60 lines
2.4 KiB
Mathematica
60 lines
2.4 KiB
Mathematica
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% [T,m]=Max_credM_GRT(Td,Tu,dT,Mmin,lamb,eps,b,Mmax)
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%EVALUATES THE MAXIMUM CREDIBLE MAGNITUDE VALUES USING THE UPPER-BOUNDED
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% G-R 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 maximum credible magnitude values are calculated for periods of
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% length starting from Td up to Tu with step dT.
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%
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% INPUT:
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% Td - starting period length for maximum credible magnitude calculations
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% Tu - ending period length for maximum credible magnitude calculations
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% dT - period length step for maximum credible magnitude calculations
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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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%
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% OUTPUT:
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% T - vector of independent variable (period lengths) T=(Td:dT:Tu)
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% m - vector of maximum credible magnitudes of the same length as T
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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 [T,m]=Max_credM_GRT(Td,Tu,dT,Mmin,lamb,eps,b,Mmax)
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% -------------- VALIDATION RULES ------------- K_21NOV2016
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if dT<=0;error('Time Step must be greater than 0');end
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%----------------------------------------------------------
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T=(Td:dT:Tu)';
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beta=b*log(10);
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mian=(1-exp(-beta*(Mmax-Mmin+eps/2)));
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m=Mmin-eps/2-1/beta*log((1-(1-1./(lamb*T))*mian));
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end
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