100 lines
3.7 KiB
Matlab
100 lines
3.7 KiB
Matlab
% [x,z]=ExcProbGRT(opt,xd,xu,dx,y,Mmin,lamb,eps,b,Mmax)
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%
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%EVALUATES THE EXCEEDANCE PROBABILITY VALUES USING THE UPPER-BOUNDED G-R
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% LED MAGNITUDE DISTRIBUTION MODEL.
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%
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% AUTHOR: S. Lasocki 06/2014 within IS-EPOS project.
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%
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% DESCRIPTION: The assumption on the upper-bounded Gutenberg-Richter
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% relation leads to the upper truncated exponential distribution to model
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% magnitude distribution from and above the catalog completness level
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% Mmin. The shape parameter of this distribution, consequently the G-R
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% b-value and the end-point of the distriobution Mmax as well as the
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% activity rate of M>=Mmin events are calculated at start-up of the
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% stationary hazard assessment services in the upper-bounded
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% Gutenberg-Richter estimation mode.
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%
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% The exceedance probability of magnitude M' in the time period of
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% length T' is the probability of an earthquake of magnitude M' or greater
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% to occur in T'. Depending on the value of the parameter opt the
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% exceedance probability values are calculated for a fixed time period T'
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% and different magnitude values or for a fixed magnitude M' and different
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% time period length values. In either case the independent variable vector
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% starts from xd, up to xu with step dx. In either case the result is
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% returned in the vector z.
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%
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%INPUT:
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% opt - determines the mode of calculations. opt=0 - fixed time period
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% length (y), different magnitude values (x), opt=1 - fixed magnitude
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% (y), different time period lengths (x)
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% xd - starting value of the changeable independent variable
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% xu - ending value of the changeable independent variable
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% dx - step change of the changeable independent variable
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% y - fixed independent variable value: time period length T' if opt=0,
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% magnitude M' if opt=1
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% Mmin - lower bound of the distribution - catalog completeness level
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% lamb - mean activity rate for events M>=Mmin
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% eps - length of the round-off interval of magnitudes.
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% b - Gutenberg-Richter b-value
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% Mmax - upper limit of magnitude distribution
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%OUTPUT:
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% x - vector of changeable independent variable: magnitudes if opt=0,
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% time period lengths if opt=1,
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% x=(xd:dx:xu)
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% z - vector of exceedance probability values of the same length as x
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%
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% LICENSE
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% This file is a part of the IS-EPOS e-PLATFORM.
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%
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% This is free software: you can redistribute it and/or modify it under
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% the terms of the GNU General Public License as published by the Free
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% Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% This program is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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function [x,z]=ExcProbGRT(opt,xd,xu,dx,y,Mmin,lamb,eps,b,Mmax)
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% -------------- VALIDATION RULES ------------- K_21NOV2016
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if dx<=0;error('Step must be greater than 0');end
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%----------------------------------------------------------
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beta=b*log(10);
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if opt==0
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if xd<Mmin; xd=Mmin;end
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if xu>Mmax; xu=Mmax;end
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end
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x=(xd:dx:xu)';
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if opt==0
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z=1-exp(-lamb*y.*(1-Cdfgr(x,beta,Mmin-eps/2,Mmax)));
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else
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z=1-exp(-lamb*(1-Cdfgr(y,beta,Mmin-eps/2,Mmax)).*x);
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end
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end
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function [y]=Cdfgr(t,beta,Mmin,Mmax)
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%CDF of the truncated upper-bounded exponential distribution (truncated G-R
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% model
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% Mmin - catalog completeness level
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% Mmax - upper limit of the distribution
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% beta - the distribution parameter
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% t - vector of magnitudes (independent variable)
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% y - CDF vector
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mian=(1-exp(-beta*(Mmax-Mmin)));
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y=(1-exp(-beta*(t-Mmin)))/mian;
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idx=find(y>1);
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y(idx)=ones(size(idx));
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end
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