Source code for openquake.hazardlib.gsim.yu_2013

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2022 GEM Foundation
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"""
Module exports :class:`YuEtAl2013Ms`, :class:`YuEtAl2013MsTibet`,
:class:`YuEtAl2013MsEastern`, :class:`YuEtAl2013MsStable`
:class:`YuEtAl2013Mw`, :class:`YuEtAl2013MwTibet`,
:class:`YuEtAl2013MwEastern`, :class:`YuEtAl2013MwStable`
"""
import numpy as np
from scipy.constants import g

from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA


[docs]def gc(coeff, mag): """ Returns the set of coefficients to be used for the calculation of GM as a function of earthquake magnitude :param coeff: A dictionary of parameters for the selected IMT :param mag: Magnitude value :returns: The set of coefficients """ if mag > 6.5: a1ca = coeff['ua'] a1cb = coeff['ub'] a1cc = coeff['uc'] a1cd = coeff['ud'] a1ce = coeff['ue'] a2ca = coeff['ia'] a2cb = coeff['ib'] a2cc = coeff['ic'] a2cd = coeff['id'] a2ce = coeff['ie'] else: a1ca = coeff['a'] a1cb = coeff['b'] a1cc = coeff['c'] a1cd = coeff['d'] a1ce = coeff['e'] a2ca = coeff['ma'] a2cb = coeff['mb'] a2cc = coeff['mc'] a2cd = coeff['md'] a2ce = coeff['me'] return a1ca, a1cb, a1cc, a1cd, a1ce, a2ca, a2cb, a2cc, a2cd, a2ce
[docs]def rbf(ra, coeff, mag): """ Calculate the median ground motion for a given magnitude and distance :param ra: Distance value [km] :param coeff: The set of coefficients :param mag: Magnitude value :returns: """ a1ca, a1cb, a1cc, a1cd, a1ce, a2ca, a2cb, a2cc, a2cd, a2ce = gc(coeff, mag) term1 = a1ca + a1cb * mag + a1cc * np.log(ra + a1cd*np.exp(a1ce*mag)) term2 = a2ca + a2cb * mag term3 = a2cd*np.exp(a2ce*mag) return np.exp((term1 - term2) / a2cc) - term3
[docs]def fnc(ra, *args): """ Function used in the minimisation problem. :param ra: Semi-axis of the ellipses used in the Yu et al. :returns: The absolute difference between the epicentral distance and the adjusted distance """ # # epicentral distance repi = args[0] # # azimuth theta = args[1] # # magnitude mag = args[2] # # coefficients coeff = args[3] # # compute the difference between epicentral distances rb = rbf(ra, coeff, mag) t1 = ra**2 * (np.sin(np.radians(theta)))**2 t2 = rb**2 * (np.cos(np.radians(theta)))**2 xx = ra * rb / (t1+t2)**0.5 return xx-repi
[docs]def get_ras(repi, theta, mag, coeff): """ Computes equivalent distance :param repi: Epicentral distance :param theta: Azimuth value :param mag: Magnitude :param coeff: GMPE coefficients """ rx = 100. ras = 200. # # calculate the difference between epicentral distances dff = fnc(ras, repi, theta, mag, coeff) while abs(dff) > 1e-3: # update the value of distance computed if dff > 0.: ras = ras - rx else: ras = ras + rx dff = fnc(ras, repi, theta, mag, coeff) rx = rx / 2. if rx < 1e-3: break return ras
[docs]class YuEtAl2013Ms(GMPE): """ Implements the Yu et al. (2013) GMPE used for the calculation of the 2015 version of the national seismic hazard maps for China. Note that magnitude supported is Ms. """ #: Supported tectonic region type is active shallow crust DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure types are peak ground velocity and #: peak ground acceleration DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA} #: Supported intensity measure component is geometric mean (supposed) DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types is total DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL} #: No site parameters required REQUIRES_SITES_PARAMETERS = set() #: Required rupture parameter is magnitude REQUIRES_RUPTURE_PARAMETERS = {'mag'} #: Required distance measures are epicentral distance and azimuth REQUIRES_DISTANCES = {'repi', 'azimuth'}
[docs] def compute(self, ctx, imts, mean, sig, tau, phi): """ See :meth:`superclass method <.base.GroundShakingIntensityModel.compute>` for spec of input and result values. """ # Set parameters mag = ctx.mag epi = ctx.repi theta = ctx.azimuth for m, imt in enumerate(imts): coeff = self.COEFFS[imt] a1ca, a1cb, a1cc, a1cd, a1ce, a2ca, a2cb, a2cc, a2cd, a2ce = gc( coeff, mag) # Get correction coefficients. Here for each site we find the # the geometry of the ellipses ras = [] for epi, theta in zip(ctx.repi, ctx.azimuth): res = get_ras(epi, theta, mag, coeff) ras.append(res) ras = np.array(ras) rbs = rbf(ras, coeff, mag) # # Compute values of ground motion for the two cases. The value of # 225 is hardcoded under the assumption that the hypocentral depth # corresponds to 15 km (i.e. 15**2) mean1 = (a1ca + a1cb * mag + a1cc * np.log((ras**2+225)**0.5 + a1cd * np.exp(a1ce * mag))) mean2 = (a2ca + a2cb * mag + a2cc * np.log((rbs**2+225)**0.5 + a2cd * np.exp(a2ce * mag))) # # Get distances x = (mean1 * np.sin(np.radians(ctx.azimuth)))**2 y = (mean2 * np.cos(np.radians(ctx.azimuth)))**2 mean_ = mean1 * mean2 / np.sqrt(x+y) if imt.string == "PGA": mean_ = np.exp(mean_)/g/100 elif imt.string == "PGV": mean_ = np.exp(mean_) else: raise ValueError('Unsupported IMT') mean[m] = np.log(mean_) sig[m] = coeff['sigma']
#: Coefficient table COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a b c d e ua ub uc ud ue ma mb mc md me ia ib ic id ie sigma PGA 4.1193 1.656 -2.389 1.772 0.424 7.8269 1.0856 -2.389 1.772 0.424 2.2609 1.6399 -2.118 0.825 0.465 6.003 1.0649 -2.118 0.825 0.465 0.5428 PGV -1.2581 1.932 -2.181 1.772 0.424 3.013 1.2742 -2.181 1.772 0.424 -3.1073 1.9389 -1.945 0.825 0.465 1.3087 1.2627 -1.945 0.825 0.465 0.6233 """)
[docs]class YuEtAl2013MsTibet(YuEtAl2013Ms): #: Supported tectonic region type is Tibetan plateau DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Coefficient table COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a b c d e ua ub uc ud ue ma mb mc md me ia ib ic id ie sigma PGA 5.4901 1.4835 -2.416 2.647 0.366 8.7561 0.9453 -2.416 2.647 0.366 2.3069 1.4007 -1.854 0.612 0.457 5.6511 0.8924 -1.854 0.612 0.457 0.5428 PGV -0.1472 1.7618 -2.205 2.647 0.366 3.9422 1.1293 -2.205 2.647 0.366 -2.9923 1.7043 -1.696 0.612 0.457 1.0189 1.0902 -1.696 0.612 0.457 0.6233 """)
[docs]class YuEtAl2013MsEastern(YuEtAl2013Ms): #: Supported tectonic region type is eastern part of China DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL #: Coefficient table COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a b c d e ua ub uc ud ue ma mb mc md me ia ib ic id ie sigma PGA 4.5517 1.5433 -2.315 2.088 0.399 8.1259 0.9936 -2.315 2.088 0.399 2.7048 1.518 -2.004 0.944 0.447 6.3319 0.9614 -2.004 0.944 0.447 0.5428 PGV -0.8349 1.8193 -2.103 2.088 0.399 3.3051 1.1799 -2.103 2.088 0.399 -2.6381 1.8124 -1.825 0.944 0.447 1.6376 1.1546 -1.825 0.944 0.447 0.6233 """)
[docs]class YuEtAl2013MsStable(YuEtAl2013Ms): #: Supported tectonic region type is stable part of China DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL #: Coefficient table COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a b c d e ua ub uc ud ue ma mb mc md me ia ib ic id ie sigma PGA 5.5591 1.1454 -2.079 2.802 0.295 8.5238 0.6854 -2.079 2.802 0.295 3.9445 1.0833 -1.723 1.295 0.331 6.187 0.7383 -1.723 1.295 0.331 0.5428 PGV 0.2139 1.4283 -1.889 2.802 0.295 3.772 0.8786 -1.889 2.802 0.295 -1.3547 1.3823 -1.559 1.295 0.331 1.5433 0.9361 -1.559 1.295 0.331 0.6233 """)
[docs]class YuEtAl2013Mw(YuEtAl2013Ms): """ This is a modified version of the original Yu et al. (2013) that supports the use of Mw rather than Ms. The Mw to Ms conversion equation used is the one proposed by Cheng et al. (2017). Note that this version does not propagate the uncertainty related to the magnitude conversion process. """
[docs] def compute(self, ctx, imts, mean, sig, tau, phi): """ See :meth:`superclass method <.base.GroundShakingIntensityModel.compute>` for spec of input and result values. """ # Set parameters magn = ctx.mag epi = ctx.repi theta = ctx.azimuth # Convert Mw into Ms if magn < 6.58: mag = (magn - 0.59) / 0.86 else: mag = (magn + 2.42) / 1.28 for m, imt in enumerate(imts): coeff = self.COEFFS[imt] a1ca, a1cb, a1cc, a1cd, a1ce, a2ca, a2cb, a2cc, a2cd, a2ce = gc( coeff, mag) # Get correction coefficients. Here for each site we find the # the geometry of the ellipses ras = [] for epi, theta in zip(ctx.repi, ctx.azimuth): res = get_ras(epi, theta, mag, coeff) ras.append(res) ras = np.array(ras) rbs = rbf(ras, coeff, mag) # Compute values of ground motion for the two cases. The value of # 225 is hardcoded under the assumption that the hypocentral depth # corresponds to 15 km (i.e. 15**2) mean1 = (a1ca + a1cb * mag + a1cc * np.log((ras**2+225)**0.5 + a1cd * np.exp(a1ce * mag))) mean2 = (a2ca + a2cb * mag + a2cc * np.log((rbs**2+225)**0.5 + a2cd * np.exp(a2ce * mag))) # # Get distances x = (mean1 * np.sin(np.radians(ctx.azimuth)))**2 y = (mean2 * np.cos(np.radians(ctx.azimuth)))**2 mean_ = mean1 * mean2 / np.sqrt(x+y) if imt.string == "PGA": mean_ = np.exp(mean_)/g/100 elif imt.string == "PGV": mean_ = np.exp(mean_) else: raise ValueError('Unsupported IMT') mean[m] = np.log(mean_) sig[m] = coeff['sigma']
[docs]class YuEtAl2013MwTibet(YuEtAl2013Mw): #: Supported tectonic region type is Tibetan plateau DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Coefficient table COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a b c d e ua ub uc ud ue ma mb mc md me ia ib ic id ie sigma PGA 5.4901 1.4835 -2.416 2.647 0.366 8.7561 0.9453 -2.416 2.647 0.366 2.3069 1.4007 -1.854 0.612 0.457 5.6511 0.8924 -1.854 0.612 0.457 0.5428 PGV -0.1472 1.7618 -2.205 2.647 0.366 3.9422 1.1293 -2.205 2.647 0.366 -2.9923 1.7043 -1.696 0.612 0.457 1.0189 1.0902 -1.696 0.612 0.457 0.6233 """)
[docs]class YuEtAl2013MwEastern(YuEtAl2013Mw): #: Supported tectonic region type is eastern part of China DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL #: Coefficient table COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a b c d e ua ub uc ud ue ma mb mc md me ia ib ic id ie sigma PGA 4.5517 1.5433 -2.315 2.088 0.399 8.1259 0.9936 -2.315 2.088 0.399 2.7048 1.518 -2.004 0.944 0.447 6.3319 0.9614 -2.004 0.944 0.447 0.5428 PGV -0.8349 1.8193 -2.103 2.088 0.399 3.3051 1.1799 -2.103 2.088 0.399 -2.6381 1.8124 -1.825 0.944 0.447 1.6376 1.1546 -1.825 0.944 0.447 0.6233 """)
[docs]class YuEtAl2013MwStable(YuEtAl2013Mw): #: Supported tectonic region type is stable part of China DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL #: Coefficient table COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a b c d e ua ub uc ud ue ma mb mc md me ia ib ic id ie sigma PGA 5.5591 1.1454 -2.079 2.802 0.295 8.5238 0.6854 -2.079 2.802 0.295 3.9445 1.0833 -1.723 1.295 0.331 6.187 0.7383 -1.723 1.295 0.331 0.5428 PGV 0.2139 1.4283 -1.889 2.802 0.295 3.772 0.8786 -1.889 2.802 0.295 -1.3547 1.3823 -1.559 1.295 0.331 1.5433 0.9361 -1.559 1.295 0.331 0.6233 """)