# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2021 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,
# 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:`BoraEtAl2019`, :class:`BoraEtAl2019Drvt`
"""
import numpy as np
from openquake.hazardlib import const
from openquake.hazardlib.imt import FAS, DRVT
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
CONSTANTS = {"r0": 1,
"r1": 50,
"Mh": 5.0,
"Vc": 1100.,
"Vref": 800.,
"Mref": 4.5}
CONST_DURATION = {"M": 5.3,
"Vs30": 450}
def _get_source_term_duration(C, ctx):
above = ctx.mag > CONST_DURATION['M']
below = ctx.mag <= CONST_DURATION['M']
fsource = np.zeros_like(ctx.mag)
if np.any(below):
fsource[below] = C['d1'] * ctx.mag[below]
if np.any(above):
fsource[above] = (C['d1'] * CONST_DURATION['M'] +
C['d2'] * (ctx.mag[above] - CONST_DURATION['M']))
return fsource
def _get_path_term_duration(C, ctx):
return (C['d3'] + C['d4'] * (ctx.mag - 6)) * np.log(ctx.rrup)
def _get_site_term_duration(C, ctx):
fsite = np.ones_like(ctx.vs30)
below = ctx.vs30 <= CONST_DURATION['Vs30']
above = ctx.vs30 > CONST_DURATION['Vs30']
fsite[below] = C['d5'] * np.log(ctx.vs30[below])
fsite[above] = C['d5'] * np.log(CONST_DURATION['Vs30'])
return fsite
def _get_source_term(C, ctx):
above = ctx.mag > CONSTANTS['Mh']
below = ctx.mag <= CONSTANTS['Mh']
fsource = np.zeros_like(ctx.mag)
if np.any(above):
fsource[above] = (C['c3'] * (ctx.mag[above] - CONSTANTS['Mh']) +
C['c2'] * (8.5 - ctx.mag[above])**2)
if np.any(below):
fsource[below] = (C['c1'] * (ctx.mag[below] - CONSTANTS['Mh']) +
C['c2'] * (8.5 - ctx.mag[below])**2)
return fsource
def _get_finite_fault_factor(C, ctx):
h = np.ones_like(ctx.mag)
h[ctx.mag <= 4] = 2
selec = (ctx.mag > 4) & (ctx.mag <= 5)
h[selec] = C['c4'] - (C['c4'] - 1)*(5 - ctx.mag[selec])
h[ctx.mag > 5] = C['c4']
return h
def _get_path_term(C, ctx):
fff = _get_finite_fault_factor(C, ctx)
t1 = np.sqrt(ctx.rrup**2 + fff**2)
t2 = np.sqrt(CONSTANTS['r1']**2 + fff**2)
m = ctx.mag - CONSTANTS['Mref']
g = np.ones_like(ctx.rrup)
dshort = ctx.rrup <= 50
dlong = ctx.rrup > 50
g[dshort] = ((C['b1'] + C['c7']*m[dshort]) *
np.log(t1[dshort] / CONSTANTS['r0']))
g[dlong] = ((C['b1'] + C['c7']*m[dlong]) *
np.log(t2[dlong] / CONSTANTS['r0']) +
(C['b2'] + C['c7']*m[dlong]) *
np.log(t1[dlong] / t2[dlong]))
fpath = g + C['c5'] * (t1 - CONSTANTS['r0'])
return fpath
def _get_site_term(C, ctx):
fsite = np.ones_like(ctx.vs30)
below = ctx.vs30 < CONSTANTS['Vc']
above = ctx.vs30 >= CONSTANTS['Vc']
fsite[below] = C['c6']*np.log(ctx.vs30[below]/CONSTANTS['Vref'])
fsite[above] = C['c6']*np.log(CONSTANTS['Vc']/CONSTANTS['Vref'])
return fsite
def _get_mean_stddevs(C, ctx):
mean = C['c0'] \
+ _get_source_term(C, ctx) \
+ _get_path_term(C, ctx) \
+ _get_site_term(C, ctx)
phi = np.sqrt(C['phiss']**2 + C['phis2s']**2)
tau = C['tau']
sigma = np.sqrt(C['phiss']**2 + C['tau']**2 + C['phis2s']**2)
return mean, sigma, tau, phi
[docs]class BoraEtAl2019(GMPE):
"""
Implements the Fourier amplitude spectra model proposed by Bora et al.,
2019 as described in Bora, S.S., Cotton, F., & Scherbaum, F. (2019).
NGA-West2 empirical Fourier and duration models to generate adjustable
response spectra. Earthquake Spectra, 35(1), 61-93.
"""
#: Supported tectonic region type is active shallow crust, see title!
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {FAS}
#: Supported intensity measure component
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL
#: Supported standard deviation types
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT}
#: Required site parameters
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measures
REQUIRES_DISTANCES = {'rrup'}
[docs] def compute(self, ctx: np.recarray, imts, mean, sigma, tau, phi):
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
mean[m], sigma[m], tau[m], phi[m] = _get_mean_stddevs(C, ctx)
TMP = """
IMT c0 c1 c2 c3 c5 c6 c7 b1 b2 c4 tau phis2s phiss
FAS(0.100000) 2.502721022594540212 -3.019871021031180103 -0.699489878261237874 -0.753382658510122871 -0.000663526369472840 -0.447088569310536033 0.022658004530799799 -0.600521004853297069 -0.616534271818211077 4.695512756528509968 0.588480822628952960 0.433800904045682001 0.618731304409973037
FAS(0.106365) 2.493093234671220237 -2.950991457891970260 -0.698331013803817902 -0.702345053547144937 -0.000575375766529017 -0.473010336996122993 0.008472958415733959 -0.558480811812944955 -0.633469461477807028 4.957987757942290408 0.599289476605178950 0.448806612314632980 0.602762279580551064
FAS(0.113136) 2.200097814344990077 -2.752070777717450234 -0.665213553374781053 -0.538500924250570057 -0.000351531830222749 -0.512475440993337972 0.001339078393139250 -0.555657634468791017 -0.668379380917146992 5.483681114674491042 0.566032844137735913 0.466240117754409988 0.598172081119088928
FAS(0.120337) 2.034254128263019989 -2.515671395969700352 -0.635100535813052924 -0.399333072210403983 0.000067971644099580 -0.559914435537282928 -0.005286554502698210 -0.580985931071911987 -0.720196134071792060 5.849424106305820104 0.590205620260948027 0.480868159478248958 0.599358224410653007
FAS(0.127997) 1.141053806149149752 -1.603872458039000026 -0.533125263623092871 -0.093856302508275896 0.000567573193981721 -0.601643463294283976 -0.001066708448104160 -0.599125945606298949 -0.807875445247379087 5.479585767835110310 0.619351025773987929 0.513743008213592978 0.595123266923756056
FAS(0.136145) 1.097930883567810101 -1.443321597298969916 -0.513488251279912045 0.000711116989402148 0.000471478220459774 -0.649213142597603099 -0.007345942610395500 -0.621231011766171015 -0.806566765858632961 5.655956204038489865 0.609747368343163898 0.547180999785885969 0.579869067743471023
FAS(0.144811) 1.483404727375449816 -1.566081523484779803 -0.524719921624065000 -0.039643110238059401 0.000094656593009214 -0.685792316316777062 -0.014700859926340499 -0.668480204675433898 -0.770633955866142029 6.277617893464900511 0.577565513334653891 0.571829774674226021 0.574022902559107040
FAS(0.154028) 1.722276945857439845 -1.532084517949950042 -0.529629551808791010 -0.082756418078219401 -0.000249112362031415 -0.729455198663002125 -0.020041529947657601 -0.687414128008660974 -0.743207187104985012 7.372562584721709555 0.568067224541579985 0.586442004940022965 0.566853276929819905
FAS(0.163833) 1.460061832200230114 -1.045958970972379998 -0.486671789668866983 0.050119627190902502 0.000079904794452668 -0.757136513057866001 -0.019793028587677799 -0.721625679328829928 -0.805301862987097938 8.475856774799581217 0.567493377501720020 0.591049931388512140 0.560264230585062029
FAS(0.174261) 1.578707195963670040 -0.976147429486504903 -0.482629149981250005 0.020786800183539698 0.000335719591923292 -0.788054689949609033 -0.017829642992326700 -0.735112011550997035 -0.880703399477094084 9.400855804550859673 0.558559224687700029 0.595600285094823989 0.552429955919354954
FAS(0.185354) 1.182895724732189846 -0.585629210490318020 -0.437617651848761002 0.178991073840818971 -0.000098018019830675 -0.811825974939115902 -0.014908985772967599 -0.732046838351504969 -0.856809026037520072 9.634206805427080411 0.551310605088821015 0.595140813656870993 0.542029860790392948
FAS(0.197152) 1.028944878879419988 -0.401910184286409011 -0.418764009782740976 0.249816920751483956 -0.000102009340222675 -0.831471942021133059 -0.017980135641335201 -0.723225281340862058 -0.882838238408401921 9.488215067692301830 0.549276058939023981 0.589499687309888998 0.534847559293664010
FAS(0.209701) 1.008199243530689904 -0.281530366031195023 -0.403386697603251021 0.274326485622819971 0.000282642262354618 -0.857238397358372040 -0.013728189407098801 -0.748505165535349959 -0.954770187899388945 9.074101982989120074 0.537859463486816014 0.583163852557681994 0.526973023366866022
FAS(0.223050) 0.952214083535355083 -0.100524685664820007 -0.381329592135126072 0.292816061786009996 0.000465364877644078 -0.878500388719588021 -0.004891352642382350 -0.779028662494515967 -0.986529146516370026 8.908124929344319654 0.536849168508442998 0.592284479109781992 0.513297762497532117
FAS(0.237248) 1.178575027637770001 -0.160341960573721992 -0.390391125691087915 0.173209062877783038 0.000122741299879163 -0.904451559537362004 0.002093170920431040 -0.781467095295025005 -0.961359950176325029 8.723395906403499822 0.513502594537827983 0.602816924830573031 0.507707468277024954
FAS(0.252349) 0.708780135345348006 0.248824882663123970 -0.345601421855248003 0.325379468791085036 -0.000450021263163198 -0.912880947534275955 0.000957617117364880 -0.754971372196290069 -0.922064611722420047 8.629659190302980676 0.493815493038287034 0.613268572027439895 0.502845184828948022
FAS(0.268412) 1.004978293941600098 0.122070719138283004 -0.364488055989922954 0.230865142691424968 -0.000863719788451891 -0.911890525934737961 -0.005947828907500821 -0.734667926891354073 -0.891611724916564929 8.583764776695399945 0.481502175277732092 0.621305501892941092 0.496708426688614035
FAS(0.285497) 1.261065086886659969 0.032291382824867002 -0.375802863118586017 0.152242049392573991 -0.001050919809684140 -0.915325187417972086 -0.005031269658473920 -0.744518105837879030 -0.886561792470585974 8.283252334204579626 0.467006407858811035 0.631639083264063927 0.486605406036418997
FAS(0.303670) 1.297380503118820139 0.092338844851424198 -0.368150181936367948 0.123975140360036998 -0.000851208585344156 -0.932075059721235943 0.000869549927931463 -0.759432872154474081 -0.907780153703750980 7.922853183533959509 0.465368669782417033 0.637448521710694993 0.481833131186140018
FAS(0.323000) 1.562149231571200003 -0.059743320080940993 -0.379727531053058953 -0.017064169449521199 -0.000373385303942172 -0.952464846372410912 0.011775101901495701 -0.781885072640022050 -0.954932005583784993 7.194634306341050056 0.464928949482427023 0.644505686093211017 0.477795924429797958
FAS(0.343560) 1.769220056094679805 -0.211335436633630025 -0.393160326784775027 -0.168477891788259004 -0.000611414891522460 -0.975668984549608931 0.020777065383791701 -0.769297708576439865 -0.936470115592560881 6.413037582106531076 0.475511785777099960 0.650128494282875002 0.471975520949308947
FAS(0.365429) 1.890658457580830065 -0.250479609268315973 -0.396678244501707911 -0.237744597416399972 -0.001480812495483090 -0.999728230130709994 0.022317840721777799 -0.759166148298237919 -0.833776534892909926 6.521672344910610875 0.472457945049025996 0.648981901767755054 0.469485760759561055
FAS(0.388689) 2.130683801531799926 -0.129224100574196976 -0.389769945851931032 -0.134336064221033002 -0.001105609259912660 -1.020442296384320047 -0.001383633794928650 -0.828360818749292904 -0.856438740963645029 8.918801729001259559 0.459026976490558958 0.643222753515050094 0.474264953191637917
FAS(0.413431) 2.361291117517209770 -0.266048169011476987 -0.398039368389469961 -0.235029873463643985 -0.000864282977971807 -1.029346821105540100 0.005013360103172870 -0.849435354935159093 -0.892611916330538935 8.863510249344338732 0.443919409274569021 0.641078776738296940 0.466337543427628953
FAS(0.439747) 2.526447974390619855 -0.353975835222572033 -0.400915885530191085 -0.318870876163908024 -0.001224570944282310 -1.034310491376940089 0.016244390866307402 -0.864688750589019950 -0.866882599537526999 8.738874989287820583 0.427872055437270027 0.641955716229769102 0.459823324936523947
FAS(0.467739) 2.712478114489979664 -0.424865222634677964 -0.406352496140182984 -0.392185019107090971 -0.001676935073627110 -1.045025388091409990 0.019552411280142599 -0.868453459478694012 -0.821506139803228064 9.011041861994778301 0.407666800569367049 0.644818749877216102 0.449622751562542000
FAS(0.497512) 2.612817885317419986 -0.300817838380562974 -0.389129948300667994 -0.356463682507150048 -0.001903834554617320 -1.059898022662359995 0.020111037809693699 -0.866729659196408986 -0.804309308380740995 9.330571830482599083 0.398756355757518999 0.646515930274845996 0.444090430549561987
FAS(0.529180) 2.319697295967570128 -0.114681771567168009 -0.357296547665871989 -0.283039180205739038 -0.002275824888184850 -1.080105908553409932 0.028976951643349701 -0.873671516399949000 -0.776718444834420874 8.836028170859311359 0.410077002109618949 0.646757617417074937 0.443034930494605017
FAS(0.562864) 2.334835881340250108 -0.049313740379160899 -0.346319346860950950 -0.296059101732377983 -0.002658851865653740 -1.078860296535770091 0.034576760290465497 -0.882866419973704075 -0.757249023460896953 8.566387509598150984 0.413933747417838005 0.647490109191039998 0.441455359253865975
FAS(0.598692) 2.397870433313529670 0.036464778620993801 -0.337456912147471033 -0.290048361734939975 -0.003081197957075320 -1.065418022810560084 0.035405459405754500 -0.897131778136861069 -0.731072144316156969 8.022384131279400421 0.419604168869344984 0.641890170333777044 0.443352869728790011
FAS(0.636801) 2.647084206513470317 -0.114577619003008002 -0.351190994109601973 -0.353195532951641022 -0.003369797210788650 -1.074561613480760069 0.032901720359310299 -0.908839038316000991 -0.701560400979207022 7.623680651728860447 0.418915052516563025 0.637685203207327023 0.441449931279451979
FAS(0.677336) 2.848014506048390349 -0.236295421340618983 -0.360716790531181997 -0.424204132852936011 -0.003631787740873220 -1.085634757141869855 0.033817073659735797 -0.918273929680213041 -0.672746429172529026 7.153077243850329836 0.417074079153188004 0.636161990923952980 0.436686605477567991
FAS(0.720450) 2.943613830263649866 -0.323764928081191006 -0.363214400127210013 -0.492163282281458947 -0.004122136278680030 -1.072912856768720058 0.042180685736825499 -0.915610098340040035 -0.636083370189713948 6.597247041429250558 0.409386910756943001 0.633402620664181959 0.435368977526132017
FAS(0.766309) 2.912696421358130117 -0.334542473972756049 -0.356047934271072952 -0.502258620691582003 -0.004653549324892010 -1.065518668249830103 0.048036106590697701 -0.913443241917395010 -0.596759536142490998 6.467297784875010613 0.403887670901603990 0.631698797055604944 0.435412517771909979
FAS(0.815088) 2.835456438076859875 -0.262488866521023045 -0.342249150602167984 -0.479608629209481052 -0.005298496912870950 -1.067293072914740071 0.050056509299579402 -0.915190368437207913 -0.539470281562923981 6.199514964925490368 0.400224214996387939 0.632177321314288942 0.433291755768260012
FAS(0.866971) 2.652585072909509734 -0.090136467423734698 -0.315409372553206002 -0.394593019481305984 -0.005770312971332490 -1.062613777828480099 0.053941843560772702 -0.934394957191602038 -0.508114904395530975 6.263060281637430116 0.408389268483085044 0.626971944616180998 0.432250367441257999
FAS(0.922156) 2.631964613958559962 -0.020550023283345500 -0.301797999431991038 -0.366646074526873034 -0.005996303574383100 -1.058997149531550219 0.056845965974488502 -0.956149528534425031 -0.501033408218898968 6.867407293350820119 0.403314713896149979 0.620558747856974957 0.431108801487243898
FAS(0.980855) 2.616111224985009809 -0.001736303354988020 -0.293826745566638015 -0.366779374517169965 -0.006359333893512661 -1.054700436683519982 0.061407562294999198 -0.962545827687454114 -0.473457507902477093 7.125266173481990428 0.397364797092185029 0.617919560226579012 0.428981857938473987
FAS(1.043289) 2.316386014099700130 0.198838918139166015 -0.263258910599950047 -0.267676866006804015 -0.007021153329969000 -1.040763493717610011 0.067259446338629000 -0.966125669257194120 -0.407852698280496029 6.944847976813269597 0.407264417147701008 0.613527900523678005 0.427656304267155007
FAS(1.109698) 2.241021726599170094 0.264156617591023990 -0.250976389936497013 -0.253382750500576959 -0.007861745870259800 -1.026116412623020002 0.070970230498249395 -0.964207513518117953 -0.319211322174382028 6.582391068275000201 0.395521004368949991 0.604894397041107923 0.425915016712619943
FAS(1.180334) 2.269478141622939926 0.211849500641538985 -0.251291064562774002 -0.290285189647782993 -0.008348216606951959 -1.022461411457650016 0.075176125899384605 -0.957412289454017129 -0.282657040255269998 6.078867653557109563 0.391499703789027931 0.599433990457188925 0.427714577468203960
FAS(1.255467) 2.499807522966320139 0.013730240546671999 -0.266120662122381002 -0.375131779135912946 -0.008403282628155970 -1.015689690162180137 0.080435208788969800 -0.972081487238992015 -0.295962977587782006 5.964107775291210167 0.396226912533207964 0.598449629277272965 0.426733497722626975
FAS(1.335381) 2.491481604594099952 0.057561163806657600 -0.254909943611511980 -0.362719017315936032 -0.008297249007011500 -1.004641085099819975 0.086904203676444802 -0.998517906331295113 -0.332486107534317010 6.147740396043769096 0.399183127739278998 0.595224371038884037 0.425148343953605012
FAS(1.420383) 2.432962776108370306 0.088293289412819706 -0.244572901062636017 -0.345552942175220978 -0.008630784142967309 -0.990512391009102044 0.091881732044760203 -1.005692810762609968 -0.326305097077344008 6.434795859690701114 0.397523011982742980 0.594756658096475044 0.425026964671159024
FAS(1.510795) 2.334814612375049947 0.191931337077721031 -0.230556192183095005 -0.294290394814178957 -0.009149978715968871 -0.970915214420055017 0.090699067514448603 -1.004291021307609943 -0.288785210873021947 7.105800862259740391 0.400002590524112966 0.592036237807510024 0.425695078614066968
FAS(1.606962) 2.273794678788979784 0.265673649877563034 -0.219752701528971972 -0.260308173647532004 -0.009355230552916920 -0.945864065122142161 0.089310519387134704 -1.003019218482720021 -0.288781722541468056 7.708343893470799735 0.399659010117432045 0.587274674716987910 0.427449117835926984
FAS(1.709251) 2.277332165499180050 0.276810682734645985 -0.216431959536553031 -0.258176394290102973 -0.009664868622764101 -0.930580309184950938 0.089909123757779194 -1.003295454395800146 -0.280762545193573021 7.951065086885110489 0.396070018269900959 0.579031521968740970 0.431992595809263968
FAS(1.818050) 2.194919495457579917 0.353264266800144999 -0.206047087803720025 -0.220656169335018026 -0.009916555974403409 -0.929167986275826974 0.090119064335879198 -1.007090121924719917 -0.277264129041976004 7.688198686949349714 0.396330928367786051 0.571162762381795086 0.435440672418478003
FAS(1.933776) 2.073758830039129641 0.445146624826465998 -0.192704575790575011 -0.161338785683713987 -0.009929148391346810 -0.930662318709149949 0.087186552547937904 -1.009811169460989921 -0.303536183841271956 7.640644506706550487 0.400646712150686035 0.562000754297667937 0.435190044587877023
FAS(10.233153) -0.209618874964315000 1.072217726525839909 -0.021111212928080200 0.305755484205412986 -0.016239185823753201 -0.219503328034676981 0.130771093919370002 -1.074730665765680104 -0.632261339399334932 8.615700840265480664 0.530334753083881116 0.745723877648974076 0.483583218381053948
FAS(10.884528) -0.590813144797872947 1.327519913603480095 0.006089767274142720 0.433989954148591039 -0.016484099498620501 -0.190698748810083002 0.126989384907950975 -1.078255016537269961 -0.631858436619976094 8.344938367083040376 0.539616529137784018 0.759351094474527977 0.492577410701642016
FAS(11.577365) -0.794289152882065919 1.411859872513180125 0.016993546395580501 0.497851007068987994 -0.016694434378872601 -0.155731563268681011 0.123957969892848005 -1.083776567205450014 -0.640712226731398937 8.048460033050789164 0.548349363976569970 0.775077463117370025 0.501089942379123965
FAS(12.314304) -0.875127985353424065 1.419564050503040020 0.019291055509810001 0.533434500351142926 -0.016656578341860500 -0.119546010049038004 0.119100078670731982 -1.098543460408959893 -0.677906883374374991 8.063852598825111073 0.556697560464489039 0.794163806704076936 0.509974710811784915
FAS(13.098151) -1.087532125643119851 1.533419947098699776 0.030969148759252899 0.611051619983936978 -0.016441609927984199 -0.088442212083798100 0.112347249988790990 -1.108904749015310109 -0.722907376583707073 7.969872804552700529 0.566131049094776961 0.812443629180207960 0.519800329213585988
FAS(13.931892) -1.328812116376870023 1.679332691854070081 0.042959612086331200 0.688804250047505895 -0.016329234248289901 -0.074177429849918305 0.104556983532634998 -1.113136498722489875 -0.751793408609464198 7.799690617169139806 0.575603092083382117 0.826440992860562051 0.531994163925623931
FAS(14.818705) -1.498357229967989923 1.763035332891299989 0.047271137863715201 0.750287993606142067 -0.016054700258360300 -0.063893044821328807 0.093011833628343393 -1.115266059006990051 -0.803599172647122884 7.731392197476780304 0.585761293310917974 0.838267548638435001 0.547850520386518935
FAS(15.761965) -1.594774667646130073 1.804876190413480019 0.045408820120141004 0.793233774035929096 -0.015567446106718900 -0.047881533808477497 0.078529725455174906 -1.119252549728720014 -0.880983114193309103 7.798978584321860197 0.595311352205806998 0.850113054804297996 0.566532224586875910
FAS(16.765268) -1.687225506547299858 1.841602935993169821 0.043180587610235702 0.831448737585770981 -0.015078100553371001 -0.037132595724561797 0.064705653768284896 -1.127958602513710051 -0.950957118974364968 7.664151524003190552 0.600039702825464927 0.859327998873569920 0.587097377509165019
FAS(17.832434) -1.733393004486639688 1.820598432366769881 0.036407902361524497 0.864677454018279001 -0.014747051451567499 -0.043133792107731599 0.049738027247880401 -1.139191127771830070 -0.993590369578250976 7.772944111619620067 0.605521617784765986 0.868930080941780925 0.606246369879168023
FAS(18.967528) -1.766743304734269993 1.827727954687589973 0.033442106618153097 0.903538852565525019 -0.014566534928056299 -0.047681704108470203 0.037749670840227498 -1.165310763269870042 -1.028395372245849870 8.260292817908389651 0.616296042289264046 0.880365454307502016 0.624572915614326041
FAS(2.056867) 1.950722612327440153 0.511381460872607052 -0.179350220924403003 -0.115822263640146986 -0.010062189742789499 -0.920702654294535017 0.088088214089653602 -1.013533028067000075 -0.316144700721367022 7.760724978037929489 0.398097673741692970 0.556703819991699933 0.435871218180977016
FAS(2.187793) 1.913675651395550181 0.506036875923698060 -0.173174548834662989 -0.118144324676435000 -0.010082673521074600 -0.903578160772396055 0.094098924173753706 -1.022749537871780134 -0.339283181739019002 7.758897394048039686 0.398616600352099004 0.557406254395655054 0.435780503604420000
FAS(2.327054) 1.796000830486730093 0.595645475396295088 -0.158644277765936009 -0.080674184950737707 -0.010314557622370100 -0.878033312603445970 0.097394492001415700 -1.027177210608150038 -0.337959770546094995 7.731090853909089233 0.393594615710041007 0.556826008840942022 0.435258326438241028
FAS(2.475179) 1.620285315109859958 0.764311583099434033 -0.138454670808604019 0.021460795291475900 -0.010597250221211300 -0.852861995867525091 0.093325134571863894 -1.029557194082360017 -0.339022071180713036 8.044114812487190846 0.392600076763116035 0.556979419274640009 0.437653234898232046
FAS(2.632732) 1.627093988262349855 0.753860085431024007 -0.137407698064522993 0.053171107906888899 -0.010704325805571300 -0.844250435795420806 0.087954033289816297 -1.031592920041620065 -0.369310288644840057 8.595810742031900986 0.396190183346697977 0.554588363884636060 0.442587061837257989
FAS(2.800315) 1.668307768602830254 0.681330290587479959 -0.141010196705142005 0.020270803484819199 -0.010972920268386300 -0.838743654918777004 0.090585462666275304 -1.030957393876759998 -0.379072131007765989 8.649041543828460021 0.399244353238977945 0.553042276809841082 0.448083200434988005
FAS(2.978564) 1.714209671191959883 0.587653237403796047 -0.144912477566619013 -0.044386768188871599 -0.011447552494321998 -0.828820680646170871 0.098000713719713195 -1.028281228090670130 -0.361646804134289013 8.304531155893540628 0.399522541986926050 0.553551162154163001 0.452000371810782009
FAS(20.174876) -1.780579369021959790 1.859323680771189924 0.032220225177018703 0.937434847747877997 -0.014284164811124199 -0.041120504172542399 0.027635379777555501 -1.200551139169780068 -1.085972103999800042 8.711637901265200767 0.628991368431012887 0.891405651368297081 0.643730684455237068
FAS(21.459075) -1.893706013752879835 1.902726065724679838 0.033557414021277800 0.984457812496492890 -0.013870740952588501 -0.043093359634551201 0.016119095506882598 -1.220211306333570001 -1.151852067609800079 8.893815429810759454 0.638458139233130995 0.903752779232336989 0.663891271767931057
FAS(22.825018) -2.164515155469469931 1.998536469815849870 0.042546109726455499 1.067264456408159923 -0.013358365830870999 -0.060096929197271803 0.004079208448600950 -1.229291703207469943 -1.213587685605250099 9.025439023043249520 0.645357922901107051 0.916123024745528980 0.686061638871032886
FAS(24.277907) -2.569154958647499765 2.144212467117970089 0.058187991506292398 1.190592941159939855 -0.012875627957906701 -0.078526214114103196 -0.009653602056897449 -1.228808143146729925 -1.259127515264110153 8.974260000777279700 0.656469133279297901 0.930473846943656979 0.711645880437019041
FAS(25.823278) -2.858158209061369970 2.272352081808190150 0.067389354480938898 1.314532935697520166 -0.012052374773800100 -0.040597519390977603 -0.030689086450752599 -1.225112873399570201 -1.340043035701590002 8.435883915713880299 0.680050243512336006 0.937978461209225900 0.739612295451622881
FAS(27.467017) -2.910308141551120276 2.158616052469560120 0.052507107017089202 1.283832909691330126 -0.011617812944882400 -0.032747934573783402 -0.046468701997043900 -1.212824253679460007 -1.364189445660429989 8.268536095173249834 0.696824914776556059 0.950489799301430849 0.766761441786662945
FAS(29.215386) -2.921080998581390364 1.994125646206420077 0.033580068523296001 1.195666906642639971 -0.011217944404457600 -0.039379828469870898 -0.057356525722447503 -1.205176580135870035 -1.378796062866769923 8.145032362615509669 0.722729184814978054 0.966892164718562097 0.796592626847953067
FAS(3.168160) 1.888433507706319903 0.370606182705787046 -0.160801288175799001 -0.156172430808219992 -0.011917512217839399 -0.815109960378089138 0.106644498213048999 -1.029103869473640076 -0.348420547392885971 7.956270330170849725 0.394332017356339048 0.553379621135952959 0.453768939057046017
FAS(3.369824) 1.841222752415719865 0.329693756488679990 -0.158176867594909010 -0.159449384176328007 -0.012333494853759600 -0.797525243622735025 0.111079243337794994 -1.030632797089819919 -0.335553850462763981 7.829499317441589668 0.389562688246129996 0.555494391737813897 0.453567078201757956
FAS(3.584325) 1.452247627236940009 0.578018944713293958 -0.126024456633502008 -0.015422924884020601 -0.012795492649099200 -0.773373246994338071 0.111379135421456998 -1.024433113326719935 -0.314192549632272999 8.106266862807130380 0.391960938264515002 0.562392887063643987 0.454009138926969036
FAS(3.812479) 1.002015855198829852 0.940987286789070954 -0.084818453495162205 0.165048589564936982 -0.013348366157634800 -0.734463509252414104 0.112160283592876997 -1.022283112187329923 -0.285849455672411989 8.441606280163268750 0.401075084682757987 0.570410581788017068 0.454121314416447042
FAS(31.075044) -2.894233900103700297 1.829165784680850226 0.014356133518117500 1.114364279186790041 -0.010572939891332400 -0.042152376906846901 -0.065475945941614794 -1.218698529547789899 -1.432312890868570276 8.090635938332709998 0.741953597581202051 0.982743874930970929 0.825808258299242093
FAS(33.053076) -3.068559902453870336 1.795816657011199968 0.011578034265810300 1.138235653354350063 -0.010037538483602400 -0.052038685774478600 -0.072716713784271705 -1.233328649793550058 -1.481914458423039926 8.077779394913418898 0.744801127075814917 0.999597153592035936 0.855189361344300902
FAS(35.157016) -3.218202896077470232 1.749713327516639882 0.006997797768027960 1.145362552115209986 -0.009505419414836241 -0.071321507614524701 -0.081633939932982805 -1.243946248185560099 -1.525713179909889972 8.321422892269300320 0.756290342490030132 1.021409589339489887 0.883427222871264961
FAS(37.394879) -3.396429115260180431 1.766780796362610095 0.006144283621304010 1.175931242171909918 -0.008732470332479940 -0.083625361598639994 -0.094992770060148099 -1.257295476639199938 -1.591637896781980199 8.777748002416378981 0.773898263230579087 1.049722529098920054 0.910205047947699075
FAS(39.775190) -3.806548591852600083 1.959988264090740007 0.022933572202815701 1.299714418243639980 -0.008065144650801751 -0.089600985576852907 -0.108512471296916990 -1.264876753615969962 -1.641371472816439914 9.212935617545118916 0.792458414222642071 1.081230389407660031 0.937564372298899995
FAS(4.055156) 0.934088259292449097 0.998121570453324169 -0.076779455715246206 0.181126480562366993 -0.013588408608514299 -0.694315144083230029 0.114045382926054983 -1.025449803901649970 -0.299310951430069971 8.457871044629440505 0.404918962664182036 0.573885777472056047 0.453376758460161011
FAS(4.313281) 0.978760406803861005 0.944300556564814930 -0.080406103879342106 0.157708059803183032 -0.013626612644736399 -0.674449810882857048 0.111770781184714008 -1.028179326764060209 -0.327427778457447971 8.584397665757411033 0.408823719332159996 0.580042985445601067 0.455730131759205959
FAS(4.587835) 0.895981393222339939 1.012460973618890092 -0.071841167383121504 0.196697420944581036 -0.013706397999668600 -0.659240069510770965 0.109685602366838011 -1.033924917894909923 -0.355237016580385034 9.058279148994449415 0.416913895421275049 0.591075266732089988 0.456808770427917010
FAS(4.879867) 0.738707275790305928 1.128370574526009973 -0.057437198519106399 0.247990626713151002 -0.013775879458194900 -0.633937608800921981 0.111991999577119999 -1.039127168724969907 -0.398739394157647919 9.436983487799690096 0.425449979113499965 0.601325984830880955 0.456186507917868966
FAS(42.307015) -4.201142708407290094 2.173735129324219972 0.047307966593178603 1.433504745135740110 -0.006942993760169260 -0.038901771903109401 -0.117509975242933010 -1.296483425631010045 -1.705301910655889763 9.900439036123160008 0.825831078608603053 1.075435867011240054 0.920789968890337041
FAS(45.000000) -4.200408689725469991 1.863641624224169790 0.013109204074609700 1.186467380905149804 -0.006308701600106889 -0.121036344599585996 -0.088168798607184601 -1.331613336822620175 -1.723189435363529975 9.846608307466429011 0.864049412982307974 1.123788784529600182 0.962902228210263944
FAS(5.190487) 0.843314389290270028 1.001349962258019977 -0.067764834378238700 0.165621654106080984 -0.013975500818050700 -0.601121602932303878 0.119192144456181010 -1.041614043345880036 -0.426150084912609028 9.285792700438250336 0.432090546511866014 0.611021687575231010 0.454473356710271004
FAS(5.520879) 0.954444967642319897 0.849786951904609067 -0.079489827151022804 0.080688770845849495 -0.014205594516716401 -0.555095707191162968 0.125357590192648999 -1.041757437726909874 -0.445741100631778964 8.920317060707850132 0.441700459389111011 0.624089519701367057 0.452538125490065002
FAS(5.872301) 0.847067662426540857 0.866019416057661973 -0.072214327030276207 0.105088918849696983 -0.014342708154161500 -0.510112620136737971 0.128363959293771007 -1.044514130917840067 -0.480477527189185016 9.016769423465689215 0.450335225434803976 0.636131175052333964 0.451592809370327974
FAS(6.246093) 0.650458261049530972 0.942741561980227072 -0.058738344539385902 0.160967323647353999 -0.014527202684471500 -0.467603672269010007 0.129486528446309007 -1.042372794359069932 -0.512960980074621986 9.064821419645399558 0.455356291702607052 0.642466466889722976 0.451601564288474033
FAS(6.643678) 0.395932850305472039 1.084612707831839939 -0.040378881007953699 0.247560917697082022 -0.014769481962669999 -0.427797662772937071 0.126353265439903023 -1.039602468192160067 -0.524215863865547083 8.990409692864618663 0.459310900598808969 0.650192412275129028 0.452811397209231026
FAS(7.066571) 0.258101618019613011 1.154304212105679905 -0.030547245654296500 0.298291601653825011 -0.014914961290852600 -0.401966205919412067 0.124262805105551988 -1.047411909426099852 -0.542402798186386037 9.245328756109129742 0.460633520582332034 0.660970849937567051 0.453915163490114959
FAS(7.516382) 0.236972748176986991 1.109398575627750017 -0.032099976753252699 0.283023971353994985 -0.015151093150525700 -0.374580256716730009 0.127293177099638000 -1.055105903779919974 -0.556395664503702925 9.163345433029750353 0.470246985027484021 0.671505349846401978 0.457201898038130050
FAS(7.994825) 0.201426860516765005 1.043349742653210122 -0.035220078202162802 0.262327932749071013 -0.015407810615977600 -0.339505956903788986 0.130053321859984000 -1.055342827154410079 -0.571700561687920938 8.829506517700810520 0.486575054952254005 0.682328569575974098 0.460281623401607054
FAS(8.503723) 0.207898405263681030 0.937583605845900947 -0.042630308272016797 0.219399073574211040 -0.015778014679178300 -0.301438490165143957 0.132443410386299004 -1.052848961641990044 -0.576775046319193962 8.526529512369179997 0.494631043029450990 0.695280185841289033 0.463065391201623988
FAS(9.045014) 0.210092314951341980 0.858955393522459976 -0.047779697256899199 0.192755085526255004 -0.016059750743852699 -0.265419090972488947 0.132554906269495010 -1.057961341972339930 -0.582931980295925078 8.401484033071481505 0.503862159243763985 0.711257639806089137 0.469515846994462971
FAS(9.620759) 0.099842361640679500 0.875281258376868987 -0.042770492873562903 0.206747585550481006 -0.016143294093816003 -0.241093370336476015 0.133255376127781988 -1.068192253488890131 -0.611051323052614004 8.493482559735490156 0.517668051643455973 0.729219849154350896 0.476089175945325072
"""
COEFFS = CoeffsTable(sa_damping=5, table=TMP, opt=1)
def _get_mean_stddevs_dur(C, ctx):
mean = (C['d0'] + _get_source_term_duration(C, ctx) +
_get_path_term_duration(C, ctx) + _get_site_term_duration(C, ctx))
phi = np.sqrt(C['phi']**2 + C['phis2s']**2)
tau = C['tau']
sigma = np.sqrt(C['phi']**2 + C['tau']**2 + C['phis2s']**2)
return mean, sigma, tau, phi
[docs]class BoraEtAl2019Drvt(BoraEtAl2019):
"""
Implements the duration model proposed by Bora et al.,
2019 as described in Bora, S.S., Cotton, F., & Scherbaum, F. (2019).
NGA-West2 empirical Fourier and duration models to generate adjustable
response spectra. Earthquake Spectra, 35(1), 61-93.
"""
#: Supported intensity measure types
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {DRVT}
[docs] def compute(self, ctx: np.recarray, imts, mean, sigma, tau, phi):
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
mean[m], sigma[m], tau[m], phi[m] = _get_mean_stddevs_dur(C, ctx)
TMP = """
IMT d0 d1 d2 d3 d4 d5 tau phis2s phi
DRVT(0.100000) -12.453125867808900296 2.265070750964019997 2.343787976452410327 0.624482385734875911 -0.403026387873397007 -0.027247547171696900 0.754093856676959051 0.241163041780326021 0.493592034082187991
DRVT(0.200000) -6.520143974112809993 1.689999610718379897 1.535317175191810213 0.482067029770475997 -0.309724383145583038 -0.286619826784507981 0.612559040651896924 0.243883341321730007 0.522043296092606024
DRVT(0.250000) -5.008938342780889563 1.480040538635470027 1.321562332056499978 0.454445581097838947 -0.279235652516796995 -0.309525589489802966 0.473919393735442007 0.270380233178010021 0.525324691843597980
DRVT(0.333000) -2.608286562814499998 1.185726020745870191 1.045334285987550071 0.393819834267916002 -0.230404711185352995 -0.387909999169650022 0.391346221024220009 0.282685706609304976 0.524179906342668978
DRVT(0.400000) -1.543230159925520040 1.036039791553069911 0.895364868473363940 0.356791268591267030 -0.202116198735990016 -0.403690671736557982 0.327018121954518959 0.298188804728176993 0.517337792658840057
DRVT(0.500000) 0.333960534472892978 0.722860333982584202 0.733305991973792870 0.328221749966453036 -0.159773539307610984 -0.424222945989308931 0.264576109960628025 0.299068836403101002 0.503190176931284983
DRVT(1.000000) 3.352207867910570016 0.196309672573529992 0.314485461712703973 0.321713861639480014 -0.061798494046040597 -0.462225253665662028 0.203465392995559990 0.266091309811819998 0.455356026751957965
DRVT(10.000000) -0.684120430793722978 0.335392352348517997 1.032043892977950073 0.470537730997860004 -0.127868332410535024 -0.247554258451504999 0.254629155926244022 0.296960230511646994 0.478635897020813994
DRVT(100.000000) -0.471808081684987002 0.478525378447060001 1.080285308770210007 0.493213457226542973 -0.144555092594704004 -0.436570591288972965 0.296931016199210973 0.333051970648100992 0.512956304082603953
DRVT(14.925000) -0.901557775920589166 0.412972908394066029 1.102590275535660025 0.484578608523549947 -0.146593980713971006 -0.293387253757383004 0.272449977974769997 0.309184126581008967 0.494911071620452947
DRVT(2.000000) 2.543344627776029654 0.109596919035278018 0.422668874081128021 0.333078387918121055 -0.059626589682534301 -0.341829991086883000 0.193235659031861989 0.260454902093160023 0.452489730270711987
DRVT(2.941000) 1.764707467445299827 0.134039162728899014 0.576623181821514064 0.347315102127133957 -0.072957138509880004 -0.297266562741991980 0.199737655346333975 0.246197734300676985 0.456325405716896004
DRVT(20.000000) -0.596865801412305053 0.389895192833306037 1.078990399007730083 0.478029151111236006 -0.140924276632781009 -0.315509916737803986 0.275404883110626053 0.324688008507653003 0.506501496777110982
DRVT(25.000000) -0.432884819448578928 0.383148149256407000 1.069735583604789930 0.470847471400426987 -0.140021138364184006 -0.332489973387724014 0.282555299866926013 0.327653626888446070 0.513584429580520974
DRVT(3.333000) 1.513555474497090048 0.144582459928320001 0.633301021194999980 0.351207788584513014 -0.079471722424804506 -0.284643140317568988 0.204775345292148997 0.243523400288019998 0.458870385544763948
DRVT(33.333000) -0.308867220286403010 0.393466618358936038 1.072528094496000062 0.476950908870955037 -0.142529832241635984 -0.369331981663112041 0.285192523677043008 0.327557647415606001 0.521909774846307961
DRVT(4.000000) 1.123971405402959922 0.171747194907011985 0.700166035410864973 0.364605512924223996 -0.084683859552102600 -0.272200417248687987 0.208262645821426035 0.249021947295400975 0.462945254205767043
DRVT(5.000000) 0.746117088434967046 0.170509958557413993 0.756681058958569075 0.379255760724008018 -0.088942144435340001 -0.237698798828760022 0.233768556448271020 0.261602925140040021 0.462929057754140061
DRVT(50.000000) -0.256358613475116071 0.414853860589568024 1.066389043467179887 0.485214931491419976 -0.139202751158666982 -0.409158387336240992 0.294321989323505007 0.331609598511373949 0.514039076789606031
DRVT(7.519000) -0.298594366137973022 0.287009958260428966 0.918043828258243932 0.432754898896367035 -0.112681829368921002 -0.228576818740991977 0.248548859910108971 0.284093931942531963 0.470221366005818042
"""
COEFFS = CoeffsTable(sa_damping=5, table=TMP, opt=1)