# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2021 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,
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
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# You should have received a copy of the GNU Affero General Public License
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"""
Module exports :class:`AkkarCagnan2010`.
"""
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g
from openquake.hazardlib.gsim.boore_atkinson_2008 import BooreAtkinson2008
from openquake.hazardlib.gsim.base import CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
[docs]class AkkarCagnan2010(BooreAtkinson2008):
"""
Implements GMPE developed by Sinnan Akkar and Zehra Cagnan and
published as "A Local Ground-Motion Predictive Model for Turkey,
and Its Comparison with Other Regional and Global Ground-Motion
Models" (2010, Bulletin of the Seismological Society of America,
Volume 100, No. 6, pages 2978-2995). It extends
:class:`openquake.hazardlib.gsim.boore_atkinson_2008.BooreAtkinson2008`
because the linear and non-linear site effects are described by
the same site response function used in Boore and Atkinson 2008.
"""
#: Supported tectonic region type is active shallow crust (the
#: equations being developed for Turkey, see paragraph 'Strong Motion
#: Databank', p. 2981)
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: peak ground velocity and peak ground acceleration, see paragraph
# 'Functional Form', p. 2981
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
PGV,
SA
])
#: Supported intensity measure component is geometric mean
#: of two horizontal components :
#: attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, see paragraph
#: 'Functional Form', p. 2981.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types are inter-event, intra-event
#: and total, see Table 3, p. 2985.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: Required site parameters is Vs30.
#: See paragraph 'Functionl Form', p. 2981.
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude, and rake.
#: See paragraph 'Functional Form', p. 2981.
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'}
#: Required distance measure is Rjb.
#: See paragraph 'Functional Form', p. 2981.
REQUIRES_DISTANCES = {'rjb'}
[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 (for soil amplification)
# specific to required intensity measure type
C_SR = self.COEFFS_SOIL_RESPONSE[imt]
# compute median PGA on rock (in g), needed to compute non-linear site
# amplification
C = self.COEFFS_AC10[PGA()]
pga4nl = np.exp(
self._compute_mean(C, rup.mag, dists.rjb, rup.rake)) * 1e-2 / g
# compute full mean value by adding site amplification terms
# (but avoiding recomputing mean on rock for PGA)
if imt == PGA():
mean = (np.log(pga4nl) +
self._get_site_amplification_linear(sites.vs30, C_SR) +
self._get_site_amplification_non_linear(sites.vs30, pga4nl,
C_SR))
else:
C = self.COEFFS_AC10[imt]
mean = (self._compute_mean(C, rup.mag, dists.rjb, rup.rake) +
self._get_site_amplification_linear(sites.vs30, C_SR) +
self._get_site_amplification_non_linear(sites.vs30, pga4nl,
C_SR))
# convert from cm/s**2 to g for SA (PGA is already computed in g)
if imt.name == "SA":
mean = np.log(np.exp(mean) * 1e-2 / g)
stddevs = self._get_stddevs(C, stddev_types, num_sites=len(sites.vs30))
return mean, stddevs
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return standard deviations as defined in table 3, p. 2985.
"""
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(C['sigma'] ** 2 + C['tau'] ** 2)
stddevs.append(sigma_t + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(C['sigma'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['tau'] + np.zeros(num_sites))
return stddevs
def _compute_linear_magnitude_term(self, C, mag):
"""
Compute and return second term in equations (1a)
and (1b), pages 2981 and 2982, respectively.
"""
if mag <= self.c1:
# this is the second term in eq. (1a), p. 2981
return C['a2'] * (mag - self.c1)
else:
# this is the second term in eq. (1b), p. 2982
return C['a3'] * (mag - self.c1)
def _compute_quadratic_magnitude_term(self, C, mag):
"""
Compute and return third term in equations (1a)
and (1b), pages 2981 and 2982, respectively.
"""
return C['a4'] * (8.5 - mag) ** 2
def _compute_logarithmic_distance_term(self, C, mag, rjb):
"""
Compute and return fourth term in equations (1a)
and (1b), pages 2981 and 2982, respectively.
"""
return ((C['a5'] + C['a6'] * (mag - self.c1)) *
np.log(np.sqrt(rjb ** 2 + C['a7'] ** 2)))
def _compute_faulting_style_term(self, C, rake):
"""
Compute and return fifth and sixth terms in equations (1a)
and (1b), pages 2981 and 2982, respectively.
"""
Fn = float(rake > -135.0 and rake < -45.0)
Fr = float(rake > 45.0 and rake < 135.0)
return C['a8'] * Fn + C['a9'] * Fr
def _compute_mean(self, C, mag, rjb, rake):
"""
Compute and return mean value without site conditions,
that is equations (1a) and (1b), p.2981-2982.
"""
mean = (C['a1'] +
self._compute_linear_magnitude_term(C, mag) +
self._compute_quadratic_magnitude_term(C, mag) +
self._compute_logarithmic_distance_term(C, mag, rjb) +
self._compute_faulting_style_term(C, rake))
return mean
# c1 is the reference magnitude, fixed to 6.5
# see paragraph 'Functional Form', p. 2982
c1 = 6.5
#: Coefficient table (from Table 3, p. 2985)
#: sigma is the 'intra-event' standard deviation,
#: while tau is the 'inter-event' standard deviation
COEFFS_AC10 = CoeffsTable(sa_damping=5, table="""\
IMT a1 a2 a3 a4 a5 a6 a7 a8 a9 sigma tau
pgv 5.60931 -0.513 -0.695 -0.25800 -0.90393 0.21576 5.57472 -0.10481 0.07791 0.6154 0.526
pga 8.92418 -0.513 -0.695 -0.18555 -1.25594 0.18105 7.33617 -0.02125 0.01851 0.6527 0.5163
0.03 8.85984 -0.513 -0.695 -0.17123 -1.25132 0.18421 7.46968 -0.0134 0.03512 0.6484 0.5148
0.05 9.05262 -0.513 -0.695 -0.15516 -1.28796 0.1984 7.26552 0.02076 0.01484 0.6622 0.5049
0.075 9.56670 -0.513 -0.695 -0.13840 -1.38817 0.20246 8.03646 0.07311 0.02492 0.6849 0.5144
0.10 9.85606 -0.513 -0.695 -0.11563 -1.43846 0.21833 8.84202 0.11044 -0.00620 0.7001 0.5182
0.15 10.43715 -0.513 -0.695 -0.17897 -1.46786 0.15588 9.39515 0.03555 0.19751 0.6958 0.549
0.20 10.63516 -0.513 -0.695 -0.21034 -1.44625 0.11590 9.60868 -0.03536 0.18594 0.6963 0.5562
0.25 10.12551 -0.513 -0.695 -0.25565 -1.27388 0.09426 7.54353 -0.10685 0.13574 0.7060 0.5585
0.30 10.12745 -0.513 -0.695 -0.27020 -1.26899 0.08352 8.03144 -0.10685 0.13574 0.6718 0.5735
0.40 9.47855 -0.513 -0.695 -0.30498 -1.09793 0.06082 6.24042 -0.11197 0.16555 0.6699 0.5857
0.50 8.95147 -0.513 -0.695 -0.29877 -1.01703 0.09099 5.67936 -0.10118 0.23546 0.6455 0.5782
0.75 8.10498 -0.513 -0.695 -0.3349 -0.84365 0.08647 4.93842 -0.0456 0.10993 0.6463 0.6168
1.00 7.61737 -0.513 -0.695 -0.35366 -0.75840 0.09623 4.12590 -0.01936 0.19729 0.6485 0.6407
1.50 7.20427 -0.513 -0.695 -0.39858 -0.70134 0.11219 3.46535 -0.02618 0.21977 0.6300 0.6751
2.00 6.70845 -0.513 -0.695 -0.39528 -0.70766 0.12032 3.8822 -0.03215 0.20584 0.6243 0.6574
""")