# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2018 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:`PhungEtAl2020SInter`
:class:`PhungEtAl2020SSlab`
:class:`PhungEtAl2020Asc`
"""
import math
import numpy as np
from openquake.hazardlib import const
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib.imt import PGA, SA
[docs]def get_stddevs(C):
"""
Return standard deviations.
"""
phi_tot = math.sqrt(C['phiss'] ** 2 + C['phis2s'] ** 2)
return [np.sqrt(C["tau"] ** 2 + phi_tot ** 2),
C["tau"],
phi_tot]
def _basin_term(region, C, vs30, z1pt0):
"""
Basin term [16].
"""
if region == 'glb':
return 0
if region == 'tw':
ez_1 = np.exp(-3.73 / 2 * np.log((vs30 ** 2 + 290.53 ** 2)
/ (1750 ** 2 + 290.53 ** 2)))
phi6 = 300
elif region in ['ca', 'jp']:
ez_1 = np.exp(-5.23 / 2 * np.log((vs30 ** 2 + 412.39 ** 2)
/ (1360 ** 2 + 412.39 ** 2)))
if region == 'ca':
phi6 = 300
else:
phi6 = 800
d_z1 = z1pt0 - ez_1
return np.where(
z1pt0 < 0, 0, C['phi5' + region] * (1 - np.exp(-d_z1 / phi6)))
def _distance_attenuation(s, region, aftershocks, C, mag, rrup, ztor):
"""
Distance scaling and attenuation term [8, 9, 10].
"""
del_c5 = C['dp'] * max(ztor / 50 - 20 / 50, 0) \
* (ztor > 20) * (mag < 7.0)
cns = (C['c5'] + del_c5) * math.cosh(C['c6'] * max(mag - C['c_hm'], 0))
f8 = s['c4'] * np.log(rrup + cns)
f9 = (s['c4_a'] - s['c4']) * np.log(np.sqrt(rrup ** 2
+ s['c_rb'] ** 2))
f10 = (C['c_g1' + region] + aftershocks * C['dc_g1as']
+ C['c_g2'] / (math.cosh(max(mag - C['c_g3'], 0)))) * rrup
return f8 + f9 + f10
def _fsof_ztor(C, mag, rake, ztor):
"""
Factors requiring type of fault.
"""
f234 = 0
if 30 <= rake <= 150:
e_ztor = (max(3.5384 - 2.60 * max(mag - 5.8530, 0), 0)) ** 2
# reverse fault [2]
f234 += C['c1_a'] \
+ C['c1_c'] / math.cosh(2 * max(mag - 4.5, 0))
else:
e_ztor = max(2.7482 - 1.7639 * max(mag - 5.5210, 0), 0) ** 2
if -120 <= rake <= -60:
# normal fault [3]
f234 += C['c1_b'] \
+ C['c1_d'] / math.cosh(2 * max(mag - 4.5, 0))
ztor = np.where(ztor < 0, e_ztor, ztor)
delta_ztor = ztor - e_ztor
# [4]
f234 += (C['c7'] + C['c7_b'] / math.cosh(2 * max(mag - 4.5, 0))) \
* delta_ztor
return f234, ztor
[docs]class PhungEtAl2020Asc(GMPE):
"""
Implements Phung et al. (2020) for crustal.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, SA])
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
DEFINED_FOR_REFERENCE_VELOCITY = 1130
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
# rx for hanging wall
REQUIRES_DISTANCES = {'rjb', 'rrup', 'rx'}
REQUIRES_RUPTURE_PARAMETERS = {'dip', 'mag', 'rake', 'ztor'}
REQUIRES_SITES_PARAMETERS = {'vs30', 'z1pt0'}
def __init__(self, region='glb', aftershocks=False, d_dpp=0, **kwargs):
super().__init__(region=region, aftershocks=aftershocks, d_dpp=d_dpp,
**kwargs)
# region options:
# 'glb', 'tw', 'ca', 'jp' (global, Taiwan, California, Japan)
self.region = region
# only for Taiwan region
self.aftershocks = aftershocks and region == 'tw'
# direct point parameter for directivity effect
self.d_dpp = d_dpp
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
s = self.CONSTANTS
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
lnmed, ztor = _fsof_ztor(C, ctx.mag, ctx.rake, ctx.ztor)
# main shock [1]
lnmed += C['c1']
# dip term [5]
lnmed += (C['c11'] + C['c11_b']
/ math.cosh(2 * max(ctx.mag - 4.5, 0))) \
* (math.cos(math.radians(ctx.dip)) ** 2)
# hanging wall term [12]
lnmed += (ctx.rx >= 0) * C['c9'] * math.cos(math.radians(ctx.dip))\
* (C['c9_a'] + (1 - C['c9_a']) * np.tanh(ctx.rx / C['c9_b']))\
* (1 - np.sqrt(ctx.rjb ** 2 + ztor ** 2) / (ctx.rrup + 1))
# directivity [11]
lnmed += C['c8'] \
* np.maximum(1 - np.maximum(ctx.rrup - 40, 0) / 30, 0) \
* min(max(ctx.mag - 5.5, 0) / 0.8, 1) \
* math.exp(s['c8_a'] * (ctx.mag - C['c8_b']) ** 2) \
* self.d_dpp
# fmag [6, 7]
lnmed += s['c2'] * (ctx.mag - 6)
lnmed += (s['c2'] - C['c3']) / C['c_n'] \
* math.log(1 + math.exp(C['c_n'] * (C['c_m'] - ctx.mag)))
lnmed += _distance_attenuation(
s, self.region, self.aftershocks, C, ctx.mag, ctx.rrup, ztor)
sa1130 = np.exp(lnmed)
# site response [14, 15]
lnmed += C['phi1' + self.region] * np.minimum(
np.log(ctx.vs30 / 1130), 0)
lnmed += C['phi2'] * (np.exp(C['phi3'] * (
np.minimum(ctx.vs30, 1130) - 360)) - math.exp(
C['phi3'] * (1130 - 360))) * np.log(
(sa1130 + C['phi4']) / C['phi4'])
# basin term [16]
lnmed += _basin_term(self.region, C, ctx.vs30, ctx.z1pt0)
mean[m] = lnmed
sig[m], tau[m], phi[m] = get_stddevs(C)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt c1 c1_a c1_b c1_c c1_d c3 c5 c6 c7 c7_b c8 c8_b c9 c9_a c9_b c11 c11_b c12 c12_b c_n c_m c_g2 c_g3 c_hm dp phi2 phi3 phi4 c_g1tw phi1tw dc_g1as c_g1ca phi1ca c_g1jp phi1jp c_g1glb phi1glb phi5tw phi5ca phi5jp tau phiss phis2s
PGA -1.4526 0.137929376 0 0.04272907 -0.165254064 1.4379 6.4551 0.4908 0.00803536 0.021034339 0.0000 0.4833 0.9228 0.1202 6.8607 -0.108037007 0.195951708 -1.282688908 0.029231406 12.14866822 5.50455 -0.007127092 4.225634814 3.0956 -6.785205271 -0.1417 -0.007010 0.102151 -0.0087980 -0.510745033 -0.00148591 -0.006937324 -0.484221897 -0.009554995 -0.535583503 -0.008207338 -0.505350491 0.07436 0.032134169 0.092181936 0.372991982 0.4397 0.3149
0.01 -1.4468 0.131008944 0 0.05491546 -0.164615502 1.4379 6.4551 0.4908 0.00803536 0.021034339 0.0000 0.4833 0.9228 0.1202 6.8607 -0.108037007 0.195951708 -1.282688908 0.029231406 12.14866822 5.51303 -0.007127092 4.225634814 3.0956 -6.750647967 -0.1417 -0.007010 0.102151 -0.0087980 -0.510415026 -0.001553994 -0.006982409 -0.481325676 -0.009621694 -0.527374167 -0.008266685 -0.504993164 0.07436 0.031948851 0.091289209 0.372455184 0.4388 0.3149
0.02 -1.4066 0.124713602 0 0.06599634 -0.166706035 1.4030 6.4551 0.4925 0.007592927 0.021638743 0.0000 1.2144 0.9296 0.1217 6.8697 -0.102071888 0.181778172 -1.219189069 0.029463211 12.24803407 5.51745 -0.007248737 4.230341898 3.0963 -6.716179208 -0.1364 -0.007279 0.108360 -0.0090670 -0.502941955 -0.001332937 -0.007105962 -0.473436602 -0.009678565 -0.509697529 -0.008372404 -0.497396753 0.07359 0.032083196 0.087461387 0.37404339 0.4391 0.3148
0.03 -1.3175 0.119040284 0 0.075907583 -0.19413385 1.3628 6.4551 0.4992 0.007250488 0.022052403 0.0000 1.6421 0.9396 0.1194 6.9113 -0.104638092 0.163170085 -1.129842391 0.029897695 12.53378414 5.51798 -0.007327856 4.236182109 3.0974 -6.681798923 -0.1403 -0.007354 0.119888 -0.0094510 -0.491366306 -0.001500854 -0.007654162 -0.460829876 -0.010021137 -0.481412435 -0.008893062 -0.484084547 0.07713 0.031462124 0.085075638 0.386799496 0.4451 0.3223
0.04 -1.1970 0.113983621 0 0.08465752 -0.2133523 1.3168 6.4551 0.5037 0.007006048 0.022283866 0.0000 1.9456 0.9661 0.1166 7.0271 -0.105159212 0.142063237 -1.009367871 0.030887621 12.99189704 5.51462 -0.007361759 4.250188668 3.0988 -6.647507037 -0.1591 -0.006977 0.133641 -0.0098320 -0.474484696 -0.001727377 -0.008235534 -0.442342385 -0.010348898 -0.433457113 -0.009471857 -0.464454841 0.08249 0.034324999 0.078902251 0.400724323 0.4516 0.3347
0.05 -1.0642 0.109535952 0 0.092384148 -0.246430796 1.2552 6.4551 0.5048 0.006860143 0.022340988 0.0000 2.1810 0.9794 0.1176 7.0959 -0.09694663 0.098053885 -0.864733627 0.03256833 13.65075358 5.50692 -0.007360913 4.303122568 3.1011 -6.613303475 -0.1862 -0.006467 0.148927 -0.0101940 -0.459984157 -0.002042414 -0.008985334 -0.404306111 -0.010606375 -0.35987791 -0.009965209 -0.441619243 0.09010 0.031188831 0.068543862 0.415407087 0.4555 0.3514
0.075 -0.7737 0.101016047 0 0.109529939 -0.240863766 1.1873 6.4551 0.5048 0.007007726 0.021712418 0.0000 2.6087 1.0260 0.1171 7.3298 -0.079174009 0.046296818 -0.543806592 0.034602039 15.71447541 5.43078 -0.007051574 4.446126947 3.1094 -6.52818049 -0.2538 -0.005734 0.190596 -0.0109620 -0.446396645 -0.002375719 -0.010178327 -0.385991895 -0.010285208 -0.227565057 -0.010848089 -0.418370706 0.10291 0.022101594 0.031193656 0.425118035 0.4558 0.3845
0.1 -0.5958 0.096066418 0 0.11002146 -0.22991286 1.2485 6.8305 0.5048 0.007246641 0.020031223 0.0000 2.9122 1.0177 0.1146 7.2588 -0.120806584 0.173997245 -0.372706269 0.035821539 16.77262242 5.42081 -0.005719182 4.610835161 3.2381 -6.443607867 -0.2943 -0.005604 0.230662 -0.0114520 -0.476282069 -0.002929177 -0.010859197 -0.431169291 -0.010753951 -0.279289236 -0.01136162 -0.448999162 0.12596 0.030782851 0.087905262 0.416469357 0.4497 0.3935
0.12 -0.5229 0.094563811 0 0.101539072 -0.171017133 1.3263 7.1333 0.5048 0.007455965 0.018584674 0.0000 3.1045 1.0008 0.1128 7.2372 -0.127655488 0.209294889 -0.361923917 0.028768271 16.77563032 5.46158 -0.00436511 4.723496543 3.3407 -6.376345237 -0.3077 -0.005696 0.253169 -0.0115970 -0.4931516 -0.002868694 -0.010797857 -0.449168755 -0.01131987 -0.348471281 -0.011514176 -0.469073942 0.11942 0.039955704 0.135335734 0.402380557 0.4429 0.3897
0.15 -0.5005 0.096331606 0 0.081268087 -0.13673324 1.4098 7.3621 0.5045 0.00770271 0.016544376 0.0000 3.3399 0.9801 0.1106 7.2109 -0.123958373 0.217339629 -0.406746707 0.025510321 16.18679785 5.55373 -0.002649555 4.878140618 3.4300 -6.276109027 -0.3113 -0.005845 0.266468 -0.0115790 -0.517925624 -0.002692777 -0.010419656 -0.468824982 -0.011809781 -0.440922758 -0.011431783 -0.499329355 0.10019 0.029374116 0.134933456 0.382176649 0.4382 0.3713
0.17 -0.5165 0.100411816 0 0.066332395 -0.085084587 1.4504 7.4365 0.5036 0.007798775 0.015412673 0.0000 3.4719 0.9652 0.1150 7.2491 -0.120234904 0.218818569 -0.430596429 0.026722101 15.84314399 5.60449 -0.001999512 4.981707053 3.4688 -6.209722535 -0.3062 -0.005959 0.265060 -0.0113030 -0.532965478 -0.002436738 -0.009960427 -0.497020598 -0.011945969 -0.509266123 -0.01109686 -0.521025765 0.08862 0.038181875 0.177785878 0.371903621 0.4385 0.3632
0.2 -0.5558 0.113754448 0 0.047001724 -0.078934463 1.5274 7.4972 0.5016 0.007823121 0.014410752 0.0000 3.6434 0.9459 0.1208 7.2988 -0.128554524 0.262936287 -0.517179185 0.024730499 15.01467129 5.64383 -0.001254506 5.066410859 3.5146 -6.110797854 -0.2927 -0.006141 0.255253 -0.0108190 -0.547665313 -0.002502554 -0.009509403 -0.524364877 -0.012104115 -0.595400115 -0.010650653 -0.542326413 0.08048 0.048572809 0.147248099 0.357414054 0.4395 0.3503
0.25 -0.6550 0.132878713 -0.034932397 0.018708157 0.000000286 1.6737 7.5416 0.4971 0.00807121 0.013237789 0.0000 3.8787 0.9196 0.1208 7.3691 -0.104990465 0.231024464 -0.683634944 0.01982955 12.69643148 5.66058 -0.00075041 5.21986472 3.5746 -5.947665543 -0.2662 -0.006439 0.231541 -0.0100190 -0.565549294 -0.002342412 -0.008707306 -0.573301197 -0.012011131 -0.708979498 -0.009707027 -0.570861885 0.08000 0.052015826 0.122156442 0.337728984 0.4433 0.3343
0.3 -0.7898 0.147312358 -0.052793111 0 0 1.8298 7.5600 0.4919 0.008395901 0.011957864 0.0000 4.0711 0.8829 0.1175 6.8789 -0.125335213 0.27034386 -0.85881890 0.018366075 10.44981091 5.65301 -0.000447155 5.32821979 3.6232 -5.786703295 -0.2405 -0.006704 0.207277 -0.0092670 -0.606451856 -0.002040929 -0.007614433 -0.60870418 -0.011583213 -0.792224081 -0.008888726 -0.616028974 0.08013 0.046520626 0.063742847 0.359262599 0.4498 0.3324
0.4 -1.0839 0.158162078 -0.096705093 0 0 2.0330 7.5735 0.4807 0.00927498 0.00946882 0.0000 4.3745 0.8302 0.1060 6.5334 -0.131458922 0.306056087 -1.167698273 0.015383491 6.802216656 5.62843 -0.000247246 5.201761713 3.6945 -5.47125339 -0.1975 -0.007125 0.165464 -0.0079030 -0.653316566 -0.001429428 -0.0063373 -0.672656694 -0.010377611 -0.867597085 -0.007382039 -0.667318538 0.07916 0.087073138 0.182053316 0.397614543 0.4590 0.3299
0.5 -1.3279 0.163112167 -0.121161057 0 0 2.2044 7.5778 0.4707 0.010165826 0.005799966 0.0991 4.6099 0.7884 0.1061 6.5260 -0.102606613 0.272617073 -1.414494521 0.015996408 4.41069375 5.59326 -0.000416797 5.187931728 3.7401 -5.164376146 -0.1633 -0.007435 0.133828 -0.0069990 -0.674933921 -0.001044295 -0.005515638 -0.733923523 -0.009392201 -0.922617109 -0.006165716 -0.693380936 0.07543 0.090202859 0.179683104 0.426900573 0.4703 0.3319
0.75 -1.9346 0.169389333 -0.158672494 0 0 2.4664 7.5808 0.4575 0.012793392 -0.003683309 0.1982 5.0376 0.6754 0.1000 6.5000 -0.072842909 0.265158493 -1.915634927 0.020897161 3.4064 5.56641 -0.001131462 4.877209058 3.7941 -4.4342041 -0.1028 -0.008120 0.085153 -0.0054380 -0.796961941 0 -0.003324985 -0.844223441 -0.007154876 -1.024238579 -0.004216545 -0.814440958 0.07573 0.068955592 0.355638284 0.466977537 0.4707 0.3384
1.0 -2.3932 0.177254643 -0.184203622 0 0 2.6194 7.5814 0.4522 0.013761922 -0.008131001 0.2154 5.3411 0.6196 0.1000 6.5000 -0.072286657 0.303895403 -2.405746274 0.013663365 3.1612 5.60836 -0.001741492 4.63975087 3.8144 -3.75596604 -0.0699 -0.008444 0.058595 -0.0045400 -0.884871551 0 -0.002895489 -0.932541432 -0.005643852 -1.052091854 -0.003321554 -0.896887535 0.07941 0.0901 0.446281385 0.495441465 0.4643 0.3480
1.5 -2.9412 0.17612706 -0.218917854 0 0 2.7708 7.5817 0.4501 0.013899933 -0.010287269 0.2154 5.7688 0.5101 0.1000 6.5000 -0.143270261 0.443286099 -3.076775856 0.012057836 2.8078 5.73551 -0.002427965 4.571203643 3.8284 -2.55026692 -0.0425 -0.007707 0.031787 -0.0036370 -0.958271065 0 -0.001749137 -0.98261014 -0.004814825 -1.088340342 -0.002382593 -0.966713194 0.12820 0.131818315 0.718324249 0.487074394 0.4568 0.3697
2.0 -3.2794 0.161185738 -0.218956446 0 0 2.8699 7.5818 0.4500 0.012559337 -0.008563294 0.2154 6.0723 0.3917 0.1000 6.5000 -0.171095562 0.520454201 -3.344039931 0.009195969 2.4631 5.85199 -0.002705545 4.425116502 3.8330 -1.536847647 -0.0302 -0.004792 0.019716 -0.0029726 -0.968084348 0 -0.001160868 -0.95905628 -0.005047271 -1.086834766 -0.002166838 -0.973218415 0.16687 0.171872332 0.767882913 0.477953808 0.4521 0.3826
3.0 -3.5891 0.112720638 -0.218956446 0 0 2.9293 7.5818 0.4500 0.009183764 -0.003058727 0.2154 6.5000 0.1244 0.1000 6.5000 -0.269171794 0.817526599 -3.621193267 0.006748877 2.2111 6.08195 -0.004107346 3.6219035 3.8361 -0.052837841 -0.0129 -0.001828 0.009643 -0.0024872 -0.96759396 0 -0.001243607 -0.913057084 -0.004730659 -1.017732708 -0.002207237 -0.965187761 0.20292 0.152581614 0.92637631 0.436531699 0.4524 0.3974
4.0 -3.8483 0.053953075 -0.218956446 0 0 3.0012 7.5818 0.4500 0.004796976 0.003919649 0.2154 6.8035 0.0086 0.1000 6.5000 -0.321537372 1.015932218 -3.870076534 0.004630924 1.9668 6.25683 -0.005776395 3.48626393 3.8369 0 -0.0016 -0.001523 0.005379 -0.0021234 -0.964753341 0 -0.001243607 -0.933614579 -0.003087049 -0.910235842 -0.001854414 -0.956076432 0.17899 0.187006538 0.881214487 0.449129802 0.4461 0.3983
5.0 -3.9458 0.053953075 -0.218956446 0 0 3.0012 7.5818 0.4500 0.001067909 0.013063958 0.2154 7.0389 0.0000 0.1000 6.5000 -0.344321787 0.892205391 -3.941815776 0 1.6671 6.39882 -0.007747849 3.277906342 3.8376 0 0.0000 -0.001440 0.003223 -0.0017638 -0.923270348 0 -0.001243607 -0.852999852 -0.001983904 -0.801 -0.001525789 -0.90692656 0.17368 0.206446726 0.891977077 0.46456534 0.4420 0.3985
7.5 -4.2514 0.053953075 -0.218956446 0 0 3.0012 7.5818 0.4500 -0.004234005 0.027920315 0.2154 7.4666 0.0000 0.1000 6.5000 -0.379466889 0.86436398 -4.193292591 0 1.5737 6.66908 -0.009141588 3.074948086 3.8380 0 0.0000 -0.001369 0.001134 -0.0010788 -0.85471647 0 -0.001243607 -0.731675782 0.000347579 -0.547 -0.001034361 -0.806827389 0.15176 0.264763991 0.83242751 0.505675779 0.4177 0.3878
10.0 -4.5075 0.053953075 -0.218956446 0 0 3.0012 7.5818 0.4500 -0.006203311 0.04195315 0.2154 7.7700 0.0000 0.1000 6.5000 -0.478010668 1.443597529 -4.33514388 0 1.5265 6.84353 -0.012633296 3.074948086 3.8380 0 0.0000 -0.001361 0.000515 -0.0007423 -0.770092758 0 -0.001243607 -0.555405551 0.001144285 -0.464975616 -0.000207365 -0.710919477 0.14062 0.228563922 0.689143919 0.448423418 0.3926 0.3717
""")
CONSTANTS = {'c2': 1.06, 'c4': -2.1, 'c4_a': -0.5, 'c8_a': -0.2695,
'c_rb': 50}
def _get_stddevs(region, C):
"""
Return standard deviations.
"""
phi_tot = np.sqrt(C['phiss4' + region] ** 2 + C['phis2s4' + region] ** 2)
return [np.sqrt(C["tau4" + region] ** 2 + phi_tot ** 2),
C["tau4" + region],
phi_tot]
def _fmag(region, C, mag, pga=False):
"""
Magnitude term.
"""
a4 = C['a4']
if region == 'jptw':
a4 += C['a4_del']
if mag <= C['mref']:
return a4 * (mag - C['mref']) + C['a13'] * (10 - mag) ** 2
return C['a5'] * (mag - C['mref']) + C['a13'] * (10 - mag) ** 2
def _fp(trt, region, s, C, mag, rrup, pga=False):
"""
Path term for subduction interface.
"""
a7, a14 = (C['a7'], C['a14']) if (
trt == const.TRT.SUBDUCTION_INTRASLAB) else (0, 0)
a1 = C['a1']
if region == 'jptw':
a1 += C['a1_del']
r = 'tw' if pga else region
return a1 + a7 + (C['a2'] + a14 + s['a3'] * (mag - 7.8)) \
* np.log(rrup + s['c4'] * math.exp(s['a9'] * (mag - 6))) \
+ C['a6' + r] * rrup
def _fsite(s, region, C, vs30, pga_1000):
"""
Non-linear component.
"""
result = C['a12' + region] * np.log(vs30 / C['vlin'])
idx = vs30 < C['vlin']
result[idx] += \
- C['b'] * np.log(pga_1000[idx] + s['c']) \
+ C['b'] * np.log(pga_1000[idx] + s['c']
* (vs30[idx] / C['vlin']) ** s['n'])
result[~idx] += C['b'] * s['n'] * np.log(vs30[~idx] / C['vlin'])
return result
def _fz1pt0(region, C, vs30, z1pt0):
"""
Basin depth term.
"""
result = np.zeros_like(z1pt0)
idx = np.where(z1pt0 >= 0)
if region == 'tw':
ez_1 = np.exp(-3.96 / 2 * np.log((vs30 ** 2 + 352.7 ** 2)
/ (1750 ** 2 + 352.7 ** 2)))
elif region == 'jptw':
ez_1 = np.exp(-5.23 / 2 * np.log((vs30 ** 2 + 412.39 ** 2)
/ (1360 ** 2 + 412.39 ** 2)))
result[idx] = C['a8' + region] * np.minimum(np.log(z1pt0[idx] / ez_1), 1)
return result
def _fztor(trt, C, ztor):
"""
Ztor factor for subduction interface.
"""
if trt == const.TRT.SUBDUCTION_INTRASLAB:
return C['a11'] * (min(ztor, 80) - 40)
return C['a10'] * (min(ztor, 40) - 20)
[docs]def pga_rock(trt, region, s, C_PGA, mag, rrup, ztor, vs30):
"""
PGA at Vs30 (as Taiwan region, C_PGA)
"""
f_mag = _fmag(region, C_PGA, mag, pga=True)
f_ztor = _fztor(trt, C_PGA, ztor)
f_p = _fp(trt, region, s, C_PGA, mag, rrup, pga=True)
# site function
f_site = C_PGA['a12tw'] * np.log(vs30 / C_PGA['vlin']) \
+ C_PGA['b'] * s['n'] * np.log(vs30 / C_PGA['vlin'])
return np.exp(f_mag + f_p + f_ztor + f_site)
[docs]class PhungEtAl2020SInter(GMPE):
"""
Implements Phung et al. (2020) for Subduction Interface.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
DEFINED_FOR_REFERENCE_VELOCITY = 1000
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
# rjb and rx not required for subduction
REQUIRES_DISTANCES = {'rrup'}
# dip and rake not required for subduction
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'ztor'}
REQUIRES_SITES_PARAMETERS = {'vs30', 'z1pt0'}
def __init__(self, region='jptw', **kwargs):
super().__init__(region=region, **kwargs)
# region options:
# 'jptw', 'tw' (Japan/Taiwan joined, Taiwan)
self.region = region
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
# extract dictionaries of coefficients specific to IM type
trt = self.DEFINED_FOR_TECTONIC_REGION_TYPE
C_PGA = self.COEFFS[PGA()]
s = self.CONSTANTS
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
f_mag = _fmag(self.region, C, ctx.mag)
f_ztor = _fztor(trt, C, ctx.ztor)
# path term
f_p = _fp(trt, self.region, s, C, ctx.mag, ctx.rrup)
# PGA at rock with Vs30 = 1000 m/s
pga_1000 = pga_rock(
trt, self.region, self.CONSTANTS, C_PGA, ctx.mag,
ctx.rrup, ctx.ztor, 1000)
# site effect
vs30 = np.minimum(ctx.vs30, 1000)
# non-linear component
f_site = _fsite(s, self.region, C, vs30, pga_1000)
# basin depth term
f_z1pt0 = _fz1pt0(self.region, C, vs30, ctx.z1pt0)
# median total and stddev
mean[m] = f_mag + f_p + f_ztor + f_site + f_z1pt0
sig[m], tau[m], phi[m] = _get_stddevs(self.region, C)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt a1 a1_del a2 a4 a4_del a5 a6jptw a6tw a7 a8jptw a8tw a10 a11 a12jptw a12tw a13 a14 b mref vlin tau4jptw phiss4jptw phis2s4jptw tau4tw phiss4tw phis2s4tw
PGA 4.4234 1.141899742 -1.552846733 0.441987425 0.328613796 0.03849929 -0.006794362 -0.000639314 0.681875399 -0.0075 -0.06276 0.016025291 0.014951807 0.8725 0.9321 -0.0256568 -0.011876681 -1.186 7.68 865.1 0.426469333 0.420489356 0.364038777 0.352252822 0.4130 0.3443
0.01 4.4415 1.152006702 -1.554174269 0.442328411 0.352192886 0.04033665 -0.006817094 -0.000607826 0.679916748 -0.0083 -0.06296 0.017193978 0.014930723 0.8733 0.9327 -0.0259617 -0.012409284 -1.186 7.68 865.1 0.424670673 0.420220542 0.364065617 0.349216437 0.4126 0.3441
0.02 4.4657 1.154339185 -1.555152194 0.436082809 0.367677006 0.04190178 -0.006816137 -0.000577165 0.697566565 -0.0083 -0.06325 0.01828222 0.01491224 0.8851 0.9395 -0.0262528 -0.016872732 -1.186 7.68 865.1 0.429099403 0.418935068 0.364403496 0.344782755 0.4113 0.3434
0.05 4.5788 1.515303155 -1.556049687 0.363261281 0.452541112 0.04509359 -0.007285287 -0.000490096 1.036117503 -0.0212 -0.08865 0.020842842 0.01487185 1.2671 1.2819 -0.0270426 -0.08510905 -1.346 7.71 1053.5 0.477262493 0.419356601 0.417921293 0.355375576 0.4095 0.3907
0.075 4.7290 1.904431142 -1.554562252 0.319469336 0.513739193 0.04623140 -0.007702243 -0.00042309 1.229932174 -0.0278 -0.09405 0.022162011 0.014854753 1.4426 1.4458 -0.0276048 -0.118005772 -1.471 7.77 1085.7 0.516365961 0.41012804 0.469674634 0.380828528 0.4003 0.4405
0.1 4.8676 1.945456526 -1.551165488 0.325896968 0.499522237 0.04819708 -0.007674043 -0.000361045 1.534436374 -0.0308 -0.09783 0.022757257 0.014852358 1.5605 1.5761 -0.0280794 -0.171218187 -1.624 7.77 1032.5 0.512863781 0.420066336 0.469076147 0.388526115 0.4094 0.4499
0.15 5.0388 1.787100626 -1.539140832 0.350561168 0.45427803 0.04325090 -0.00782682 -0.000251542 1.263659339 -0.0193 -0.08546 0.021797461 0.014893477 1.6752 1.7975 -0.0287650 -0.124720279 -1.931 7.78 877.6 0.461620132 0.433030041 0.437340846 0.368100637 0.4280 0.4104
0.2 5.1375 1.562515125 -1.520764226 0.401101385 0.363869484 0.03692059 -0.007547403 -0.000161014 1.177341019 -0.0087 -0.07070 0.020180594 0.015004213 1.8029 2.0219 -0.0291017 -0.120958201 -2.188 7.72 748.2 0.441284014 0.446059203 0.397161802 0.368643954 0.4438 0.3782
0.25 5.1106 1.356740101 -1.489051706 0.440779304 0.314270529 0.06597319 -0.007323965 -0.0000890 1.046187707 -0.0062 -0.06045 0.018556649 0.015194298 1.8843 2.2014 -0.0290970 -0.116255248 -2.381 7.62 654.3 0.434871493 0.456165064 0.384511586 0.375291842 0.4503 0.3559
0.3 5.0573 1.206013896 -1.464118878 0.486141867 0.282854636 0.06197944 -0.006976346 -0.0000354 0.783076472 -0.0045 -0.05366 0.016978648 0.01540766 1.9457 2.3240 -0.0287552 -0.077408811 -2.518 7.54 587.1 0.417105574 0.459407794 0.373773022 0.365828808 0.4532 0.3460
0.4 4.9001 0.760110718 -1.414761429 0.593885499 0.176621233 0.06979644 -0.006143907 0.0000145 0.56945524 0.0240 -0.01430 0.014555899 0.015952307 2.1491 2.4684 -0.0269993 -0.054966213 -2.657 7.42 503 0.412231943 0.452177558 0.372643333 0.383635154 0.4428 0.3546
0.5 4.7813 0.431629072 -1.383170353 0.719248494 0.077343234 0.08783791 -0.005504091 -0.0000421 0.437054838 0.0488 0.02962 0.012627818 0.016437613 2.2064 2.4869 -0.0235859 -0.034173086 -2.669 7.38 456.6 0.396422531 0.443446716 0.369406327 0.378521294 0.4383 0.3589
0.6 4.6503 0.214072689 -1.360022278 0.848115514 0.044354701 0.09612877 -0.004739568 -0.0000726 0.497762038 0.0640 0.06271 0.011191399 0.01652538 2.1559 2.3983 -0.0180673 -0.06069315 -2.599 7.36 430.3 0.403512982 0.4378372 0.397812841 0.369787955 0.4426 0.3812
0.75 4.3917 -0.01782956 -1.313716982 0.96522535 -0.012346815 0.10612877 -0.004285202 -0.000119483 0.262897537 0.0720 0.08935 0.009211979 0.016212382 1.9770 2.0760 -0.0150673 -0.039053473 -2.401 7.32 410.5 0.409058414 0.446095737 0.419424271 0.375567859 0.4556 0.3856
1.0 3.7367 -0.204991951 -1.236841977 1.174894012 -0.083175191 0.22744484 -0.003957479 -0.000199116 -0.126754198 0.0791 0.12475 0.006851124 0.015784785 1.4834 1.4846 -0.0031849 0.017806808 -1.955 7.25 400 0.428087961 0.44128784 0.408446403 0.375762655 0.4518 0.3692
1.5 2.8030 -0.382378342 -1.100570482 1.360979471 -0.226959428 0.16136621 -0.003379651 -0.000362196 -0.121313834 0.0864 0.16430 0.003814084 0.01399451 0.5185 0.3763 -0.0031849 -0.005705423 -1.025 7.25 400 0.440164103 0.42093392 0.420315802 0.39959416 0.4305 0.3703
2.0 1.8695 -0.352611734 -0.990254902 1.38307024 -0.206168741 0.22767232 -0.003469497 -0.000611716 -0.496676074 0.0905 0.17542 0.001733925 0.011927777 -0.3208 -0.4191 -0.0031849 0.053155037 -0.299 7.25 400 0.451402135 0.425797447 0.416797894 0.411391314 0.4413 0.3713
2.5 1.0159 -0.228719047 -0.896093506 1.382803719 -0.163340854 0.27153377 -0.003409644 -0.000869846 -0.513466165 0.0976 0.16991 0 0.009749305 -0.6999 -0.7674 -0.0031849 0.068765677 0 7.25 400 0.461009777 0.419978946 0.404296599 0.428877733 0.4379 0.3578
3.0 0.4461 -0.16534756 -0.818199517 1.391730855 -0.154799226 0.28822087 -0.003614492 -0.00106641 -0.600511124 0.0987 0.16367 0 0.007785629 -0.6077 -0.7527 -0.0031849 0.071577687 0 7.25 400 0.457681279 0.413207757 0.362727332 0.432913094 0.4302 0.3500
4.0 -0.4692 0.010400184 -0.730697376 1.36799257 -0.112793712 0.32589322 -0.003749858 -0.001185004 -0.425097306 0.0890 0.15060 0 0.00494863 -0.5689 -0.7088 -0.0031849 0.042405486 0 7.25 400 0.470193371 0.36936182 0.354026172 0.435941037 0.4268 0.3234
5.0 -0.8403 0.135306871 -0.734817372 1.379913313 -0.003105582 0.30383949 -0.003243671 -0.0009885 -0.528599974 0.0758 0.15646 0 0.003408571 -0.4942 -0.7305 -0.0031849 0.054712361 0 7.25 400 0.461834624 0.349936999 0.300771328 0.415321618 0.4286 0.3040
""")
CONSTANTS = {'a3': 0.1, 'a9': 0.25, 'c': 1.88, 'c4': 10, 'n': 1.18}
[docs]class PhungEtAl2020SSlab(PhungEtAl2020SInter):
"""
Implements Phung et al. (2020) for Subduction Intraslab.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB