G-R LED MAGNITUDE DISTRIBUTION MODEL
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UPPER-BOUNDED
|
||||||
|
% GUTENBERG-RICHETR HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki ver 2 01/2015 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution and consequently the G-R
|
||||||
|
% b-value is estimated by maximum likelihood method (Aki-Utsu procedure).
|
||||||
|
% The upper limit of the distribution Mmax is evaluated using
|
||||||
|
% the Kijko-Sellevol generic formula. If convergence is not reached the
|
||||||
|
% Whitlock @ Robson simplified formula is used:
|
||||||
|
% Mmaxest= 2(max obs M) - (second max obs M)).
|
||||||
|
% The mean activity rate, lamb, is the number of events >=Mmin into the
|
||||||
|
% length of the period in which they occurred. Upon the value of the input
|
||||||
|
% parameter, iop, the used unit of time can be either day ot month or year.
|
||||||
|
% The round-off interval length - eps is the least non-zero difference
|
||||||
|
% between sample data or 0.1 if the least difference is greater than 0.1.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Kijko, A., and M.A. Sellevoll (1989) Bull. Seismol. Soc. Am. 79, 3,645-654
|
||||||
|
%Lasocki, S., Urban, P. (2011) Acta Geophys 59, 659-673,
|
||||||
|
% doi: 10.2478/s11600-010-0049-y
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of magnitudes from a user selected catalog
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - catalog completeness level. Must be determined externally.
|
||||||
|
% Can take any value from [min(M), max(M)].
|
||||||
|
% Mmax - upper limit of Magnitude Distribution. Can be set by user, or
|
||||||
|
% estimate within the program - it then should be set as Mmax=[].
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
%
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 15 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
% err - error parameter on Mmax estimation, err=0 - convergence, err=1 -
|
||||||
|
% no converegence of Kijko-Sellevol estimator, Robinson @ Whitlock
|
||||||
|
% method used.
|
||||||
|
% BIAS - Mmax estimation Bias (Lasocki and Urban, 2011)
|
||||||
|
% SD - Mmax standard deviation (Lasocki ands Urban, 2011)
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [lamb_all,lamb,lamb_err,unit,eps,b,Mmax,err,BIAS,SD]=TruncGR_O(t,M,iop,Mmin,Mmax,Nsynth)
|
||||||
|
if nargin==5;Nsynth=[];end % K08DEC2019
|
||||||
|
if isempty(t) || numel(t)<3 || isempty(M(M>=Mmin)) %K03OCT
|
||||||
|
t=[1 2];M=[1 2]; end %K30SEP
|
||||||
|
|
||||||
|
n=length(M);
|
||||||
|
lamb_err=0;
|
||||||
|
t1=t(1);
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
[NM,unit]=time_diff(t(1),t(n),iop);
|
||||||
|
lamb_all=n/NM;
|
||||||
|
[NM,unit]=time_diff(t1,t2,iop);
|
||||||
|
lamb=nn/NM;
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
|
||||||
|
if nn<15
|
||||||
|
eps=0;b=0;Mmax=0;err=0;
|
||||||
|
lamb_err=1;
|
||||||
|
BIAS=NaN;SD=NaN; %%% K 08NOV2019
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
xx=M(M>=Mmin); %K21OCT2014
|
||||||
|
% x=sort(M,'descend');
|
||||||
|
% for i=1:n
|
||||||
|
% if x(i)<Mmin; break; end
|
||||||
|
% xx(i)=x(i); %
|
||||||
|
% end
|
||||||
|
|
||||||
|
clear x;
|
||||||
|
nn=length(xx);
|
||||||
|
|
||||||
|
Max_obs=max(xx);
|
||||||
|
beta0=0;
|
||||||
|
Mmax1=Max_obs;
|
||||||
|
if isempty(Mmax)==0 %%% K 28JUL2015
|
||||||
|
err_Mmax=0; %%% K 04DEC2019
|
||||||
|
fun = @(b) bet_est(b,mean(xx),Mmin-eps/2,Mmax); %%% K 28JUL2015
|
||||||
|
x0 = 1; %[0.05,4.0]; %%% K 28JUL2015 - See exception line 155
|
||||||
|
beta = fzero(fun,x0); %%% K 28JUL2015
|
||||||
|
err=0; %%% K 28JUL2015
|
||||||
|
else %%% K 28JUL2015 - line 150
|
||||||
|
err_Mmax=1; %%% K 04DEC2019
|
||||||
|
for i=1:50,
|
||||||
|
fun = @(b) bet_est(b,mean(xx),Mmin-eps/2,Mmax1);
|
||||||
|
x0 =1; %[0.05,4.0]; %%% K29JUL2015 - See exception line 155
|
||||||
|
beta = fzero(fun,x0);
|
||||||
|
Mmax=Max_obs+moja_calka('f_podc',Mmin,Max_obs,1e-5,nn,beta,Mmin-eps/2,Mmax1);
|
||||||
|
if ((abs(Mmax-Mmax1)<0.01)&&(abs(beta-beta0)<0.0001))
|
||||||
|
err=0;
|
||||||
|
break;
|
||||||
|
end
|
||||||
|
Mmax1=Mmax;
|
||||||
|
beta0=beta;
|
||||||
|
end
|
||||||
|
if i==50;
|
||||||
|
err=1.0;
|
||||||
|
Mmax=2*xx(1)-xx(2);
|
||||||
|
fun = @(b) bet_est(b,mean(xx),Mmin-eps/2,Mmax);
|
||||||
|
x0 =1;
|
||||||
|
beta = fzero(fun,x0);
|
||||||
|
end
|
||||||
|
end %%% K 28JUL2015
|
||||||
|
b=beta/log(10);
|
||||||
|
clear xx
|
||||||
|
|
||||||
|
% Exception for v-value
|
||||||
|
if b<0.05 || b>6.0; error('Unacceptable b-value, abort and select different dataset');end
|
||||||
|
beta;
|
||||||
|
|
||||||
|
|
||||||
|
% Estimation of Mmax Bias %%% K 04DEC2019
|
||||||
|
% (Lasocki and Urban, 2011, doi:10.2478/s11600-010-0049-y)
|
||||||
|
if isempty(Nsynth)==0 && err_Mmax==1 % set number of synthetic datasets, e.g. 10000
|
||||||
|
[BIAS,SD]=Mmax_Bias_GR(t,M,Mmin,Mmax,b,err,Nsynth);
|
||||||
|
elseif isempty(Nsynth)==0 && err_Mmax==0;
|
||||||
|
warning('Mmax must be empty for BIAS calculation');BIAS=[];SD=[];
|
||||||
|
else; BIAS=0;SD=0;
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
function [NM,unit]=time_diff(t1,t2,iop) % SL 03MAR2015
|
||||||
|
|
||||||
|
% TIME DIFFERENCE BETWEEEN t1,t2 EXPRESSED IN DAY, MONTH OR YEAR UNIT
|
||||||
|
%
|
||||||
|
% t1 - start time (in MATLAB numerical format)
|
||||||
|
% t2 - end time (in MATLAB numerical format) t2>=t1
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
%
|
||||||
|
% NM - number of time units from t1 to t2
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
NM=(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM=V2(3)/eomday(V2(1),V2(2))+V2(2)+12-V1(2)-V1(3)/eomday(V1(1),V1(2))...
|
||||||
|
+(V2(1)-V1(1)-1)*12;
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM2=V2(3);
|
||||||
|
if V2(2)>1
|
||||||
|
for k=1:V2(2)-1
|
||||||
|
NM2=NM2+eomday(V2(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day2=365; if eomday(V2(1),2)==29; day2=366; end;
|
||||||
|
NM2=NM2/day2;
|
||||||
|
NM1=V1(3);
|
||||||
|
if V1(2)>1
|
||||||
|
for k=1:V1(2)-1
|
||||||
|
NM1=NM1+eomday(V1(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day1=365; if eomday(V1(1),2)==29; day1=366; end;
|
||||||
|
NM1=(day1-NM1)/day1;
|
||||||
|
NM=NM2+NM1+V2(1)-V1(1)-1;
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [zero]=bet_est(b,ms,Mmin,Mmax)
|
||||||
|
|
||||||
|
%First derivative of the log likelihood function of the upper-bounded
|
||||||
|
% exponential distribution (truncated GR model)
|
||||||
|
% b - parameter of the distribution 'beta'
|
||||||
|
% ms - mean of the observed magnitudes
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
|
||||||
|
M_max_min=Mmax-Mmin;
|
||||||
|
e_m=exp(-b*M_max_min);
|
||||||
|
zero=1/b-ms+Mmin-M_max_min*e_m/(1-e_m);
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [calka,ier]=moja_calka(funfc,a,b,eps,varargin)
|
||||||
|
|
||||||
|
% Integration by means of 16th poit Gauss method. Adopted from CERNLIBRARY
|
||||||
|
|
||||||
|
% funfc - string with the name of function to be integrated
|
||||||
|
% a,b - integration limits
|
||||||
|
% eps - accurracy
|
||||||
|
% varargin - other parameters of function to be integrated
|
||||||
|
% calka - integral
|
||||||
|
% ier=0 - convergence, ier=1 - no conbergence
|
||||||
|
|
||||||
|
persistent W X CONST
|
||||||
|
W=[0.101228536290376 0.222381034453374 0.313706645877887 ...
|
||||||
|
0.362683783378362 0.027152459411754 0.062253523938648 ...
|
||||||
|
0.095158511682493 0.124628971255534 0.149595988816577 ...
|
||||||
|
0.169156519395003 0.182603415044924 0.189450610455069];
|
||||||
|
X=[0.960289856497536 0.796666477413627 0.525532409916329 ...
|
||||||
|
0.183434642495650 0.989400934991650 0.944575023073233 ...
|
||||||
|
0.865631202387832 0.755404408355003 0.617876244402644 ...
|
||||||
|
0.458016777657227 0.281603550779259 0.095012509837637];
|
||||||
|
CONST=1E-12;
|
||||||
|
delta=CONST*abs(a-b);
|
||||||
|
calka=0.;
|
||||||
|
aa=a;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
while abs(y)>delta,
|
||||||
|
bb=aa+y;
|
||||||
|
c1=0.5*(aa+bb);
|
||||||
|
c2=c1-aa;
|
||||||
|
s8=0.;
|
||||||
|
s16=0.;
|
||||||
|
for i=1:4,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s8=s8+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
for i=5:12,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s16=s16+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
s8=s8*c2;
|
||||||
|
s16=s16*c2;
|
||||||
|
if abs(s16-s8)>eps*(1+abs(s16))
|
||||||
|
y=0.5*y;
|
||||||
|
calka=0.;
|
||||||
|
ier=1;
|
||||||
|
else
|
||||||
|
calka=calka+s16;
|
||||||
|
aa=bb;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=f_podc(z,n,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
% Integrated function for Mmax estimation. Truncated GR model
|
||||||
|
% z - column vector of independent variable
|
||||||
|
% n - the size of 'z'
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% Mmin - the catalog completeness level
|
||||||
|
% Mmax - the upper limit of the distribution
|
||||||
|
|
||||||
|
y=Cdfgr(z,beta,Mmin,Mmax).^n;
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=Cdfgr(t,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
%CDF of the truncated upper-bounded exponential distribution (truncated G-R
|
||||||
|
% model
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% t - vector of magnitudes (independent variable)
|
||||||
|
% y - CDF vector
|
||||||
|
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin)));
|
||||||
|
y=(1-exp(-beta*(t-Mmin)))/mian;
|
||||||
|
idx=find(y>1);
|
||||||
|
y(idx)=ones(size(idx));
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
|
|
||||||
|
% --------------------- Mmax BIAS estimation routine ---------------------- K 08NOV2019
|
||||||
|
|
||||||
|
function [BIAS,SD]=Mmax_Bias_GR(t,m,Mc,Mmax1,b,err,synth)
|
||||||
|
|
||||||
|
if err~=0
|
||||||
|
warning('process did not converge!!'),pause
|
||||||
|
end
|
||||||
|
|
||||||
|
MAXm=max(m);beta=b*log(10);N=numel(m(m>=Mc));DeltaM=MAXm-Mc;
|
||||||
|
|
||||||
|
for j=1:synth %set number of synthetic datasets, default is 10000
|
||||||
|
% % CDF:
|
||||||
|
M=Mc:0.0001:MAXm;upt=1-exp(-beta*(M-Mc));
|
||||||
|
dwt=1-exp(-beta*(MAXm-Mc));F=upt./dwt; % j
|
||||||
|
% linear interpolation to assign magnitude values from a uniform distribution sample
|
||||||
|
iM=rand(1,N);M1=interp1q(F',M',iM');
|
||||||
|
br(j)=1/(log(10)*(mean(M1)-min(M1)));DM=range(M1);
|
||||||
|
Mmax=max(M1);
|
||||||
|
|
||||||
|
% Iteration Process to estimate b and Mmax
|
||||||
|
b1=1;best=[1.0 10.0];i=1;
|
||||||
|
while min(abs(diff(best)))>0.00001
|
||||||
|
w=exp(b1*(Mmax-Mc));E1=expint(N/(w-1));E2=expint(N*w/(w-1));
|
||||||
|
%E=expint(w);
|
||||||
|
Mme=Mmax+(E1-E2)/(b1*exp(-N/(w-1)))+(Mc)*exp(-N); %Mme=round(Mme/EPS)*EPS;
|
||||||
|
|
||||||
|
if isnan(Mme)
|
||||||
|
KM=sort(unique(M1),'descend');
|
||||||
|
Mme=2*KM(1)-KM(2);
|
||||||
|
end
|
||||||
|
|
||||||
|
fun=@(bb) 1/bb+(Mme-Mc)/(1-exp(bb*(Mme-Mc)))-mean(M1)+Mc; %consider th5 last 0.05 term
|
||||||
|
b1=fzero(fun,1);best(i)=b1;i=i+1;
|
||||||
|
|
||||||
|
if i==50
|
||||||
|
warning('process did not converge!!');break
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
be(j)=b1/log(10);
|
||||||
|
Me(j)=Mme;dm(j)=DM;Mm(j)=Mmax;
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
BIAS=mean(MAXm-Me)
|
||||||
|
SD=std(MAXm-Me);
|
||||||
|
|
||||||
|
%b-mean(be) %check b-value difference
|
||||||
|
%histogram(be)
|
||||||
|
|
||||||
|
% MAXm: maximum magnitude in the real catalog
|
||||||
|
% Mmax: maximum magnitudes observed in the synthetic catalogs (rounded)
|
||||||
|
% Me: maximum magnitude estimates for the synthetic catalogs
|
||||||
|
% Mmax1: maximum magnitude estimated by GRT
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
387
SHAPE_Package/SHAPE_ver2b.0/SSH/TruncGR_O_CI.m
Executable file
387
SHAPE_Package/SHAPE_ver2b.0/SSH/TruncGR_O_CI.m
Executable file
@ -0,0 +1,387 @@
|
|||||||
|
%
|
||||||
|
%[lamb_all,lamb,lamb_err,unit,eps,b,Mmax,err,BIAS,SD]=TruncGR_Ob(t,M,iop,Mmin,Mmax,Nsynth)
|
||||||
|
%
|
||||||
|
% ESTIMATES THE MEAN ACTIVITY RATE WITHIN THE WHOLE SAMPLE AND WITHIN THE
|
||||||
|
% COMPLETE PART OF THE SAMPLE, THE ROUND-OFF ERROR OF MAGNITUDE,
|
||||||
|
% THE GUTENBERG-RICHTER B-VALUE AND THE UPPER BOUND OF MAGNITUDE
|
||||||
|
% DISTRIBUTION USING THE UPPER-BOUNDED G-R LED MAGNITUDE DISTRIBUTION MODEL
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UPPER-BOUNDED
|
||||||
|
% GUTENBERG-RICHETR HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki ver 2 01/2015 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution and consequently the G-R
|
||||||
|
% b-value is estimated by maximum likelihood method (Aki-Utsu procedure).
|
||||||
|
% The upper limit of the distribution Mmax is evaluated using
|
||||||
|
% the Kijko-Sellevol generic formula. If convergence is not reached the
|
||||||
|
% Whitlock @ Robson simplified formula is used:
|
||||||
|
% Mmaxest= 2(max obs M) - (second max obs M)).
|
||||||
|
% The mean activity rate, lamb, is the number of events >=Mmin into the
|
||||||
|
% length of the period in which they occurred. Upon the value of the input
|
||||||
|
% parameter, iop, the used unit of time can be either day ot month or year.
|
||||||
|
% The round-off interval length - eps is the least non-zero difference
|
||||||
|
% between sample data or 0.1 if the least difference is greater than 0.1.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Kijko, A., and M.A. Sellevoll (1989) Bull. Seismol. Soc. Am. 79, 3,645-654
|
||||||
|
%Lasocki, S., Urban, P. (2011) Acta Geophys 59, 659-673,
|
||||||
|
% doi: 10.2478/s11600-010-0049-y
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of magnitudes from a user selected catalog
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - catalog completeness level. Must be determined externally.
|
||||||
|
% Can take any value from [min(M), max(M)].
|
||||||
|
% Mmax - upper limit of Magnitude Distribution. Can be set by user, or
|
||||||
|
% estimate within the program - it then should be set as Mmax=[].
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
%
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 15 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
% err - error parameter on Mmax estimation, err=0 - convergence, err=1 -
|
||||||
|
% no converegence of Kijko-Sellevol estimator, Robinson @ Whitlock
|
||||||
|
% method used.
|
||||||
|
% BIAS - Mmax estimation Bias (Lasocki and Urban, 2011)
|
||||||
|
% SD - Mmax standard deviation (Lasocki ands Urban, 2011)
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [b,lamb_all,lamb,lamb_err,unit,eps,Mmax,err,BIAS,SD]=TruncGR_O_CI(t,M,iop,Mmin,Mmax,Nsynth)
|
||||||
|
if nargin==5;Nsynth=[];end % K08DEC2019
|
||||||
|
if isempty(t) || numel(t)<3 || isempty(M(M>=Mmin)) %K03OCT
|
||||||
|
t=[1 2];M=[1 2]; end %K30SEP
|
||||||
|
|
||||||
|
n=length(M);
|
||||||
|
lamb_err=0;
|
||||||
|
t1=t(1);
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
[NM,unit]=time_diff(t(1),t(n),iop);
|
||||||
|
lamb_all=n/NM;
|
||||||
|
[NM,unit]=time_diff(t1,t2,iop);
|
||||||
|
lamb=nn/NM;
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
|
||||||
|
if nn<15
|
||||||
|
eps=0;b=0;Mmax=0;err=0;
|
||||||
|
lamb_err=1;
|
||||||
|
BIAS=NaN;SD=NaN; %%% K 08NOV2019
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
xx=M(M>=Mmin); %K21OCT2014
|
||||||
|
% x=sort(M,'descend');
|
||||||
|
% for i=1:n
|
||||||
|
% if x(i)<Mmin; break; end
|
||||||
|
% xx(i)=x(i); %
|
||||||
|
% end
|
||||||
|
|
||||||
|
clear x;
|
||||||
|
nn=length(xx);
|
||||||
|
|
||||||
|
Max_obs=max(xx);
|
||||||
|
beta0=0;
|
||||||
|
Mmax1=Max_obs;
|
||||||
|
if isempty(Mmax)==0 %%% K 28JUL2015
|
||||||
|
err_Mmax=0; %%% K 04DEC2019
|
||||||
|
fun = @(b) bet_est(b,mean(xx),Mmin-eps/2,Mmax); %%% K 28JUL2015
|
||||||
|
x0 = 1; %[0.05,4.0]; %%% K 28JUL2015 - See exception line 155
|
||||||
|
beta = fzero(fun,x0); %%% K 28JUL2015
|
||||||
|
err=0; %%% K 28JUL2015
|
||||||
|
else %%% K 28JUL2015 - line 150
|
||||||
|
err_Mmax=1; %%% K 04DEC2019
|
||||||
|
for i=1:50,
|
||||||
|
fun = @(b) bet_est(b,mean(xx),Mmin-eps/2,Mmax1);
|
||||||
|
x0 =1; %[0.05,4.0]; %%% K29JUL2015 - See exception line 155
|
||||||
|
beta = fzero(fun,x0);
|
||||||
|
Mmax=Max_obs+moja_calka('f_podc',Mmin,Max_obs,1e-5,nn,beta,Mmin-eps/2,Mmax1);
|
||||||
|
if ((abs(Mmax-Mmax1)<0.01)&&(abs(beta-beta0)<0.0001))
|
||||||
|
err=0;
|
||||||
|
break;
|
||||||
|
end
|
||||||
|
Mmax1=Mmax;
|
||||||
|
beta0=beta;
|
||||||
|
end
|
||||||
|
if i==50;
|
||||||
|
err=1.0;
|
||||||
|
Mmax=2*xx(1)-xx(2);
|
||||||
|
fun = @(b) bet_est(b,mean(xx),Mmin-eps/2,Mmax);
|
||||||
|
x0 =1;
|
||||||
|
beta = fzero(fun,x0);
|
||||||
|
end
|
||||||
|
end %%% K 28JUL2015
|
||||||
|
b=beta/log(10);
|
||||||
|
clear xx
|
||||||
|
|
||||||
|
% Exception for v-value
|
||||||
|
if b<0.05 || b>6.0; error('Unacceptable b-value, abort and select different dataset');end
|
||||||
|
beta;
|
||||||
|
|
||||||
|
|
||||||
|
% Estimation of Mmax Bias %%% K 04DEC2019
|
||||||
|
% (Lasocki and Urban, 2011, doi:10.2478/s11600-010-0049-y)
|
||||||
|
if isempty(Nsynth)==0 && err_Mmax==1 % set number of synthetic datasets, e.g. 10000
|
||||||
|
[BIAS,SD]=Mmax_Bias_GR(t,M,Mmin,Mmax,b,err,Nsynth);
|
||||||
|
elseif isempty(Nsynth)==0 && err_Mmax==0;
|
||||||
|
warning('Mmax must be empty for BIAS calculation');BIAS=[];SD=[];
|
||||||
|
else; BIAS=0;SD=0;
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
function [NM,unit]=time_diff(t1,t2,iop) % SL 03MAR2015
|
||||||
|
|
||||||
|
% TIME DIFFERENCE BETWEEEN t1,t2 EXPRESSED IN DAY, MONTH OR YEAR UNIT
|
||||||
|
%
|
||||||
|
% t1 - start time (in MATLAB numerical format)
|
||||||
|
% t2 - end time (in MATLAB numerical format) t2>=t1
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
%
|
||||||
|
% NM - number of time units from t1 to t2
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
NM=(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM=V2(3)/eomday(V2(1),V2(2))+V2(2)+12-V1(2)-V1(3)/eomday(V1(1),V1(2))...
|
||||||
|
+(V2(1)-V1(1)-1)*12;
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM2=V2(3);
|
||||||
|
if V2(2)>1
|
||||||
|
for k=1:V2(2)-1
|
||||||
|
NM2=NM2+eomday(V2(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day2=365; if eomday(V2(1),2)==29; day2=366; end;
|
||||||
|
NM2=NM2/day2;
|
||||||
|
NM1=V1(3);
|
||||||
|
if V1(2)>1
|
||||||
|
for k=1:V1(2)-1
|
||||||
|
NM1=NM1+eomday(V1(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day1=365; if eomday(V1(1),2)==29; day1=366; end;
|
||||||
|
NM1=(day1-NM1)/day1;
|
||||||
|
NM=NM2+NM1+V2(1)-V1(1)-1;
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [zero]=bet_est(b,ms,Mmin,Mmax)
|
||||||
|
|
||||||
|
%First derivative of the log likelihood function of the upper-bounded
|
||||||
|
% exponential distribution (truncated GR model)
|
||||||
|
% b - parameter of the distribution 'beta'
|
||||||
|
% ms - mean of the observed magnitudes
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
|
||||||
|
M_max_min=Mmax-Mmin;
|
||||||
|
e_m=exp(-b*M_max_min);
|
||||||
|
zero=1/b-ms+Mmin-M_max_min*e_m/(1-e_m);
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [calka,ier]=moja_calka(funfc,a,b,eps,varargin)
|
||||||
|
|
||||||
|
% Integration by means of 16th poit Gauss method. Adopted from CERNLIBRARY
|
||||||
|
|
||||||
|
% funfc - string with the name of function to be integrated
|
||||||
|
% a,b - integration limits
|
||||||
|
% eps - accurracy
|
||||||
|
% varargin - other parameters of function to be integrated
|
||||||
|
% calka - integral
|
||||||
|
% ier=0 - convergence, ier=1 - no conbergence
|
||||||
|
|
||||||
|
persistent W X CONST
|
||||||
|
W=[0.101228536290376 0.222381034453374 0.313706645877887 ...
|
||||||
|
0.362683783378362 0.027152459411754 0.062253523938648 ...
|
||||||
|
0.095158511682493 0.124628971255534 0.149595988816577 ...
|
||||||
|
0.169156519395003 0.182603415044924 0.189450610455069];
|
||||||
|
X=[0.960289856497536 0.796666477413627 0.525532409916329 ...
|
||||||
|
0.183434642495650 0.989400934991650 0.944575023073233 ...
|
||||||
|
0.865631202387832 0.755404408355003 0.617876244402644 ...
|
||||||
|
0.458016777657227 0.281603550779259 0.095012509837637];
|
||||||
|
CONST=1E-12;
|
||||||
|
delta=CONST*abs(a-b);
|
||||||
|
calka=0.;
|
||||||
|
aa=a;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
while abs(y)>delta,
|
||||||
|
bb=aa+y;
|
||||||
|
c1=0.5*(aa+bb);
|
||||||
|
c2=c1-aa;
|
||||||
|
s8=0.;
|
||||||
|
s16=0.;
|
||||||
|
for i=1:4,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s8=s8+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
for i=5:12,
|
||||||
|
u=X(i)*c2;
|
||||||
|
s16=s16+W(i)*(feval(funfc,c1+u,varargin{:})+feval(funfc,c1-u,varargin{:}));
|
||||||
|
end
|
||||||
|
s8=s8*c2;
|
||||||
|
s16=s16*c2;
|
||||||
|
if abs(s16-s8)>eps*(1+abs(s16))
|
||||||
|
y=0.5*y;
|
||||||
|
calka=0.;
|
||||||
|
ier=1;
|
||||||
|
else
|
||||||
|
calka=calka+s16;
|
||||||
|
aa=bb;
|
||||||
|
y=b-aa;
|
||||||
|
ier=0;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=f_podc(z,n,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
% Integrated function for Mmax estimation. Truncated GR model
|
||||||
|
% z - column vector of independent variable
|
||||||
|
% n - the size of 'z'
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% Mmin - the catalog completeness level
|
||||||
|
% Mmax - the upper limit of the distribution
|
||||||
|
|
||||||
|
y=Cdfgr(z,beta,Mmin,Mmax).^n;
|
||||||
|
end
|
||||||
|
|
||||||
|
function [y]=Cdfgr(t,beta,Mmin,Mmax)
|
||||||
|
|
||||||
|
%CDF of the truncated upper-bounded exponential distribution (truncated G-R
|
||||||
|
% model
|
||||||
|
% Mmin - catalog completeness level
|
||||||
|
% Mmax - upper limit of the distribution
|
||||||
|
% beta - the distribution parameter
|
||||||
|
% t - vector of magnitudes (independent variable)
|
||||||
|
% y - CDF vector
|
||||||
|
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin)));
|
||||||
|
y=(1-exp(-beta*(t-Mmin)))/mian;
|
||||||
|
idx=find(y>1);
|
||||||
|
y(idx)=ones(size(idx));
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
|
|
||||||
|
% --------------------- Mmax BIAS estimation routine ---------------------- K 08NOV2019
|
||||||
|
|
||||||
|
function [BIAS,SD]=Mmax_Bias_GR(t,m,Mc,Mmax1,b,err,synth)
|
||||||
|
|
||||||
|
if err~=0
|
||||||
|
warning('process did not converge!!'),pause
|
||||||
|
end
|
||||||
|
|
||||||
|
MAXm=max(m);beta=b*log(10);N=numel(m(m>=Mc));DeltaM=MAXm-Mc;
|
||||||
|
|
||||||
|
for j=1:synth %set number of synthetic datasets, default is 10000
|
||||||
|
% % CDF:
|
||||||
|
M=Mc:0.0001:MAXm;upt=1-exp(-beta*(M-Mc));
|
||||||
|
dwt=1-exp(-beta*(MAXm-Mc));F=upt./dwt; % j
|
||||||
|
% linear interpolation to assign magnitude values from a uniform distribution sample
|
||||||
|
iM=rand(1,N);M1=interp1q(F',M',iM');
|
||||||
|
br(j)=1/(log(10)*(mean(M1)-min(M1)));DM=range(M1);
|
||||||
|
Mmax=max(M1);
|
||||||
|
|
||||||
|
% Iteration Process to estimate b and Mmax
|
||||||
|
b1=1;best=[1.0 10.0];i=1;
|
||||||
|
while min(abs(diff(best)))>0.00001
|
||||||
|
w=exp(b1*(Mmax-Mc));E1=expint(N/(w-1));E2=expint(N*w/(w-1));
|
||||||
|
%E=expint(w);
|
||||||
|
Mme=Mmax+(E1-E2)/(b1*exp(-N/(w-1)))+(Mc)*exp(-N); %Mme=round(Mme/EPS)*EPS;
|
||||||
|
|
||||||
|
if isnan(Mme)
|
||||||
|
KM=sort(unique(M1),'descend');
|
||||||
|
Mme=2*KM(1)-KM(2);
|
||||||
|
end
|
||||||
|
|
||||||
|
fun=@(bb) 1/bb+(Mme-Mc)/(1-exp(bb*(Mme-Mc)))-mean(M1)+Mc; %consider th5 last 0.05 term
|
||||||
|
b1=fzero(fun,1);best(i)=b1;i=i+1;
|
||||||
|
|
||||||
|
if i==50
|
||||||
|
warning('process did not converge!!');break
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
be(j)=b1/log(10);
|
||||||
|
Me(j)=Mme;dm(j)=DM;Mm(j)=Mmax;
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
BIAS=mean(MAXm-Me)
|
||||||
|
SD=std(MAXm-Me);
|
||||||
|
|
||||||
|
%b-mean(be) %check b-value difference
|
||||||
|
%histogram(be)
|
||||||
|
|
||||||
|
% MAXm: maximum magnitude in the real catalog
|
||||||
|
% Mmax: maximum magnitudes observed in the synthetic catalogs (rounded)
|
||||||
|
% Me: maximum magnitude estimates for the synthetic catalogs
|
||||||
|
% Mmax1: maximum magnitude estimated by GRT
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
167
SHAPE_Package/SHAPE_ver2b.0/SSH/UnlimitGR.m
Executable file
167
SHAPE_Package/SHAPE_ver2b.0/SSH/UnlimitGR.m
Executable file
@ -0,0 +1,167 @@
|
|||||||
|
% [lamb_all,lamb,lmab_err,unit,eps,b]=UnlimitGR(t,M,iop,Mmin)
|
||||||
|
%
|
||||||
|
% ESTIMATES THE MEAN ACTIVITY RATE WITHIN THE WHOLE SAMPLE AND WITHIN THE
|
||||||
|
% COMPLETE PART OF THE SAMPLE, THE ROUND-OFF ERROR OF MAGNITUDE AND THE
|
||||||
|
% GUTENBERG-RICHTER B-VALUE USING THE UNLIMITED G-R LED MAGNITUDE
|
||||||
|
% DISTRIBUTION MODEL
|
||||||
|
%
|
||||||
|
% !! THIS FUNCTION MUST BE EXECUTED AT START-UP OF THE UNBOUNDED
|
||||||
|
% GUTENBERG-RICHETR HAZARD ESTIMATION MODE !!
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki ver 2 01/2015 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the unlimited Gutenberg-Richter relation
|
||||||
|
% leads to the exponential distribution model of magnitude distribution
|
||||||
|
% from and above the catalog completness level Mmin. The shape parameter of
|
||||||
|
% this distribution and consequently the G-R b-value is estimated by
|
||||||
|
% maximum likelihood method (Aki-Utsu procedure).
|
||||||
|
% The mean activity rate, lamb, is the number of events >=Mmin into the
|
||||||
|
% length of the period in which they occurred. Upon the value of the input
|
||||||
|
% parameter, iop, the used unit of time can be either day ot month or year.
|
||||||
|
% The round-off interval length - eps if the least non-zero difference
|
||||||
|
% between sample data or 0.1 is the least difference is greater than 0.1.
|
||||||
|
%
|
||||||
|
% INPUT:
|
||||||
|
% t - vector of earthquake occurrence times
|
||||||
|
% M - vector of magnitudes from a user selected catalog
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
% Mmin - catalog completeness level. Must be determined externally.
|
||||||
|
% can take any value from [min(M), max(M)].
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% lamb_all - mean activity rate for all events
|
||||||
|
% lamb - mean activity rate for events >= Mmin
|
||||||
|
% lamb_err - error paramter on the number of events >=Mmin. lamb_err=0
|
||||||
|
% for 7 or more events >=Mmin and the parameter estimation is
|
||||||
|
% continued, lamb_err=1 otherwise, all output paramters except
|
||||||
|
% lamb_all and lamb are set to zero and the function execution is
|
||||||
|
% terminated.
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
% You should have received a copy of the GNU General Public License
|
||||||
|
% along with this program. If not, see <http://www.gnu.org/licenses/>.
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
function [lamb_all,lamb,lamb_err,unit,eps,b,bCI]=UnlimitGR(t,M,iop,Mmin,Nbst)
|
||||||
|
if isempty(t) || numel(t)<3 || isempty(M(M>=Mmin)) %K03OCT
|
||||||
|
t=[1 2];M=[1 2]; end %K30SEP
|
||||||
|
|
||||||
|
|
||||||
|
lamb_err=0;
|
||||||
|
n=length(M);
|
||||||
|
t1=t(1);
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t1=t(i+1);
|
||||||
|
end
|
||||||
|
t2=t(n);
|
||||||
|
for i=n:1
|
||||||
|
if M(i)>=Mmin; break; end
|
||||||
|
t2=t(i-1);
|
||||||
|
end
|
||||||
|
nn=0;
|
||||||
|
for i=1:n
|
||||||
|
if M(i)>=Mmin
|
||||||
|
nn=nn+1;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
[NM,unit]=time_diff(t(1),t(n),iop);
|
||||||
|
lamb_all=n/NM;
|
||||||
|
[NM,unit]=time_diff(t1,t2,iop);
|
||||||
|
lamb=nn/NM;
|
||||||
|
% SL 03MAR2015 ----------------------------------
|
||||||
|
|
||||||
|
if nn<7
|
||||||
|
eps=0;b=0;
|
||||||
|
lamb_err=1;
|
||||||
|
return;
|
||||||
|
end
|
||||||
|
|
||||||
|
eps=magn_accur(M);
|
||||||
|
xx=M(M>=Mmin); %K21OCT2014
|
||||||
|
% x=sort(M,'descend');
|
||||||
|
% for i=1:n
|
||||||
|
% if x(i)<Mmin; break; end
|
||||||
|
% xx(i)=x(i); %
|
||||||
|
% end
|
||||||
|
clear x;
|
||||||
|
beta=1/(mean(xx)-Mmin+eps/2);
|
||||||
|
b=beta/log(10);
|
||||||
|
% Add bootstrap CI of b-value %K03JUN2020
|
||||||
|
b_aki=@(xx)1/(log(10)*(mean(xx)-min(xx)+eps/2)); %K03JUN2020
|
||||||
|
bCI=bootci(Nbst,{b_aki,xx},'alpha',0.05); %K03JUN2020
|
||||||
|
clear xx
|
||||||
|
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
function [NM,unit]=time_diff(t1,t2,iop) % SL 03MAR2015
|
||||||
|
|
||||||
|
% TIME DIFFERENCE BETWEEEN t1,t2 EXPRESSED IN DAY, MONTH OR YEAR UNIT
|
||||||
|
%
|
||||||
|
% t1 - start time (in MATLAB numerical format)
|
||||||
|
% t2 - end time (in MATLAB numerical format) t2>=t1
|
||||||
|
% iop - determines the used unit of time. iop=0 - 'day', iop=1 - 'month',
|
||||||
|
% iop=2 - 'year'
|
||||||
|
%
|
||||||
|
% NM - number of time units from t1 to t2
|
||||||
|
% unit - string with name of time unit used ('year' or 'month' or 'day').
|
||||||
|
|
||||||
|
if iop==0
|
||||||
|
NM=(t2-t1);
|
||||||
|
unit='day';
|
||||||
|
elseif iop==1
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM=V2(3)/eomday(V2(1),V2(2))+V2(2)+12-V1(2)-V1(3)/eomday(V1(1),V1(2))...
|
||||||
|
+(V2(1)-V1(1)-1)*12;
|
||||||
|
unit='month';
|
||||||
|
else
|
||||||
|
V1=datevec(t1);
|
||||||
|
V2=datevec(t2);
|
||||||
|
NM2=V2(3);
|
||||||
|
if V2(2)>1
|
||||||
|
for k=1:V2(2)-1
|
||||||
|
NM2=NM2+eomday(V2(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day2=365; if eomday(V2(1),2)==29; day2=366; end;
|
||||||
|
NM2=NM2/day2;
|
||||||
|
NM1=V1(3);
|
||||||
|
if V1(2)>1
|
||||||
|
for k=1:V1(2)-1
|
||||||
|
NM1=NM1+eomday(V1(1),k);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
day1=365; if eomday(V1(1),2)==29; day1=366; end;
|
||||||
|
NM1=(day1-NM1)/day1;
|
||||||
|
NM=NM2+NM1+V2(1)-V1(1)-1;
|
||||||
|
unit='year';
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
function [eps]=magn_accur(M)
|
||||||
|
x=sort(M);
|
||||||
|
d=x(2:length(x))-x(1:length(x)-1);
|
||||||
|
eps=min(d(d>0));
|
||||||
|
if eps>0.1; eps=0.1;end
|
||||||
|
end
|
||||||
64
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRT.m
Executable file
64
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRT.m
Executable file
@ -0,0 +1,64 @@
|
|||||||
|
% [m, PDF_GRT, CDF_GRT]=dist_GRT(Md,Mu,dM,Mmin,eps,b,Mmax)
|
||||||
|
%
|
||||||
|
% EVALUATES THE DENSITY AND CUMULATIVE DISTRIBUTION FUNCTIONS OF MAGNITUDE
|
||||||
|
% UNDER THE UPPER-BOUNDED G-R LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution, consequently the G-R
|
||||||
|
% b-value and the end-point of the distribution Mmax are calculated at
|
||||||
|
% start-up of the stationary hazard assessment services in the
|
||||||
|
% upper-bounded Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The distribution function values are calculated for magnitude starting
|
||||||
|
% from Md up to Mu with step dM.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% m - vector of the independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% PDF_GRT - PDF vector of the same length as m
|
||||||
|
% CDF_GRT - CDF vector of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
function [m, PDF_GRT, CDF_GRT]=dist_GRT(Md,Mu,dM,Mmin,eps,b,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
beta=b*log(10);
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin+eps/2)));
|
||||||
|
PDF_GRT=beta*exp(-beta*(m-Mmin+eps/2))/mian;
|
||||||
|
CDF_GRT=(1-exp(-beta*(m-Mmin+eps/2)))/mian;
|
||||||
|
idx=find(CDF_GRT<0);
|
||||||
|
PDF_GRT(idx)=zeros(size(idx));CDF_GRT(idx)=zeros(size(idx));
|
||||||
|
idx=find(CDF_GRT>1);
|
||||||
|
PDF_GRT(idx)=zeros(size(idx));CDF_GRT(idx)=ones(size(idx));
|
||||||
|
end
|
||||||
|
|
||||||
69
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRT_CI.m
Executable file
69
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRT_CI.m
Executable file
@ -0,0 +1,69 @@
|
|||||||
|
% [m, PDF_GRT, CDF_GRT]=dist_GRT(Md,Mu,dM,Mmin,eps,b,Mmax)
|
||||||
|
%
|
||||||
|
% EVALUATES THE DENSITY AND CUMULATIVE DISTRIBUTION FUNCTIONS OF MAGNITUDE
|
||||||
|
% UNDER THE UPPER-BOUNDED G-R LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
|
||||||
|
% relation leads to the upper truncated exponential distribution to model
|
||||||
|
% magnitude distribution from and above the catalog completness level
|
||||||
|
% Mmin. The shape parameter of this distribution, consequently the G-R
|
||||||
|
% b-value and the end-point of the distribution Mmax are calculated at
|
||||||
|
% start-up of the stationary hazard assessment services in the
|
||||||
|
% upper-bounded Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The distribution function values are calculated for magnitude starting
|
||||||
|
% from Md up to Mu with step dM.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% m - vector of the independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% PDF_GRT - PDF vector of the same length as m
|
||||||
|
% CDF_GRT - CDF vector of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
|
||||||
|
function [m, PDF_GRT, CDF_GRT]=dist_GRT_CI(Md,Mu,dM,Mmin,eps,b,Mmax,bCI)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
beta=b*log(10);beta_low=bCI(1)*log(10);beta_high=bCI(2)*log(10);
|
||||||
|
mian=(1-exp(-beta*(Mmax-Mmin+eps/2)));
|
||||||
|
PDF_GRT=beta*exp(-beta*(m-Mmin+eps/2))/mian;
|
||||||
|
CDF_GRT=(1-exp(-beta*(m-Mmin+eps/2)))/mian;
|
||||||
|
idx=find(CDF_GRT<0);
|
||||||
|
PDF_GRT(idx)=zeros(size(idx));CDF_GRT(idx)=zeros(size(idx));
|
||||||
|
idx=find(CDF_GRT>1);
|
||||||
|
PDF_GRT(idx)=zeros(size(idx));CDF_GRT(idx)=ones(size(idx));
|
||||||
|
|
||||||
|
CDF_low=1-exp(-beta_low*(m-Mmin+eps/2));
|
||||||
|
CDF_high=1-exp(-beta_high*(m-Mmin+eps/2));
|
||||||
|
|
||||||
|
CDF_GRT=[CDF_GRT CDF_low CDF_high];
|
||||||
|
end
|
||||||
|
|
||||||
61
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRU.m
Executable file
61
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRU.m
Executable file
@ -0,0 +1,61 @@
|
|||||||
|
% [m, PDF_GRU, CDF_GRU]=dist_GRU(Md,Mu,dM,Mmin,eps,b)
|
||||||
|
%
|
||||||
|
% EVALUATES THE DENSITY AND CUMULATIVE DISTRIBUTION FUNCTIONS OF MAGNITUDE
|
||||||
|
% UNDER THE UNLIMITED G-R LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the unlimited Gutenberg-Richter relation
|
||||||
|
% leads to the exponential distribution model of magnitude distribution
|
||||||
|
% from and above the catalog completness level Mmin. The shape parameter of
|
||||||
|
% this distribution and consequently the G-R b-value are calculated at
|
||||||
|
% start-up of the stationary hazard assessment services in the
|
||||||
|
% unlimited Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The distribution function values are calculated for magnitude starting
|
||||||
|
% from Md up to Mu with step dM.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% m - vector of the independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% PDF_GRT - PDF vector of the same length as m
|
||||||
|
% CDF_GRT - CDF vector of the same length as m
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [m, PDF_GRU, CDF_GRU]=dist_GRU(Md,Mu,dM,Mmin,eps,b)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
beta=b*log(10);
|
||||||
|
PDF_GRU=beta*exp(-beta*(m-Mmin+eps/2));
|
||||||
|
CDF_GRU=1-exp(-beta*(m-Mmin+eps/2));
|
||||||
|
idx=find(CDF_GRU<0);
|
||||||
|
PDF_GRU(idx)=zeros(size(idx));CDF_GRU(idx)=zeros(size(idx));
|
||||||
|
idx=find(CDF_GRU>1);
|
||||||
|
PDF_GRU(idx)=zeros(size(idx));CDF_GRU(idx)=ones(size(idx));
|
||||||
|
end
|
||||||
|
|
||||||
67
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRU_CI.m
Executable file
67
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_GRU_CI.m
Executable file
@ -0,0 +1,67 @@
|
|||||||
|
% [m, PDF_GRU, CDF_GRU]=dist_GRU(Md,Mu,dM,Mmin,eps,b)
|
||||||
|
%
|
||||||
|
% EVALUATES THE DENSITY AND CUMULATIVE DISTRIBUTION FUNCTIONS OF MAGNITUDE
|
||||||
|
% UNDER THE UNLIMITED G-R LED MAGNITUDE DISTRIBUTION MODEL.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The assumption on the unlimited Gutenberg-Richter relation
|
||||||
|
% leads to the exponential distribution model of magnitude distribution
|
||||||
|
% from and above the catalog completness level Mmin. The shape parameter of
|
||||||
|
% this distribution and consequently the G-R b-value are calculated at
|
||||||
|
% start-up of the stationary hazard assessment services in the
|
||||||
|
% unlimited Gutenberg-Richter estimation mode.
|
||||||
|
%
|
||||||
|
% The distribution function values are calculated for magnitude starting
|
||||||
|
% from Md up to Mu with step dM.
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of the round-off interval of magnitudes.
|
||||||
|
% b - Gutenberg-Richter b-value
|
||||||
|
%
|
||||||
|
%OUTPUT:
|
||||||
|
% m - vector of the independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% PDF_GRT - PDF vector of the same length as m
|
||||||
|
% CDF_GRT - CDF vector of the same length as m
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [m, PDF_GRU, CDF_GRU]=dist_GRU_CI(Md,Mu,dM,Mmin,eps,b,bCI)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
beta=b*log(10);beta_low=bCI(1)*log(10);beta_high=bCI(2)*log(10);
|
||||||
|
PDF_GRU=beta*exp(-beta*(m-Mmin+eps/2));
|
||||||
|
CDF_GRU=1-exp(-beta*(m-Mmin+eps/2));
|
||||||
|
idx=find(CDF_GRU<0);
|
||||||
|
PDF_GRU(idx)=zeros(size(idx));CDF_GRU(idx)=zeros(size(idx));
|
||||||
|
idx=find(CDF_GRU>1);
|
||||||
|
PDF_GRU(idx)=zeros(size(idx));CDF_GRU(idx)=ones(size(idx));
|
||||||
|
|
||||||
|
CDF_low=1-exp(-beta_low*(m-Mmin+eps/2));
|
||||||
|
CDF_high=1-exp(-beta_high*(m-Mmin+eps/2));
|
||||||
|
|
||||||
|
CDF_GRU=[CDF_GRU CDF_low CDF_high];
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
116
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPT.m
Executable file
116
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPT.m
Executable file
@ -0,0 +1,116 @@
|
|||||||
|
% [m,PDF_NPT,CDF_NPT]=dist_NPT(Md,Mu,dM,Mmin,eps,h,xx,ambd,Mmax)
|
||||||
|
%
|
||||||
|
% USING THE NONPARAMETRIC ADAPTATIVE KERNEL ESTIMATORS EVALUATES THE DENSITY
|
||||||
|
% AND CUMULATIVE DISTRIBUTION FUNCTIONS FOR THE UPPER-BOUNDED MAGNITUDE
|
||||||
|
% DISTRIBUTION.
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution has a hard end point Mmax from the right hand
|
||||||
|
% side.The estimation makes use of the previously estimated parameters
|
||||||
|
% namely the mean activity rate lamb, the length of magnitude round-off
|
||||||
|
% interval, eps, the smoothing factor, h, the background sample, xx, the
|
||||||
|
% scaling factors for the background sample, ambd, and the end-point of
|
||||||
|
% magnitude distribution Mmax. The background sample,xx, comprises the
|
||||||
|
% randomized values of observed magnitude doubled symmetrically with
|
||||||
|
% respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
% Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
% Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
% Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% m - vector of the independent variable (magnitude)
|
||||||
|
% PDF_NPT - PDF vector
|
||||||
|
% CDF_NPT - CDF vector
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [m,PDF_NPT,CDF_NPT]=dist_NPT(Md,Mu,dM,Mmin,eps,h,xx,ambd,Mmax)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
nn=length(m);
|
||||||
|
|
||||||
|
mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
for i=1:nn
|
||||||
|
if m(i)<Mmin-eps/2
|
||||||
|
PDF_NPT(i)=0;CDF_NPT(i)=0;
|
||||||
|
elseif m(i)>Mmax
|
||||||
|
PDF_NPT(i)=0;CDF_NPT(i)=1;
|
||||||
|
else
|
||||||
|
PDF_NPT(i)=dens_npr1(m(i),xx,ambd,h,Mmin-eps/2)/mian;
|
||||||
|
CDF_NPT(i)=2*(Dystr_npr(m(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h))/mian;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
PDF_NPT=PDF_NPT';CDF_NPT=CDF_NPT';
|
||||||
|
end
|
||||||
|
|
||||||
|
function [gau]=dens_npr1(y,x,ambd,h,x1)
|
||||||
|
|
||||||
|
%Nonparametric adaptive density for a variable from the interval [x1,inf)
|
||||||
|
|
||||||
|
% x - the sample data doubled and sorted in the ascending order. Use
|
||||||
|
% "podwajanie.m" first to accmoplish that.
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
if y<x1
|
||||||
|
gau=0;
|
||||||
|
else
|
||||||
|
gau=2*sum(exp(-0.5*(((y-x)./ambd')./h).^2)./ambd')/c/n/h;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
116
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPT_CI.m
Executable file
116
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPT_CI.m
Executable file
@ -0,0 +1,116 @@
|
|||||||
|
% [m,PDF_NPT,CDF_NPT]=dist_NPT(Md,Mu,dM,Mmin,eps,h,xx,ambd,Mmax)
|
||||||
|
%
|
||||||
|
% USING THE NONPARAMETRIC ADAPTATIVE KERNEL ESTIMATORS EVALUATES THE DENSITY
|
||||||
|
% AND CUMULATIVE DISTRIBUTION FUNCTIONS FOR THE UPPER-BOUNDED MAGNITUDE
|
||||||
|
% DISTRIBUTION.
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution has a hard end point Mmax from the right hand
|
||||||
|
% side.The estimation makes use of the previously estimated parameters
|
||||||
|
% namely the mean activity rate lamb, the length of magnitude round-off
|
||||||
|
% interval, eps, the smoothing factor, h, the background sample, xx, the
|
||||||
|
% scaling factors for the background sample, ambd, and the end-point of
|
||||||
|
% magnitude distribution Mmax. The background sample,xx, comprises the
|
||||||
|
% randomized values of observed magnitude doubled symmetrically with
|
||||||
|
% respect to the value Mmin-eps/2.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
% Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
% Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
% Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
% Mmax - upper limit of magnitude distribution
|
||||||
|
%
|
||||||
|
% OUTPUT:
|
||||||
|
% m - vector of the independent variable (magnitude)
|
||||||
|
% PDF_NPT - PDF vector
|
||||||
|
% CDF_NPT - CDF vector
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [CDF_NPT]=dist_NPT_CI(Md,Mu,dM,Mmin,eps,h,data,Mmax)
|
||||||
|
xx=data(:,1);ambd=data(:,2)';
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
nn=length(m);
|
||||||
|
|
||||||
|
mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
for i=1:nn
|
||||||
|
if m(i)<Mmin-eps/2
|
||||||
|
PDF_NPT(i)=0;CDF_NPT(i)=0;
|
||||||
|
elseif m(i)>Mmax
|
||||||
|
PDF_NPT(i)=0;CDF_NPT(i)=1;
|
||||||
|
else
|
||||||
|
PDF_NPT(i)=dens_npr1(m(i),xx,ambd,h,Mmin-eps/2)/mian;
|
||||||
|
CDF_NPT(i)=2*(Dystr_npr(m(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h))/mian;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
PDF_NPT=PDF_NPT';CDF_NPT=CDF_NPT';
|
||||||
|
end
|
||||||
|
|
||||||
|
function [gau]=dens_npr1(y,x,ambd,h,x1)
|
||||||
|
|
||||||
|
%Nonparametric adaptive density for a variable from the interval [x1,inf)
|
||||||
|
|
||||||
|
% x - the sample data doubled and sorted in the ascending order. Use
|
||||||
|
% "podwajanie.m" first to accmoplish that.
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
if y<x1
|
||||||
|
gau=0;
|
||||||
|
else
|
||||||
|
gau=2*sum(exp(-0.5*(((y-x)./ambd')./h).^2)./ambd')/c/n/h;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
114
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPU.m
Executable file
114
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPU.m
Executable file
@ -0,0 +1,114 @@
|
|||||||
|
% [m, PDF_NPU, CDF_NPU]=dist_NPU(Md,Mu,dM,Mmin,eps,h,xx,ambd)
|
||||||
|
%
|
||||||
|
% USING THE NONPARAMETRIC ADAPTATIVE KERNEL ESTIMATORS EVALUATES THE DENSITY
|
||||||
|
% AND CUMULATIVE DISTRIBUTION FUNCTIONS FOR THE UNLIMITED MAGNITUDE
|
||||||
|
% DISTRIBUTION.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution is unlimited from the right hand side.
|
||||||
|
% The estimation makes use of the previously estimated parameters of kernel
|
||||||
|
% estimation, namely the smoothing factor, the background sample and the
|
||||||
|
% scaling factors for the background sample. The background sample
|
||||||
|
% - xx comprises the randomized values of observed magnitude doubled
|
||||||
|
% symmetrically with respect to the value Mmin-eps/2
|
||||||
|
%
|
||||||
|
% The distribution function values are calculated for magnitude starting
|
||||||
|
% from Md up to Mu with step dM.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation fro Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%OUTPUT
|
||||||
|
% m - vector of the independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% PDF_NPU - PDF vector of the same length as m
|
||||||
|
% CDF_NPU - CDF vector of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [m, PDF_NPU, CDF_NPU]=dist_NPU(Md,Mu,dM,Mmin,eps,h,xx,ambd)
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
nn=length(m);
|
||||||
|
|
||||||
|
for i=1:nn
|
||||||
|
if m(i)>=Mmin-eps/2
|
||||||
|
PDF_NPU(i)=dens_npr1(m(i),xx,ambd,h,Mmin-eps/2);
|
||||||
|
CDF_NPU(i)=2*(Dystr_npr(m(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
else
|
||||||
|
PDF_NPU(i)=0;
|
||||||
|
CDF_NPU(i)=0;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
PDF_NPU=PDF_NPU';CDF_NPU=CDF_NPU';
|
||||||
|
end
|
||||||
|
|
||||||
|
function [gau]=dens_npr1(y,x,ambd,h,x1)
|
||||||
|
|
||||||
|
%Nonparametric adaptive density for a variable from the interval [x1,inf)
|
||||||
|
|
||||||
|
% x - the sample data doubled and sorted in the ascending order. Use
|
||||||
|
% "podwajanie.m" first to accmoplish that.
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
if y<x1
|
||||||
|
gau=0;
|
||||||
|
else
|
||||||
|
gau=2*sum(exp(-0.5*(((y-x)./ambd')./h).^2)./ambd')/c/n/h;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
118
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPU_CI.m
Executable file
118
SHAPE_Package/SHAPE_ver2b.0/SSH/dist_NPU_CI.m
Executable file
@ -0,0 +1,118 @@
|
|||||||
|
% [m, PDF_NPU, CDF_NPU]=dist_NPU(Md,Mu,dM,Mmin,eps,h,xx,ambd)
|
||||||
|
%
|
||||||
|
% USING THE NONPARAMETRIC ADAPTATIVE KERNEL ESTIMATORS EVALUATES THE DENSITY
|
||||||
|
% AND CUMULATIVE DISTRIBUTION FUNCTIONS FOR THE UNLIMITED MAGNITUDE
|
||||||
|
% DISTRIBUTION.
|
||||||
|
%
|
||||||
|
% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
|
||||||
|
%
|
||||||
|
% DESCRIPTION: The kernel estimator approach is a model-free alternative
|
||||||
|
% to estimating the magnitude distribution functions. It is assumed that
|
||||||
|
% the magnitude distribution is unlimited from the right hand side.
|
||||||
|
% The estimation makes use of the previously estimated parameters of kernel
|
||||||
|
% estimation, namely the smoothing factor, the background sample and the
|
||||||
|
% scaling factors for the background sample. The background sample
|
||||||
|
% - xx comprises the randomized values of observed magnitude doubled
|
||||||
|
% symmetrically with respect to the value Mmin-eps/2
|
||||||
|
%
|
||||||
|
% The distribution function values are calculated for magnitude starting
|
||||||
|
% from Md up to Mu with step dM.
|
||||||
|
%
|
||||||
|
% REFERENCES:
|
||||||
|
%Silverman B.W. (1986) Density Estimation fro Statistics and Data Analysis,
|
||||||
|
% Chapman and Hall, London
|
||||||
|
%Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
|
||||||
|
%Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
|
||||||
|
%
|
||||||
|
%INPUT:
|
||||||
|
% Md - starting magnitude for distribution functions calculations
|
||||||
|
% Mu - ending magnitude for distribution functions calculations
|
||||||
|
% dM - magnitude step for distribution functions calculations
|
||||||
|
% Mmin - lower bound of the distribution - catalog completeness level
|
||||||
|
% eps - length of round-off interval of magnitudes.
|
||||||
|
% h - kernel smoothing factor.
|
||||||
|
% xx - the background sample
|
||||||
|
% ambd - the weigthing factors for the adaptive kernel
|
||||||
|
%
|
||||||
|
%
|
||||||
|
%OUTPUT
|
||||||
|
% m - vector of the independent variable (magnitude) m=(Md:dM:Mu)
|
||||||
|
% PDF_NPU - PDF vector of the same length as m
|
||||||
|
% CDF_NPU - CDF vector of the same length as m
|
||||||
|
%
|
||||||
|
% LICENSE
|
||||||
|
% This file is a part of the IS-EPOS e-PLATFORM.
|
||||||
|
%
|
||||||
|
% This is free software: you can redistribute it and/or modify it under
|
||||||
|
% the terms of the GNU General Public License as published by the Free
|
||||||
|
% Software Foundation, either version 3 of the License, or
|
||||||
|
% (at your option) any later version.
|
||||||
|
%
|
||||||
|
% This program is distributed in the hope that it will be useful,
|
||||||
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||||
|
% GNU General Public License for more details.
|
||||||
|
%
|
||||||
|
|
||||||
|
function [CDF_NPU]=dist_NPU_CI(Md,Mu,dM,Mmin,eps,h,data)
|
||||||
|
xx=data(:,1);ambd=data(:,2)';
|
||||||
|
|
||||||
|
% -------------- VALIDATION RULES ------------- K_21NOV2016
|
||||||
|
if dM<=0;error('Magnitude Step must be greater than 0');end
|
||||||
|
%----------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
m=(Md:dM:Mu)';
|
||||||
|
nn=length(m);
|
||||||
|
|
||||||
|
Mmax=10000;
|
||||||
|
mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
|
||||||
|
% mian=1;
|
||||||
|
for i=1:nn
|
||||||
|
if m(i)>=Mmin-eps/2
|
||||||
|
PDF_NPU(i)=dens_npr1(m(i),xx,ambd,h,Mmin-eps/2)/mian;
|
||||||
|
CDF_NPU(i)=2*(Dystr_npr(m(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h))/mian;
|
||||||
|
else
|
||||||
|
PDF_NPU(i)=0;
|
||||||
|
CDF_NPU(i)=0;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
PDF_NPU=PDF_NPU';CDF_NPU=CDF_NPU';
|
||||||
|
end
|
||||||
|
|
||||||
|
function [gau]=dens_npr1(y,x,ambd,h,x1)
|
||||||
|
|
||||||
|
%Nonparametric adaptive density for a variable from the interval [x1,inf)
|
||||||
|
|
||||||
|
% x - the sample data doubled and sorted in the ascending order. Use
|
||||||
|
% "podwajanie.m" first to accmoplish that.
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
c=sqrt(2*pi);
|
||||||
|
if y<x1
|
||||||
|
gau=0;
|
||||||
|
else
|
||||||
|
gau=2*sum(exp(-0.5*(((y-x)./ambd')./h).^2)./ambd')/c/n/h;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [Fgau]=Dystr_npr(y,x,ambd,h)
|
||||||
|
|
||||||
|
%Nonparametric adaptive cumulative distribution for a variable from the
|
||||||
|
%interval (-inf,inf)
|
||||||
|
|
||||||
|
% x - the sample data
|
||||||
|
% ambd - the local scaling factors for the adaptive estimation
|
||||||
|
% h - the optimal smoothing factor
|
||||||
|
% y - the value of random variable X for which the density is calculated
|
||||||
|
% gau - the density value f(y)
|
||||||
|
|
||||||
|
n=length(x);
|
||||||
|
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
|
||||||
|
end
|
||||||
|
|
||||||
5
SHAPE_Package/SHAPE_ver2b.0/TIME_WINDOWS/ST2_test_timewindows.txt
Executable file
5
SHAPE_Package/SHAPE_ver2b.0/TIME_WINDOWS/ST2_test_timewindows.txt
Executable file
@ -0,0 +1,5 @@
|
|||||||
|
735470.75 735679.15
|
||||||
|
735679.15 735808.95
|
||||||
|
735808.95 735968.08
|
||||||
|
735968.08 736027.27
|
||||||
|
736027.27 736191.58
|
||||||
148
SHAPE_Package/SHAPE_ver2b.0/Zplo_ver2b_1.m
Executable file
148
SHAPE_Package/SHAPE_ver2b.0/Zplo_ver2b_1.m
Executable file
@ -0,0 +1,148 @@
|
|||||||
|
close all;d=figure('Position',[25 00 1500 800]);
|
||||||
|
|
||||||
|
% check whether the selected time windows are overlapping or not
|
||||||
|
TT=[];Tcat=Catalog(1).val;Ncat=Tcat(Tcat>=time_windows(1).Tstart & Tcat<=time_windows(length(ExPr)).Tend);
|
||||||
|
for i=1:length(MRPer);
|
||||||
|
TW1(i)=time_windows(i).Tstart;Tw2(i)=time_windows(i).Tend;
|
||||||
|
tplo(i)=mean([time_windows(i).Tstart time_windows(i).Tend]);meanM(i)=mean(time_windows(i).M);hold on
|
||||||
|
TT=[TT;time_windows(i).Time];
|
||||||
|
lambda(i)=HP(i).lamb;
|
||||||
|
if strcmp(HP(1).method,'GRU') || strcmp(HP(1).method,'GRT');yyaxis right;bval(i)=HP(i).b;end
|
||||||
|
end
|
||||||
|
if (strcmp(Plotopt,'ON'))
|
||||||
|
%if numel(TT)==numel(Ncat)
|
||||||
|
DTW=TW1(2:length(TW1))-Tw2(1:length(Tw2)-1); %%% THIS SEEMS TO WORK!!!!
|
||||||
|
if isempty(find(DTW<0))
|
||||||
|
overlap='NO';
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
for i=1:length(MRPer);
|
||||||
|
|
||||||
|
subplot(3,1,1) % plot Mean return period
|
||||||
|
hold on;fill([time_windows(i).Tstart time_windows(i).Tend time_windows(i).Tend time_windows(i).Tstart],...
|
||||||
|
[MRPer_high(i) MRPer_high(i) MRPer_low(i) MRPer_low(i)],[0.91 0.91 0.91],'facealpha',0.25)
|
||||||
|
plot([time_windows(i).Tstart time_windows(i).Tend],[MRPer(i) MRPer(i)],'k-','LineWidth',2)
|
||||||
|
if i<length(MRPer);plot([time_windows(i).Tend time_windows(i+1).Tstart],[MRPer(i) MRPer(i+1)],'k--');end
|
||||||
|
datetick('x',20);title(['Mean Return Period for M\geq',num2str(MaG)],'FontSize',16);ylabel([Tunit,'s'],'FontSize',18)
|
||||||
|
|
||||||
|
subplot(3,1,2) % plot Exceedance Probability
|
||||||
|
hold on;fill([time_windows(i).Tstart time_windows(i).Tend time_windows(i).Tend time_windows(i).Tstart],...
|
||||||
|
[ExPr_high(i) ExPr_high(i) ExPr_low(i) ExPr_low(i)],[0.91 0.91 0.91],'facealpha',0.25)
|
||||||
|
plot([time_windows(i).Tstart time_windows(i).Tend],[ExPr(i) ExPr(i)],'k-','LineWidth',2)
|
||||||
|
if i<length(ExPr);plot([time_windows(i).Tend time_windows(i+1).Tstart],[ExPr(i) ExPr(i+1)],'k--');end
|
||||||
|
datetick('x',20);title(['Exceedance Probability for M\geq',num2str(MaG),' within ',num2str(Plength), ' ',Tunit,'(s) period'],'FontSize',16);ylabel('probability','FontSize',14)
|
||||||
|
|
||||||
|
subplot(3,1,3) % plot Activity rate
|
||||||
|
hold on;yyaxis left;plot([time_windows(i).Tstart time_windows(i).Tend],[HP(i).lamb HP(i).lamb],'k-','LineWidth',2)
|
||||||
|
if i<length(ExPr);plot([time_windows(i).Tend time_windows(i+1).Tstart],[HP(i).lamb HP(i+1).lamb],'k--');end
|
||||||
|
datetick('x',20);title(['Activity Rate'],'FontSize',16);ylabel(['Events/',Tunit],'FontSize',14,'Color','k')
|
||||||
|
set(gca,'YColor','k');
|
||||||
|
% plot b-value (GR) or mean M (NP)
|
||||||
|
if strcmp(HP(1).method,'GRU') || strcmp(HP(1).method,'GRT');yyaxis right;
|
||||||
|
fill([time_windows(i).Tstart time_windows(i).Tend time_windows(i).Tend time_windows(i).Tstart],...
|
||||||
|
[HP(i).bCI(2) HP(i).bCI(2) HP(i).bCI(1) HP(i).bCI(1)],[0.99 0.81 0.31],'LineStyle','-','Marker','none','facealpha',0.25)
|
||||||
|
plot([time_windows(i).Tstart time_windows(i).Tend],[HP(i).b HP(i).b],'-','LineWidth',2)
|
||||||
|
ylabel('b-value','FontSize',14);
|
||||||
|
else
|
||||||
|
yyaxis right;plot([time_windows(i).Tstart time_windows(i).Tend],[mean(time_windows(i).M) mean(time_windows(i).M)],'-','LineWidth',2)
|
||||||
|
ylabel('mean Magnitude','FontSize',14);
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
else
|
||||||
|
|
||||||
|
overlap='YES';
|
||||||
|
|
||||||
|
subplot(3,1,1) % plot Mean return period
|
||||||
|
errorbar(tplo,MRPer,MRPer-MRPer_low,MRPer_high-MRPer,'o','LineWidth',1,'MarkerSize',8);hold on;
|
||||||
|
plot(tplo,MRPer,'ko','LineWidth',2,'MarkerSize',4);
|
||||||
|
datetick('x',20);title(['Mean Return Period for M\geq',num2str(MaG)],'FontSize',16);ylabel([Tunit,'s'],'FontSize',18)
|
||||||
|
subplot(3,1,2) % plot Exceedance Probability
|
||||||
|
errorbar(tplo,ExPr,ExPr-ExPr_low,ExPr_high-ExPr,'o','LineWidth',1,'MarkerSize',8);hold on
|
||||||
|
plot(tplo,ExPr,'ko','LineWidth',2,'MarkerSize',4);
|
||||||
|
datetick('x',20);title(['Exceedance Probability for M\geq',num2str(MaG),' within ',num2str(Plength), ' ',Tunit,'(s) period'],'FontSize',16);ylabel('probability','FontSize',14)
|
||||||
|
subplot(3,1,3) % plot Activity rate
|
||||||
|
plot(tplo,lambda,'o','LineWidth',2,'MarkerSize',8);ylabel(['Events/',Tunit],'FontSize',14)
|
||||||
|
if strcmp(HP(1).method,'GRU') || strcmp(HP(1).method,'GRT');
|
||||||
|
yyaxis right;
|
||||||
|
for i=1:length(HP);bval_low(i)=HP(i).bCI(1);bval_high(i)=HP(i).bCI(2);end
|
||||||
|
errorbar(tplo,bval,bval-bval_low,bval_high-bval,'o','LineWidth',1,'MarkerSize',8);hold on
|
||||||
|
plot(tplo,bval,'ko','LineWidth',2,'MarkerSize',4);
|
||||||
|
ylabel('b-value','FontSize',14);
|
||||||
|
else; yyaxis right;plot(tplo,meanM,'o','LineWidth',2,'MarkerSize',8)
|
||||||
|
ylabel('mean Magnitude','FontSize',14);end
|
||||||
|
datetick('x',20);title('Activity Rate','FontSize',16);
|
||||||
|
end
|
||||||
|
|
||||||
|
if isempty(PROD_Data)==0
|
||||||
|
subplot(3,1,1);yyaxis right;plot(PROD_Data(1).val,PROD_Data(PROD_FIELD).val,'-','Linewidth',1);ylabel(PROD_Data(PROD_FIELD).field,'interpreter','none','FontSize',14);
|
||||||
|
subplot(3,1,2);yyaxis right;plot(PROD_Data(1).val,PROD_Data(PROD_FIELD).val,'-','Linewidth',1);ylabel(PROD_Data(PROD_FIELD).field,'interpreter','none','FontSize',14);
|
||||||
|
end
|
||||||
|
subplot(3,1,3);xlabel('Date','FontSize',18)
|
||||||
|
|
||||||
|
% option to switch linear-log Y axis Scale
|
||||||
|
|
||||||
|
txt = uicontrol('Parent',d,...
|
||||||
|
'Style','text',...
|
||||||
|
'Position',[200 470 150 30],...
|
||||||
|
'String','Select Y Axis Scale:');
|
||||||
|
|
||||||
|
popup = uicontrol('Parent',d,...
|
||||||
|
'Style','popup',...
|
||||||
|
'Position',[350 480 120 25],...
|
||||||
|
'String',{'Linear';'Log'},...
|
||||||
|
'Callback',@popup_callback);
|
||||||
|
|
||||||
|
btn = uicontrol('Parent',d,...
|
||||||
|
'Position',[210 688 210 50],...
|
||||||
|
'String','SAVE and CLOSE',...
|
||||||
|
'FontSize',18,...
|
||||||
|
'ForeGroundColor','r',...
|
||||||
|
'FontWeight','Bold',...
|
||||||
|
'Callback',@savefig_callback);
|
||||||
|
|
||||||
|
choice = 'Linear';
|
||||||
|
|
||||||
|
% Wait for d to close before running to completion
|
||||||
|
uiwait(d);
|
||||||
|
elseif (strcmp(Plotopt,'OFF'));close all
|
||||||
|
if numel(TT)==numel(Ncat)
|
||||||
|
overlap='NO';else; overlap='YES';end
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
function popup_callback(popup,event)
|
||||||
|
idx = popup.Value;
|
||||||
|
popup_items = popup.String;
|
||||||
|
% This code uses dot notation to get properties.
|
||||||
|
% Dot notation runs in R2014b and later.
|
||||||
|
% For R2014a and earlier:
|
||||||
|
% idx = get(popup,'Value');
|
||||||
|
% popup_items = get(popup,'String');
|
||||||
|
choice = char(popup_items(idx,:));
|
||||||
|
subplot(3,1,1);yyaxis left;
|
||||||
|
set(gca,'YScale',choice)
|
||||||
|
end
|
||||||
|
|
||||||
|
function savefig_callback(popup,event)
|
||||||
|
cd Outputs_SHA
|
||||||
|
print(gcf,'SHA.jpeg','-djpeg','-r300')
|
||||||
|
savefig(gcf,'SHA.fig')
|
||||||
|
% This code uses dot notation to get properties.
|
||||||
|
% Dot notation runs in R2014b and later.
|
||||||
|
% For R2014a and earlier:
|
||||||
|
% idx = get(popup,'Value');
|
||||||
|
% popup_items = get(popup,'String');
|
||||||
|
cd ../
|
||||||
|
delete(gcf)
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
93
SHAPE_Package/SHAPE_ver2b.0/Zsave_output_ver2b_1.m
Executable file
93
SHAPE_Package/SHAPE_ver2b.0/Zsave_output_ver2b_1.m
Executable file
@ -0,0 +1,93 @@
|
|||||||
|
% ---- Save *.txt file with Parameters Report ----
|
||||||
|
cd Outputs_SHA
|
||||||
|
fid=fopen('REPORT_Hazard_Analysis.txt','w');
|
||||||
|
fprintf(fid,['Parameters Report & Results for HAZARD ANALYSIS (created on ', datestr(now),')\n']);
|
||||||
|
fprintf(fid,['Parameters Estimated: Mean Return Period (MRP) and Exceedance Probability (EP) \n']);
|
||||||
|
fprintf(fid,'------------------------------------------------------------------------------------\n');
|
||||||
|
fprintf(fid,['<Magnitude Scale Selected >: ', MScale,'\n']);
|
||||||
|
fprintf(fid,['<Time Unit >: ', Tunit,'\n']);
|
||||||
|
fprintf(fid,['<Magnitude Range >: ', num2str(Mc), ' to ', num2str(max(Cmag)),'\n']);
|
||||||
|
if strcmp(method,'GRT')==1 || strcmp(method,'NPT')==1
|
||||||
|
fprintf(fid,['<Maximum Magnitude >: ', num2str(HP(1).Mmax),'\n']);
|
||||||
|
else
|
||||||
|
fprintf(fid,['<Maximum Magnitude >: Unbounded','\n']);
|
||||||
|
end
|
||||||
|
fprintf(fid,['<Magnitude Distribution Model >: ', method,'\n']);
|
||||||
|
fprintf(fid,['<Magnitude (for EPP and MRP) >: ', num2str(MaG),'\n']);
|
||||||
|
fprintf(fid,['<Time Period (for EPR) >: ', num2str(Plength),' ',Tunit,'s','\n']);
|
||||||
|
fprintf(fid,['<Time Window Creation Mode >: ', winmode,'\n']);
|
||||||
|
if strcmp(winmode,'Time')==1
|
||||||
|
fprintf(fid,['< Window Size >: ', num2str(window_size),'(days) \n']);
|
||||||
|
fprintf(fid,['< Window Step >: ', num2str(dt),'(days) \n']);
|
||||||
|
elseif strcmp(winmode,'Events')==1
|
||||||
|
fprintf(fid,['< Window Size >: ', num2str(window_size),'(events) \n']);
|
||||||
|
fprintf(fid,['< Window Step >: ', num2str(dt),'(days) \n']);
|
||||||
|
elseif strcmp(winmode,'Graphical')==1
|
||||||
|
fprintf(fid,['< Window Size >: variable \n']);
|
||||||
|
fprintf(fid,['< Window Step >: variable \n']);
|
||||||
|
end
|
||||||
|
fprintf(fid,['<Overlapping Time Windows >: ', overlap,'\n']);
|
||||||
|
fprintf(fid,['<Bootstrap Iterations >: ', num2str(Nbst),'\n']);
|
||||||
|
fprintf(fid,'------------------------------------------------------------------------------------\n');
|
||||||
|
|
||||||
|
for j=1:numel(HP)
|
||||||
|
SN(j)=j;Nevents(j)=numel(time_windows(j).M);TS(j)=time_windows(j).Tstart;TE(j)=time_windows(j).Tend;
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
fprintf(fid,[' Set N Starting Date/Time Ending Date/Time events MRP MRP0.95CI EP E)0.95CI b-value b-value0.95CI \n']);
|
||||||
|
fprintf(fid,[' per ',Tunit, ' ',Tunit,'s' '\n']);
|
||||||
|
for i=1:numel(HP)
|
||||||
|
if strcmp(method,'GRU')==1 || strcmp(method,'GRT')==1;
|
||||||
|
fprintf(fid,['%4d %5d %s %s %9.3f %13.3f %13.3f - %13.3f %13.11f %13.11f - %13.11f %5.3f %5.3f %5.3f \n'],SN(i),Nevents(i),datestr(TS(i),0),datestr(TE(i),0),lambda(i),MRPer(i),...
|
||||||
|
MRPer_low(i),MRPer_high(i),ExPr(i),ExPr_low(i),ExPr_high(i),bval(i),HP(i).bCI(1),HP(i).bCI(2));
|
||||||
|
else
|
||||||
|
fprintf(fid,['%4d %5d %s %s %9.3f %13.3f %13.3f - %13.3f %13.11f %13.3f - %13.11f %s %s \n'],SN(i),Nevents(i),datestr(TS(i),0),datestr(TE(i),0),lambda(i),MRPer(i),...
|
||||||
|
MRPer_low(i),MRPer_high(i),ExPr(i),ExPr_low(i),ExPr_high(i),'NaN','NaN');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
fclose(fid);
|
||||||
|
|
||||||
|
% Save output structure time_window merged with HP
|
||||||
|
for i=1:length(HP)
|
||||||
|
SHA(i).Time=time_windows(i).Time;
|
||||||
|
SHA(i).M=time_windows(i).M;
|
||||||
|
SHA(i).Mmin=HP(i).mmin;
|
||||||
|
SHA(i).eps=HP(i).eps;
|
||||||
|
SHA(i).lambd=HP(i).lamb;
|
||||||
|
SHA(i).lambd_err=HP(i).lamb_err;
|
||||||
|
SHA(i).unit=HP(i).unit;
|
||||||
|
SHA(i).method=HP(i).method;
|
||||||
|
if strcmp(method,'GRU')==1 || strcmp(method,'GRT')==1
|
||||||
|
SHA(i).b=HP(i).b;
|
||||||
|
SHA(i).b_0025=HP(i).bCI(1);
|
||||||
|
SHA(i).b_0975=HP(i).bCI(2);
|
||||||
|
else
|
||||||
|
SHA(i).h=HP(i).h;
|
||||||
|
SHA(i).xx=HP(i).xx;
|
||||||
|
SHA(i).ambd=HP(i).ambd;
|
||||||
|
SHA(i).ierr=HP(i).ierr;
|
||||||
|
end
|
||||||
|
if strcmp(method,'GRT')==1 || strcmp(method,'NPT')==1
|
||||||
|
SHA(i).Mmax=HP(i).Mmax;
|
||||||
|
SHA(i).err=HP(i).err;
|
||||||
|
else
|
||||||
|
end
|
||||||
|
SHA(i).PDF=HP(i).PDF; %K29JAN2020
|
||||||
|
SHA(i).CDF=HP(i).CDF; %K29JAN2020
|
||||||
|
SHA(i).MRP=MRPer(i); %K03JUN2020
|
||||||
|
SHA(i).MRP_0025=MRPer_low(i); %K03JUN2020
|
||||||
|
SHA(i).MRP_0975=MRPer_high(i); %K03JUN2020
|
||||||
|
SHA(i).EP_=ExPr(i); %K03JUN2020
|
||||||
|
SHA(i).EP_0025=ExPr_low(i); %K03JUN2020
|
||||||
|
SHA(i).EP_0975=ExPr_high(i); %K03JUN2020
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
save('SHA.mat','SHA')
|
||||||
|
|
||||||
|
cd ../
|
||||||
Loading…
Reference in New Issue
Block a user