# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2016 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 exports :class:`ZhaoEtAl2006Asc`, :class:`ZhaoEtAl2006SInter`,
:class:`ZhaoEtAl2006SSlab`, :class:`ZhaoEtAl2006SInterNSHMP2008` and
:class:`ZhaoEtAl2006SSlabNSHMP2014`
"""
from __future__ import division
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g
import copy
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
[docs]class ZhaoEtAl2006Asc(GMPE):
"""
Implements GMPE developed by John X. Zhao et al. and published as
"Attenuation Relations of Strong Ground Motion in Japan Using Site
Classification Based on Predominant Period" (2006, Bulletin of the
Seismological Society of America, Volume 96, No. 3, pages 898-913).
This class implements the equations for 'Active Shallow Crust'
(that's why the class name ends with 'Asc').
"""
#: Supported tectonic region type is active shallow crust, this means
#: that factors SI, SS and SSL are assumed 0 in equation 1, p. 901.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration, see paragraph 'Development of Base Model'
#: p. 901.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is geometric mean
#: of two horizontal components :
#: attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, see paragraph
#: 'Development of Base Model', p. 901.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types are inter-event, intra-event
#: and total, see equation 3, p. 902.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: Required site parameters is Vs30.
#: See table 2, p. 901.
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude, rake, and focal depth.
#: See paragraph 'Development of Base Model', p. 901.
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'rake', 'hypo_depth'))
#: Required distance measure is Rrup.
#: See paragraph 'Development of Base Model', p. 902.
REQUIRES_DISTANCES = set(('rrup', ))
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS_ASC[imt]
# mean value as given by equation 1, p. 901, without considering the
# interface and intraslab terms (that is SI, SS, SSL = 0) and the
# inter and intra event terms, plus the magnitude-squared term
# correction factor (equation 5 p. 909).
mean = self._compute_magnitude_term(C, rup.mag) +\
self._compute_distance_term(C, rup.mag, dists.rrup) +\
self._compute_focal_depth_term(C, rup.hypo_depth) +\
self._compute_faulting_style_term(C, rup.rake) +\
self._compute_site_class_term(C, sites.vs30) +\
self._compute_magnitude_squared_term(P=0.0, M=6.3, Q=C['QC'],
W=C['WC'], mag=rup.mag)
# convert from cm/s**2 to g
mean = np.log(np.exp(mean) * 1e-2 / g)
stddevs = self._get_stddevs(C['sigma'], C['tauC'], stddev_types,
num_sites=len(sites.vs30))
return mean, stddevs
def _get_stddevs(self, sigma, tau, stddev_types, num_sites):
"""
Return standard deviations as defined in equation 3 p. 902.
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigma_t = np.sqrt(sigma ** 2 + tau ** 2)
stddevs.append(sigma_t + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(sigma + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(tau + np.zeros(num_sites))
return stddevs
def _compute_magnitude_term(self, C, mag):
"""
Compute first term in equation 1, p. 901.
"""
return C['a'] * mag
def _compute_distance_term(self, C, mag, rrup):
"""
Compute second and third terms in equation 1, p. 901.
"""
term1 = C['b'] * rrup
term2 = - np.log(rrup + C['c'] * np.exp(C['d'] * mag))
return term1 + term2
def _compute_focal_depth_term(self, C, hypo_depth):
"""
Compute fourth term in equation 1, p. 901.
"""
# p. 901. "(i.e, depth is capped at 125 km)".
focal_depth = hypo_depth
if focal_depth > 125.0:
focal_depth = 125.0
# p. 902. "We used the value of 15 km for the
# depth coefficient hc ...".
hc = 15.0
# p. 901. "When h is larger than hc, the depth terms takes
# effect ...". The next sentence specifies h>=hc.
return float(focal_depth >= hc) * C['e'] * (focal_depth - hc)
def _compute_faulting_style_term(self, C, rake):
"""
Compute fifth term in equation 1, p. 901.
"""
# p. 900. "The differentiation in focal mechanism was
# based on a rake angle criterion, with a rake of +/- 45
# as demarcation between dip-slip and strike-slip."
return float(rake > 45.0 and rake < 135.0) * C['FR']
def _compute_site_class_term(self, C, vs30):
"""
Compute nine-th term in equation 1, p. 901.
"""
# map vs30 value to site class, see table 2, p. 901.
site_term = np.zeros(len(vs30))
# hard rock
site_term[vs30 > 1100.0] = C['CH']
# rock
site_term[(vs30 > 600) & (vs30 <= 1100)] = C['C1']
# hard soil
site_term[(vs30 > 300) & (vs30 <= 600)] = C['C2']
# medium soil
site_term[(vs30 > 200) & (vs30 <= 300)] = C['C3']
# soft soil
site_term[vs30 <= 200] = C['C4']
return site_term
def _compute_magnitude_squared_term(self, P, M, Q, W, mag):
"""
Compute magnitude squared term, equation 5, p. 909.
"""
return P * (mag - M) + Q * (mag - M) ** 2 + W
#: Coefficient table obtained by joining table 4 (except columns for
#: SI, SS, SSL), table 5 (both at p. 903) and table 6 (only columns for
#: QC WC TauC), p. 907.
COEFFS_ASC = CoeffsTable(sa_damping=5, table="""\
IMT a b c d e FR CH C1 C2 C3 C4 sigma QC WC tauC
pga 1.101 -0.00564 0.0055 1.080 0.01412 0.251 0.293 1.111 1.344 1.355 1.420 0.604 0.0 0.0 0.303
0.05 1.076 -0.00671 0.0075 1.060 0.01463 0.251 0.939 1.684 1.793 1.747 1.814 0.640 0.0 0.0 0.326
0.10 1.118 -0.00787 0.0090 1.083 0.01423 0.240 1.499 2.061 2.135 2.031 2.082 0.694 0.0 0.0 0.342
0.15 1.134 -0.00722 0.0100 1.053 0.01509 0.251 1.462 1.916 2.168 2.052 2.113 0.702 0.0 0.0 0.331
0.20 1.147 -0.00659 0.0120 1.014 0.01462 0.260 1.280 1.669 2.085 2.001 2.030 0.692 0.0 0.0 0.312
0.25 1.149 -0.00590 0.0140 0.966 0.01459 0.269 1.121 1.468 1.942 1.941 1.937 0.682 0.0 0.0 0.298
0.30 1.163 -0.00520 0.0150 0.934 0.01458 0.259 0.852 1.172 1.683 1.808 1.770 0.670 0.0 0.0 0.300
0.40 1.200 -0.00422 0.0100 0.959 0.01257 0.248 0.365 0.655 1.127 1.482 1.397 0.659 0.0 0.0 0.346
0.50 1.250 -0.00338 0.0060 1.008 0.01114 0.247 -0.207 0.071 0.515 0.934 0.955 0.653 -0.0126 0.0116 0.338
0.60 1.293 -0.00282 0.0030 1.088 0.01019 0.233 -0.705 -0.429 -0.003 0.394 0.559 0.653 -0.0329 0.0202 0.349
0.70 1.336 -0.00258 0.0025 1.084 0.00979 0.220 -1.144 -0.866 -0.449 -0.111 0.188 0.652 -0.0501 0.0274 0.351
0.80 1.386 -0.00242 0.0022 1.088 0.00944 0.232 -1.609 -1.325 -0.928 -0.620 -0.246 0.647 -0.0650 0.0336 0.356
0.90 1.433 -0.00232 0.0020 1.109 0.00972 0.220 -2.023 -1.732 -1.349 -1.066 -0.643 0.653 -0.0781 0.0391 0.348
1.00 1.479 -0.00220 0.0020 1.115 0.01005 0.211 -2.451 -2.152 -1.776 -1.523 -1.084 0.657 -0.0899 0.0440 0.338
1.25 1.551 -0.00207 0.0020 1.083 0.01003 0.251 -3.243 -2.923 -2.542 -2.327 -1.936 0.660 -0.1148 0.0545 0.313
1.50 1.621 -0.00224 0.0020 1.091 0.00928 0.248 -3.888 -3.548 -3.169 -2.979 -2.661 0.664 -0.1351 0.0630 0.306
2.00 1.694 -0.00201 0.0025 1.055 0.00833 0.263 -4.783 -4.410 -4.039 -3.871 -3.640 0.669 -0.1672 0.0764 0.283
2.50 1.748 -0.00187 0.0028 1.052 0.00776 0.262 -5.444 -5.049 -4.698 -4.496 -4.341 0.671 -0.1921 0.0869 0.287
3.00 1.759 -0.00147 0.0032 1.025 0.00644 0.307 -5.839 -5.431 -5.089 -4.893 -4.758 0.667 -0.2124 0.0954 0.278
4.00 1.826 -0.00195 0.0040 1.044 0.00590 0.353 -6.598 -6.181 -5.882 -5.698 -5.588 0.647 -0.2445 0.1088 0.273
5.00 1.825 -0.00237 0.0050 1.065 0.00510 0.248 -6.752 -6.347 -6.051 -5.873 -5.798 0.643 -0.2694 0.1193 0.275
""")
[docs]class ZhaoEtAl2006SInter(ZhaoEtAl2006Asc):
"""
Implements GMPE developed by John X. Zhao et al and published as
"Attenuation Relations of Strong Ground Motion in Japan Using Site
Classification Based on Predominant Period" (2006, Bulletin of the
Seismological Society of America, Volume 96, No. 3, pages
898-913). This class implements the equations for 'Subduction
Interface' (that's why the class name ends with 'SInter'). This
class extends the
:class:`openquake.hazardlib.gsim.zhao_2006.ZhaoEtAl2006Asc`
because the equation for subduction interface is obtained from the
equation for active shallow crust, by removing the faulting style
term and adding a subduction interface term.
"""
#: Supported tectonic region type is subduction interface, this means
#: that factors FR, SS and SSL are assumed 0 in equation 1, p. 901.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
#: Required rupture parameters are magnitude and focal depth.
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth'))
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS_ASC[imt]
C_SINTER = self.COEFFS_SINTER[imt]
# mean value as given by equation 1, p. 901, without considering the
# faulting style and intraslab terms (that is FR, SS, SSL = 0) and the
# inter and intra event terms, plus the magnitude-squared term
# correction factor (equation 5 p. 909)
mean = self._compute_magnitude_term(C, rup.mag) +\
self._compute_distance_term(C, rup.mag, dists.rrup) +\
self._compute_focal_depth_term(C, rup.hypo_depth) +\
self._compute_site_class_term(C, sites.vs30) + \
self._compute_magnitude_squared_term(P=0.0, M=6.3,
Q=C_SINTER['QI'],
W=C_SINTER['WI'],
mag=rup.mag) +\
C_SINTER['SI']
# convert from cm/s**2 to g
mean = np.log(np.exp(mean) * 1e-2 / g)
stddevs = self._get_stddevs(C['sigma'], C_SINTER['tauI'], stddev_types,
num_sites=len(sites.vs30))
return mean, stddevs
#: Coefficient table containing subduction interface coefficients,
#: taken from table 4, p. 903 (only column SI), and table 6, p. 907
#: (only columns QI, WI, TauI)
COEFFS_SINTER = CoeffsTable(sa_damping=5, table="""\
IMT SI QI WI tauI
pga 0.000 0.0 0.0 0.308
0.05 0.000 0.0 0.0 0.343
0.10 0.000 0.0 0.0 0.403
0.15 0.000 -0.0138 0.0286 0.367
0.20 0.000 -0.0256 0.0352 0.328
0.25 0.000 -0.0348 0.0403 0.289
0.30 0.000 -0.0423 0.0445 0.280
0.40 -0.041 -0.0541 0.0511 0.271
0.50 -0.053 -0.0632 0.0562 0.277
0.60 -0.103 -0.0707 0.0604 0.296
0.70 -0.146 -0.0771 0.0639 0.313
0.80 -0.164 -0.0825 0.0670 0.329
0.90 -0.206 -0.0874 0.0697 0.324
1.00 -0.239 -0.0917 0.0721 0.328
1.25 -0.256 -0.1009 0.0772 0.339
1.50 -0.306 -0.1083 0.0814 0.352
2.00 -0.321 -0.1202 0.0880 0.360
2.50 -0.337 -0.1293 0.0931 0.356
3.00 -0.331 -0.1368 0.0972 0.338
4.00 -0.390 -0.1486 0.1038 0.307
5.00 -0.498 -0.1578 0.1090 0.272
""")
[docs]class ZhaoEtAl2006SSlab(ZhaoEtAl2006Asc):
"""
Implements GMPE developed by John X. Zhao et al and published as
"Attenuation Relations of Strong Ground Motion in Japan Using Site
Classification Based on Predominant Period" (2006, Bulletin of the
Seismological Society of America, Volume 96, No. 3, pages
898-913). This class implements the equations for 'Subduction
Slab'. (that's why the class name ends with 'SSlab'). This class
extends the
:class:`openquake.hazardlib.gsim.zhao_2006.ZhaoEtAl2006Asc`
because the equation for subduction slab is obtained from the
equation for active shallow crust, by removing the faulting style
term and adding subduction slab terms.
"""
#: Supported tectonic region type is subduction interface, this means
#: that factors FR, SS and SSL are assumed 0 in equation 1, p. 901.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB
#: Required rupture parameters are magnitude and focal depth.
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth'))
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS_ASC[imt]
C_SSLAB = self.COEFFS_SSLAB[imt]
# to avoid singularity at 0.0 (in the calculation of the
# slab correction term), replace 0 values with 0.1
d = dists.rrup
d[d == 0.0] = 0.1
# mean value as given by equation 1, p. 901, without considering the
# faulting style and intraslab terms (that is FR, SS, SSL = 0) and the
# inter and intra event terms, plus the magnitude-squared term
# correction factor (equation 5 p. 909)
mean = self._compute_magnitude_term(C, rup.mag) +\
self._compute_distance_term(C, rup.mag, d) +\
self._compute_focal_depth_term(C, rup.hypo_depth) +\
self._compute_site_class_term(C, sites.vs30) +\
self._compute_magnitude_squared_term(P=C_SSLAB['PS'], M=6.5,
Q=C_SSLAB['QS'],
W=C_SSLAB['WS'],
mag=rup.mag) +\
C_SSLAB['SS'] + self._compute_slab_correction_term(C_SSLAB, d)
# convert from cm/s**2 to g
mean = np.log(np.exp(mean) * 1e-2 / g)
stddevs = self._get_stddevs(C['sigma'], C_SSLAB['tauS'], stddev_types,
num_sites=len(sites.vs30))
return mean, stddevs
def _compute_slab_correction_term(self, C, rrup):
"""
Compute path modification term for slab events, that is
the 8-th term in equation 1, p. 901.
"""
slab_term = C['SSL'] * np.log(rrup)
return slab_term
#: Coefficient table containing subduction slab coefficients taken from
#: table 4, p. 903 (only columns for SS and SSL), and table 6, p. 907
#: (only columns for PS, QS, WS, TauS)
COEFFS_SSLAB = CoeffsTable(sa_damping=5, table="""\
IMT SS SSL PS QS WS tauS
pga 2.607 -0.528 0.1392 0.1584 -0.0529 0.321
0.05 2.764 -0.551 0.1636 0.1932 -0.0841 0.378
0.10 2.156 -0.420 0.1690 0.2057 -0.0877 0.420
0.15 2.161 -0.431 0.1669 0.1984 -0.0773 0.372
0.20 1.901 -0.372 0.1631 0.1856 -0.0644 0.324
0.25 1.814 -0.360 0.1588 0.1714 -0.0515 0.294
0.30 2.181 -0.450 0.1544 0.1573 -0.0395 0.284
0.40 2.432 -0.506 0.1460 0.1309 -0.0183 0.278
0.50 2.629 -0.554 0.1381 0.1078 -0.0008 0.272
0.60 2.702 -0.575 0.1307 0.0878 0.0136 0.285
0.70 2.654 -0.572 0.1239 0.0705 0.0254 0.290
0.80 2.480 -0.540 0.1176 0.0556 0.0352 0.299
0.90 2.332 -0.522 0.1116 0.0426 0.0432 0.289
1.00 2.233 -0.509 0.1060 0.0314 0.0498 0.286
1.25 2.029 -0.469 0.0933 0.0093 0.0612 0.277
1.50 1.589 -0.379 0.0821 -0.0062 0.0674 0.282
2.00 0.966 -0.248 0.0628 -0.0235 0.0692 0.300
2.50 0.789 -0.221 0.0465 -0.0287 0.0622 0.292
3.00 1.037 -0.263 0.0322 -0.0261 0.0496 0.274
4.00 0.561 -0.169 0.0083 -0.0065 0.0150 0.281
5.00 0.225 -0.120 -0.0117 0.0246 -0.0268 0.296
""")
[docs]class ZhaoEtAl2006SInterNSHMP2008(ZhaoEtAl2006SInter):
"""
Extend :class:`ZhaoEtAl2006SInter` and fix hypocentral depth at 20 km
as defined the by National Seismic Hazard Mapping Project for the 2008 US
hazard model.
The calculation of the total standard deviation is done considering the
inter-event standard deviation as defined in table 5, page 903 of Zhao's
paper.
The class implement the equation as coded in ``subroutine zhao`` in
``hazSUBXnga.f`` Fotran code available at:
http://earthquake.usgs.gov/hazards/products/conterminous/2008/software/
"""
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
Call super class method with hypocentral depth fixed at 20 km
"""
# create new rupture context to avoid changing the original one
new_rup = copy.deepcopy(rup)
new_rup.hypo_depth = 20.
mean, stddevs = super(ZhaoEtAl2006SInterNSHMP2008, self). \
get_mean_and_stddevs(sites, new_rup, dists, imt, stddev_types)
return mean, stddevs
COEFFS_SINTER = CoeffsTable(sa_damping=5, table="""\
IMT SI QI WI tauI
pga 0.000 0.0 0.0 0.3976
0.05 0.000 0.0 0.0 0.4437
0.10 0.000 0.0 0.0 0.4903
0.15 0.000 -0.0138 0.0286 0.4603
0.20 0.000 -0.0256 0.0352 0.4233
0.25 0.000 -0.0348 0.0403 0.3908
0.30 0.000 -0.0423 0.0445 0.3790
0.40 -0.041 -0.0541 0.0511 0.3897
0.50 -0.053 -0.0632 0.0562 0.3890
0.60 -0.103 -0.0707 0.0604 0.4014
0.70 -0.146 -0.0771 0.0639 0.4079
0.80 -0.164 -0.0825 0.0670 0.4183
0.90 -0.206 -0.0874 0.0697 0.4106
1.00 -0.239 -0.0917 0.0721 0.4101
1.25 -0.256 -0.1009 0.0772 0.4021
1.50 -0.306 -0.1083 0.0814 0.4076
2.00 -0.321 -0.1202 0.0880 0.4138
2.50 -0.337 -0.1293 0.0931 0.4108
3.00 -0.331 -0.1368 0.0972 0.3961
4.00 -0.390 -0.1486 0.1038 0.3821
5.00 -0.498 -0.1578 0.1090 0.3766
""")
class ZhaoEtAl2006SSlabNSHMP2014(ZhaoEtAl2006SSlab):
"""
For the 2014 US National Seismic Hazard Maps the magnitude of Zhao et al.
(2006) for the subduction inslab events is capped at magnitude Mw 7.8
"""
def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS_ASC[imt]
C_SSLAB = self.COEFFS_SSLAB[imt]
# to avoid singularity at 0.0 (in the calculation of the
# slab correction term), replace 0 values with 0.1
d = dists.rrup
d[d == 0.0] = 0.1
if rup.mag > 7.8:
rup_mag = 7.8
else:
rup_mag = rup.mag
# mean value as given by equation 1, p. 901, without considering the
# faulting style and intraslab terms (that is FR, SS, SSL = 0) and the
# inter and intra event terms, plus the magnitude-squared term
# correction factor (equation 5 p. 909)
mean = self._compute_magnitude_term(C, rup_mag) +\
self._compute_distance_term(C, rup_mag, d) +\
self._compute_focal_depth_term(C, rup.hypo_depth) +\
self._compute_site_class_term(C, sites.vs30) +\
self._compute_magnitude_squared_term(P=C_SSLAB['PS'], M=6.5,
Q=C_SSLAB['QS'],
W=C_SSLAB['WS'],
mag=rup_mag) +\
C_SSLAB['SS'] + self._compute_slab_correction_term(C_SSLAB, d)
# convert from cm/s**2 to g
mean = np.log(np.exp(mean) * 1e-2 / g)
stddevs = self._get_stddevs(C['sigma'], C_SSLAB['tauS'], stddev_types,
num_sites=len(sites.vs30))
return mean, stddevs