Implementation of Stafford (2014) source-scaling relation

openquake/hazardlib/scalerel/stafford2014.py

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+# -*- 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 <http://www.gnu.org/licenses/>.
+
+"""
+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 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)