# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2020 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:`GulerceEtAl2017`
:class:`GulerceEtAl2017RegTWN`
:class:`GulerceEtAl2017RegITA`
:class:`GulerceEtAl2017RegMID`
:class:`GulerceEtAl2017RegCHN`
:class:`GulerceEtAl2017RegJPN`
"""
import numpy as np
from openquake.hazardlib import const
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib.imt import SA
[docs]class GulerceEtAl2017(GMPE):
"""
Implements the GKAS16 GMPE by Gulerce et al. (2017) for vertical-component
ground motions from the PEER NGA-West2 Project.
This model follows the same functional form as in ASK14 by Abrahamson et
al. (2014) with minor modifications to the underlying parameters.
Note that this is a more updated version than the GMPE described in the
original PEER Report 2013/24.
**Reference:**
Gulerce, Z., Kamai, R., Abrahamson, N., & Silva, W. (2017). Ground Motion
Prediction Equations for the Vertical Ground Motion Component Based on the
NGA-W2 Database. *Earthquake Spectra*, *33*(2), 499-528.
"""
#: Supported tectonic region type is active shallow crust, as part of the
#: NGA-West2 Database; re-defined here for clarity.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure type is spectral acceleration
#: at T=0.01 to 10.0 s; see Tables 1a and 1b.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {SA}
#: Supported intensity measure component is the
#: :attr:`~openquake.hazardlib.const.IMC.Vertical` direction component;
#: see title.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.VERTICAL
#: Supported standard deviation types are inter-event, intra-event
#: and total; see the section for "Equations for Standard Deviation".
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: Required site parameter is Vs30 only. Unlike in ASK14, the nonlinear
#: site response and Z1.0 scaling is not incorporated; see the section
#: for "Site Amplification Effects".
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude, rake, dip, ztor, and width;
#: see the section for "Functional Form of the Model".
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'dip', 'ztor', 'width'}
#: Required distance measures are Rrup, Rjb, Ry0 and Rx;
#: see the section for "Functional Form of the Model".
REQUIRES_DISTANCES = {'rrup', 'rjb', 'rx', 'ry0'}
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
for spec of input and result values.
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
"""
# get the necessary set of coefficients
C = self.COEFFS[imt]
# get the mean value
mean = (self._get_basic_term(C, rup, dists) +
self._get_faulting_style_term(C, rup) +
self._get_site_response_term(C, imt, sites.vs30) +
self._get_hanging_wall_term(C, dists, rup) +
self._get_top_of_rupture_depth_term(C, imt, rup)
)
mean += self._get_regional_term(C, imt, sites.vs30, dists.rrup)
# get standard deviations
stddevs = self._get_stddevs(C, imt, rup, sites, stddev_types, dists)
return mean, stddevs
def _get_basic_term(self, C, rup, dists):
"""
Compute and return basic form, see Equation 11 to 13.
"""
# Fictitious depth calculation, Equation 13. Unlike ASK14, the break in
# the c4m function is shifted to M6.0.
# The equation for c4m for M4.0-6.0 is different from GKAS16 EQS paper,
# but used the supplementary material instead after code verification.
if rup.mag > 6.:
c4m = C['c4']
elif rup.mag > 4.:
c4m = C['c4'] - ((C['c4'] - 1.) * (6. - rup.mag) / (6. - 4.))
else:
c4m = 1.
# Equation 12
R = np.sqrt(dists.rrup**2. + c4m**2.)
# basic form, Equation 11
base_term = C['a1'] * np.ones_like(dists.rrup) + C['a17'] * dists.rrup
if rup.mag >= self.CONSTS['m1']:
base_term += (C['a5'] * (rup.mag - self.CONSTS['m1']) +
C['a8'] * (8.5 - rup.mag)**2. +
(C['a2'] + C['a3'] * (rup.mag - self.CONSTS['m1'])) *
np.log(R))
elif rup.mag >= self.CONSTS['m2']:
base_term += (C['a4'] * (rup.mag - self.CONSTS['m1']) +
C['a8'] * (8.5 - rup.mag)**2. +
(C['a2'] + C['a3'] * (rup.mag - self.CONSTS['m1'])) *
np.log(R))
else:
base_term += (C['a4'] * (self.CONSTS['m2'] - self.CONSTS['m1']) +
C['a8'] * (8.5 - self.CONSTS['m2'])**2. +
C['a6'] * (rup.mag - self.CONSTS['m2']) +
(C['a2'] + C['a3'] * (self.CONSTS['m2'] -
self.CONSTS['m1'])) * np.log(R))
return base_term
def _get_faulting_style_term(self, C, rup):
"""
Compute and return faulting style term, that is the sum of the second
and third terms in Equation 1.
"""
# this implements Equations 3 and 4;
# f7 is the term for reverse fault mechanisms;
# f8 is the term for normal fault mechanisms.
if rup.mag > 5.:
f7 = C['a11']
f8 = C['a12']
elif rup.mag >= 4.:
f7 = C['a11'] * (rup.mag - 4.)
f8 = C['a12'] * (rup.mag - 4.)
else:
f7 = 0.0
f8 = 0.0
# ranges of rake values for each faulting mechanism are same with ASK14
return (f7 * float(rup.rake > 30 and rup.rake < 150) +
f8 * float(rup.rake > -150 and rup.rake < -30))
def _get_vs30star(self, vs30, imt):
"""
This computes and returns the tapered Vs30, in Equations 15 and 16.
"""
# compute the limiting v1 value, see Equation 16.
t = imt.period
if t <= 0.50:
v1 = 1500.0
elif t < 3.0:
# changed to -0.351 for additional significant figures
v1 = np.exp(-0.351 * np.log(t / 0.5) + np.log(1500.))
else:
v1 = 800.0
# set the vs30 star value, see Equation 15.
vs30_star = np.ones_like(vs30) * vs30
vs30_star[vs30 >= v1] = v1
return vs30_star
def _get_site_response_term(self, C, imt, vs30):
"""
Compute and return site response model term; see section
"Site Amplification Effects".
"""
# vs30 star, Equation 15
vs30_star = self._get_vs30star(vs30, imt)
# compute the site term
site_resp_term = np.zeros_like(vs30)
# Unlike ASK14, the site term here is independent of nonlinear response
# parameters b, c, and n.
vs30_rat = vs30_star / C['vlin']
site_resp_term = C['a10'] * np.log(vs30_rat)
return site_resp_term
def _get_hanging_wall_term(self, C, dists, rup):
"""
Compute and return hanging wall model term, see section on
"Hanging Wall Effects".
"""
if rup.dip == 90.0:
return np.zeros_like(dists.rx)
else:
Fhw = np.zeros_like(dists.rx)
Fhw[dists.rx > 0] = 1.
# Compute dip taper t1, Equation 6
T1 = np.ones_like(dists.rx)
T1 *= 60./45. if rup.dip <= 30. else (90.-rup.dip)/45.0
# Compute magnitude taper t2, Equation 7, with a2hw set to 0.2.
T2 = np.zeros_like(dists.rx)
a2hw = 0.2
if rup.mag >= 6.5:
T2 += (1. + a2hw * (rup.mag - 6.5))
elif rup.mag > 5.5:
T2 += (1. + a2hw * (rup.mag - 6.5) - (1. - a2hw) *
(rup.mag - 6.5)**2)
else:
T2 *= 0.
# Compute distance taper t3, Equation 8
T3 = np.zeros_like(dists.rx)
r1 = rup.width * np.cos(np.radians(rup.dip))
# The r2 term is different here from ASK14 where r2 = 3*r1.
r2 = 4. * r1
#
idx = dists.rx < r1
T3[idx] = (np.ones_like(dists.rx)[idx] * self.CONSTS['h1'] +
self.CONSTS['h2'] * (dists.rx[idx] / r1) +
self.CONSTS['h3'] * (dists.rx[idx] / r1)**2)
#
idx = ((dists.rx >= r1) & (dists.rx <= r2))
T3[idx] = 1. - (dists.rx[idx] - r1) / (r2 - r1)
# Compute depth taper t4, Equation 9
T4 = np.zeros_like(dists.rx)
#
if rup.ztor <= 10.:
T4 += (1. - rup.ztor**2. / 100.)
# Compute off-edge distance taper T5, Equation 10
# ry1 computed same as in ASK14
T5 = np.zeros_like(dists.rx)
ry1 = dists.rx * np.tan(np.radians(20.))
#
idx = (dists.ry0 - ry1) <= 0.0
T5[idx] = 1.
#
idx = (((dists.ry0 - ry1) > 0.0) & ((dists.ry0 - ry1) < 5.0))
T5[idx] = 1. - (dists.ry0[idx] - ry1[idx]) / 5.0
# Finally, compute the hanging wall term, Equation 5
return Fhw*C['a13']*T1*T2*T3*T4*T5
def _get_top_of_rupture_depth_term(self, C, imt, rup):
"""
Compute and return top-of-rupture depth term, see section
"Deph Scaling Effects".
"""
if rup.ztor >= 20.0:
return C['a15']
else:
return C['a15'] * rup.ztor / 20.0
def _get_regional_term(self, C, imt, vs30, rrup):
"""
As with ASK14, we assume California as the default region,
hence here the regional term is assumed = 0.
"""
return 0.
def _get_stddevs(self, C, imt, rup, sites, stddev_types, dists):
"""
Return standard deviations as described in section "Equations for
Standard Deviation".
"""
std_intra = self._get_intra_event_std(C, rup.mag)
std_inter = self._get_inter_event_std(C, rup.mag)
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(np.sqrt(std_intra ** 2 +
std_inter ** 2))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(std_intra)
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(std_inter)
return stddevs
def _get_intra_event_std(self, C, mag):
"""
Returns intra-event std dev, Phi, Equation 19.
"""
# Intra-event standard deviation model is simplified since the effect
# of nonlinearity of the rock motion is not incorporated
# (Equations 27-30 in ASK14 are not used).
phi = self._get_phi_regional(C, mag)
return phi
def _get_phi_regional(self, C, mag):
"""
Returns regional (default) intra-event standard deviation
"""
if mag < 4:
phi_reg = C['s1']
elif mag <= 6:
phi_reg = C['s1'] + (C['s2_noJP'] - C['s1']) / 2. * (mag - 4.)
else:
phi_reg = C['s2_noJP']
return phi_reg
def _get_inter_event_std(self, C, mag):
"""
Returns inter-event standard deviation, Tau, Equation 20
"""
tau = self._get_tau_regional(C, mag)
return tau
def _get_tau_regional(self, C, mag):
"""
Returns regional (default) inter-event standard deviation
"""
if mag < 5:
tau_reg = C['s3']
elif mag <= 7:
tau_reg = C['s3'] + (C['s4_noJP'] - C['s3']) / 2. * (mag - 5.)
else:
tau_reg = C['s4_noJP']
return tau_reg
#: Coefficients obtained from Tables 1a, 1b, 2, and 3 in
#: Gulerce et al. (2017). This coefficient table is also provided in a free
#: supplementary material distributed by the authors.
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT vlin c c4 a1 a2 a3 a4 a5 a6 a8 a10 a11 a12 a13 a14 a15 a17 a25 a26 a27 a28 a29 a31 a35 s1 s2_all s3 s4_all s2_noJP s4_noJP
0.01 660 2.4 8.6 1.3504 -1.087 0.275 0.121 -0.592 1.78 0 -0.397 -0.2 -0.12 0.67 -0.168 1.1 -0.0062 0.0015 -0.0007 0.0031 0.0035 -0.001 0.252 0.38 0.734 0.52 0.4402 0.3501 0.45 0.3219
0.02 680 2.4 8.6 1.4832 -1.106 0.275 0.111 -0.592 1.78 0 -0.36 -0.2 -0.12 0.67 -0.165 1.1 -0.0064 0.0017 -0.0007 0.0031 0.0035 -0.0009 0.215 0.343 0.734 0.5396 0.4546 0.3586 0.473 0.3328
0.03 770 2.4 8.6 1.7798 -1.15 0.275 0.105 -0.592 1.759 0 -0.34 -0.2 -0.12 0.67 -0.18 1.1 -0.0069 0.0016 -0.0008 0.0032 0.0037 -0.001 0.195 0.323 0.734 0.551 0.4958 0.3904 0.4865 0.3613
0.05 915 2.4 8.6 1.9652 -1.108 0.26 0.148 -0.559 1.708 0 -0.405 -0.2 -0.12 0.67 -0.212 1.1 -0.0092 0.0013 -0.0011 0.003 0.0047 -0.0006 0.26 0.388 0.734 0.5654 0.5365 0.4604 0.5035 0.4108
0.075 960 2.4 8.6 1.7821 -1.006 0.247 0.202 -0.531 1.689 0 -0.46 -0.2 -0.12 0.67 -0.112 1.1 -0.0102 -0.0009 -0.0021 0.003 0.0054 -0.0009 0.315 0.443 0.734 0.5769 0.5078 0.468 0.504 0.3945
0.1 910 2.4 8.6 1.6862 -0.952 0.239 0.258 -0.514 1.742 0 -0.474 -0.2 -0.12 0.67 -0.09 1.1 -0.0097 -0.0014 -0.0035 0.0026 0.0051 -0.0014 0.329 0.457 0.734 0.585 0.4714 0.4165 0.504 0.3621
0.15 740 2.4 8.6 1.6087 -0.94 0.227 0.309 -0.488 1.831 0 -0.474 -0.159 -0.12 0.67 -0.075 1.1 -0.0075 -0.0014 -0.0045 0.002 0.0041 -0.0024 0.329 0.457 0.734 0.585 0.4189 0.3713 0.504 0.3283
0.2 590 2.4 8.6 1.4836 -0.928 0.218 0.346 -0.469 1.937 0 -0.474 -0.129 -0.12 0.67 -0.075 1.1 -0.006 -0.0012 -0.0045 0.002 0.0038 -0.0029 0.329 0.457 0.7098 0.585 0.3955 0.3389 0.504 0.3058
0.25 495 2.4 8.6 1.3777 -0.928 0.211 0.374 -0.454 2.032 0 -0.474 -0.106 -0.12 0.62 -0.075 1.1 -0.0045 -0.0015 -0.0047 0.0015 0.0029 -0.0037 0.329 0.457 0.6909 0.585 0.3819 0.3138 0.504 0.2884
0.3 430 1.8 8.6 1.3091 -0.928 0.206 0.397 -0.443 2.109 0 -0.474 -0.088 -0.12 0.579 -0.075 1.031 -0.0036 -0.0015 -0.0044 0.0013 0.0025 -0.004 0.329 0.457 0.6756 0.585 0.3835 0.2932 0.504 0.2741
0.4 360 1.8 8.6 1.1237 -0.928 0.197 0.434 -0.352 2.227 0 -0.474 -0.059 -0.12 0.515 -0.075 0.922 -0.0024 -0.0015 -0.0034 0.0011 0.0016 -0.0041 0.329 0.457 0.6513 0.585 0.4 0.2608 0.504 0.2516
0.5 340 1.8 8.6 0.961 -0.928 0.19 0.462 -0.281 2.351 0 -0.49 -0.036 -0.12 0.465 -0.075 0.837 -0.0017 -0.0012 -0.0025 0.0007 0.0011 -0.0041 0.345 0.473 0.6325 0.585 0.4277 0.2357 0.5249 0.2342
0.75 330 1.8 8.6 0.6477 -0.928 0.178 0.513 -0.152 2.577 0 -0.575 0.006 -0.12 0.374 -0.06 0.683 -0.001 -0.0002 -0.0006 0 0.0004 -0.0038 0.43 0.558 0.5983 0.611 0.4686 0.19 0.563 0.2025
1 330 1.8 8.6 0.4024 -0.928 0.169 0.6 -0.061 2.7 0 -0.626 0.035 -0.12 0.31 0.017 0.574 -0.001 0 0 0 0.0004 -0.0031 0.481 0.609 0.5741 0.6295 0.5 0.19 0.59 0.18
1.5 330 1.8 8.6 0.0656 -0.928 0.157 0.838 0.068 2.821 0 -0.721 0.076 -0.12 0.219 0.147 0.42 -0.001 0 0 0 0.0004 -0.0023 0.576 0.704 0.5399 0.6555 0.5337 0.19 0.628 0.184
2 330 1.8 8.6 -0.2475 -0.928 0.148 1.006 0.159 2.869 0 -0.73 0.106 -0.12 0.155 0.246 0.311 -0.001 0 0 0 0.0004 -0.0018 0.585 0.713 0.5157 0.674 0.5337 0.19 0.655 0.184
3 330 1.8 8.6 -0.7131 -0.928 0.136 1.244 0.288 2.92 0 -0.649 0.147 -0.12 0.064 0.385 0.157 -0.001 0 0 0 0.0004 -0.0018 0.504 0.632 0.4815 0.7 0.5337 0.19 0.693 0.184
4 330 1.8 8.6 -1.0571 -0.928 0.128 1.413 0.494 2.95 0 -0.575 0.176 -0.12 0 0.484 0.048 -0.001 0 0 0 0.0004 -0.0018 0.43 0.558 0.4572 0.7 0.5337 0.19 0.72 0.184
5 330 1.8 8.6 -1.7084 -0.848 0.121 1.544 0.654 2.95 0 -0.5 0.199 -0.12 0 0.561 -0.037 -0.001 0 0 0 0.0004 -0.0018 0.355 0.483 0.4384 0.7 0.5337 0.19 0.72 0.184
6 330 1.8 8.6 -2.2393 -0.783 0.115 1.651 0.784 2.95 0 -0.427 0.218 -0.12 0 0.624 -0.106 -0.001 0 0 0 0.0004 -0.0018 0.282 0.41 0.4231 0.7 0.5337 0.19 0.72 0.184
7.5 330 1.8 8.6 -2.9456 -0.704 0.109 1.78 0.9425 2.95 0 -0.3185 0.2405 -0.12 0 0.7 -0.19 -0.001 0 0 0 0.0004 -0.0018 0.1735 0.3015 0.4044 0.7 0.5337 0.19 0.72 0.184
10 330 1.8 8.6 -4.0143 -0.6 0.1 1.95 1.15 2.95 0 -0.209 0.27 -0.12 0 0.8 -0.3 -0.001 0 0 0 0.0004 -0.0018 0.064 0.192 0.38 0.7 0.5337 0.19 0.72 0.184
""")
#: equation constants (that are IMT independent)
CONSTS = {
# m1, m2 specified at section "Moderate-to-Large Magnitude Scaling"
'm1': 6.75,
'm2': 5.50,
# h1, h2, h3 specified at section "Hanging Wall Effects"
'h1': +0.25,
'h2': +1.50,
'h3': -0.75,
}
[docs]class GulerceEtAl2017RegTWN(GulerceEtAl2017):
"""
Implements the GKAS16 GMPE by Gulerce et al. (2017) for vertical-component
ground motions from the PEER NGA-West2 Project.
Regional corrections for Taiwan
"""
def _get_regional_term(self, C, imt, vs30, rrup):
"""
Compute regional term for Taiwan, see section "Regionalization and
Aftershocks"
"""
vs30star = self._get_vs30star(vs30, imt)
return C['a31'] * np.log(vs30star/C['vlin']) + C['a25'] * rrup
[docs]class GulerceEtAl2017RegITA(GulerceEtAl2017):
"""
Implements the GKAS16 GMPE by Gulerce et al. (2017) for vertical-component
ground motions from the PEER NGA-West2 Project.
Regional corrections for Italy
"""
def _get_regional_term(self, C, imt, vs30, rrup):
"""
Compute regional term for Italy, see section "Regionalization and
Aftershocks"
"""
# removed regional linear vs30 scaling term since a32=0
return C['a26'] * rrup
[docs]class GulerceEtAl2017RegMID(GulerceEtAl2017):
"""
Implements the GKAS16 GMPE by Gulerce et al. (2017) for vertical-component
ground motions from the PEER NGA-West2 Project.
Regional corrections for Middle East
"""
def _get_regional_term(self, C, imt, vs30, rrup):
"""
Compute regional term for Middle East, see section "Regionalization and
Aftershocks"
"""
return C['a27'] * rrup
[docs]class GulerceEtAl2017RegCHN(GulerceEtAl2017):
"""
Implements the GKAS16 GMPE by Gulerce et al. (2017) for vertical-component
ground motions from the PEER NGA-West2 Project.
Regional corrections for China
"""
def _get_regional_term(self, C, imt, vs30, rrup):
"""
Compute regional term for China, see section "Regionalization and
Aftershocks"
"""
return C['a28'] * rrup
[docs]class GulerceEtAl2017RegJPN(GulerceEtAl2017):
"""
Implements the GKAS16 GMPE by Gulerce et al. (2017) for vertical-component
ground motions from the PEER NGA-West2 Project.
Regional corrections for Japan
"""
def _get_regional_term(self, C, imt, vs30, rrup):
"""
Compute regional term for Japan, see section "Regionalization and
Aftershocks"
"""
vs30star = self._get_vs30star(vs30, imt)
return C['a35'] * np.log(vs30star/C['vlin']) + C['a29'] * rrup
def _get_phi_regional(self, C, mag):
"""
Returns regional intra-event standard deviation (Phi) for Japan
"""
if mag < 4:
phi_reg = C['s1']
elif mag <= 6:
phi_reg = C['s1'] + (C['s2_all'] - C['s1']) / 2. * (mag - 4.)
else:
phi_reg = C['s2_all']
return phi_reg
def _get_tau_regional(self, C, mag):
"""
Returns regional inter-event standard deviation (Tau) for Japan
"""
if mag < 5:
tau_reg = C['s3']
elif mag <= 7:
tau_reg = C['s3'] + (C['s4_all'] - C['s3']) / 2. * (mag - 5.)
else:
tau_reg = C['s4_all']
return tau_reg