From 4589905ca0bf8afc439c112ca5f5dea975a3d8c7 Mon Sep 17 00:00:00 2001 From: Peter J Stafford Date: Sun, 23 Apr 2017 21:05:55 +0100 Subject: [PATCH 1/2] Add implementation of Stafford (2014) source scaling relation --- openquake/hazardlib/scalerel/stafford2014.py | 158 +++++++++++++++++++ 1 file changed, 158 insertions(+) create mode 100644 openquake/hazardlib/scalerel/stafford2014.py diff --git a/openquake/hazardlib/scalerel/stafford2014.py b/openquake/hazardlib/scalerel/stafford2014.py new file mode 100644 index 000000000..1ab954275 --- /dev/null +++ b/openquake/hazardlib/scalerel/stafford2014.py @@ -0,0 +1,158 @@ +# -*- coding: utf-8 -*- +# vim: tabstop=4 shiftwidth=4 softtabstop=4 +# +# Copyright (C) 2012-2017 GEM Foundation +# +# OpenQuake is free software: you can redistribute it and/or modify it +# under the terms of the GNU Affero General Public License as published +# by the Free Software Foundation, either version 3 of the License, or +# (at your option) any later version. +# +# OpenQuake 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 Affero General Public License for more details. +# +# You should have received a copy of the GNU Affero General Public License +# along with OpenQuake. If not, see . + +""" +Module :mod:`openquake.hazardlib.scalerel.stafford2014` implements :class:`Stafford2014`. +""" +from math import log, exp, sin, radians, pi, sqrt +from scipy.stats import norm, chi2 +from openquake.hazardlib.scalerel.base import BaseMSRSigma + + +class Stafford2014(BaseMSRSigma): + """ + Stafford magnitude -- rupture dimension relationships, + see 2014, Bull. Seism. Soc. Am., vol. 104, no. 4, pages 1620-1635. + + Implements magnitude-area, magnitude-width and magnitude length scaling relationships. + """ + def get_median_area(self, mag, rake, dip, seismogenic_depth): + """ + The values are a bilinear function of magnitude, + with the break in scaling depending upon the rake, dip and seismogenic depth. + + """ + assert -180 <= rake <= 180 + max_log_width = log(seismogenic_depth / sin(radians(dip))) + + if (-30 <= rake <= 30) or (rake >= 150) or (rake <= -150): + # strike slip + # coefficients for the mean rupture width + beta0 = -2.3000 + beta1 = 0.7167 + # coefficients for the area calculations + gamma0 = -9.3137 + elif rake > 0: + # thrust/reverse + # coefficients for the mean rupture width + beta0 = -3.8300 + beta1 = 0.9982 + # coefficients for the area calculations + gamma0 = -9.2749 + else: + # normal + # coefficients for the mean rupture width + beta0 = -4.1055 + beta1 = 1.0370 + # coefficients for the area calculations + gamma0 = -9.2483 + + mag_crit = (max_log_width - beta0) / beta1 + mean_log_area = gamma0 + log(10.0) * mag + if mag > mag_crit: + mean_log_area -= log(10.0)*(mag - mag_crit)/4.0 + + return exp(mean_log_area) + + def get_std_dev_area(self, mag, rake, dip, seismogenic_depth): + """ + Standard deviation for Stafford2014. + Relatively complicated expression due to effects of censoring upon the rupture width + """ + assert -180 <= rake <= 180 + max_log_width = log(seismogenic_depth / sin(radians(dip))) + + if (-30 <= rake <= 30) or (rake >= 150) or (rake <= -150): + # strike slip + # coefficients for prob of exceeding max width + alpha0 = -30.8395 + alpha1 = 5.4184 + alpha2 = -0.3044 + # coefficients for the mean rupture width + beta0 = -2.3000 + beta1 = 0.7167 + # uncensored variability + sigma_width_ucens = 0.2337 + # coefficients for the area calculations + sigma_length = 0.3138 + rho_length_width = 0.3104 + elif rake > 0: + # thrust/reverse + # coefficients for prob of exceeding max width + alpha0 = -35.8239 + alpha1 = 5.0680 + alpha2 = -0.0457 + # coefficients for the mean rupture width + beta0 = -3.8300 + beta1 = 0.9982 + # uncensored variability + sigma_width_ucens = 0.2285 + # coefficients for the area calculations + sigma_length = 0.2534 + rho_length_width = 0.1376 + else: + # normal + # coefficients for prob of exceeding max width + alpha0 = -36.9770 + alpha1 = 6.3070 + alpha2 = -0.1696 + # coefficients for the mean rupture width + beta0 = -4.1055 + beta1 = 1.0370 + # uncensored variability + sigma_width_ucens = 0.2509 + # coefficients for the area calculations + sigma_length = 0.3454 + rho_length_width = 0.4336 + + # transformed parameters for width prediction + z = alpha0 + alpha1 * mag + alpha2 * exp(max_log_width) + p = 1 / (1 + exp(-z)) + + # censored and uncensored mean + mean_log_width_ucens = beta0 + beta1 * mag + # define a random variate + psi = (max_log_width - mean_log_width_ucens) / sigma_width_ucens + + # define the chi-squared cdf value for psi**2 + psi2_cdf = chi2.cdf(psi**2, 3) + + # define the uncensored variance of the width + var_width_ucens = sigma_width_ucens**2 + # get normal cdf for psi + psi_cdf = norm.cdf(psi) + # define exponential function of psi + exp_psi = exp(-psi**2) / psi_cdf + + # compute the censored variance for the rupture width + if psi < 0: + var_width_cens = var_width_ucens / (2*pi * psi_cdf) * (pi*(1 - psi2_cdf) - exp_psi) + else: + var_width_cens = var_width_ucens / (2*pi * psi_cdf) * (pi*(1 + psi2_cdf) - exp_psi) + + # define the censored standard deviation + sigma_width_cens = sqrt(var_width_cens) + + # compute the standard deviation of the width + sigma_width = (1 - p) * sigma_width_cens + + # variance of the area + var_area = sigma_length**2 + sigma_width**2 + 2 * rho_length_width * sigma_length * sigma_width + + # return the standard deviation + return sqrt(var_area) From 672943f13e659248d8fb61c5dd3ab7393740408c Mon Sep 17 00:00:00 2001 From: Peter J Stafford Date: Sun, 23 Apr 2017 21:09:47 +0100 Subject: [PATCH 2/2] Update class comment --- openquake/hazardlib/scalerel/stafford2014.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/openquake/hazardlib/scalerel/stafford2014.py b/openquake/hazardlib/scalerel/stafford2014.py index 1ab954275..d7035ca2c 100644 --- a/openquake/hazardlib/scalerel/stafford2014.py +++ b/openquake/hazardlib/scalerel/stafford2014.py @@ -29,7 +29,7 @@ class Stafford2014(BaseMSRSigma): Stafford magnitude -- rupture dimension relationships, see 2014, Bull. Seism. Soc. Am., vol. 104, no. 4, pages 1620-1635. - Implements magnitude-area, magnitude-width and magnitude length scaling relationships. + Implements magnitude-area scaling relationships. """ def get_median_area(self, mag, rake, dip, seismogenic_depth): """