# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2018 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:`KothaEtAl2019`,
:class:`KothaEtAl2019SERA`
"""
import os
import h5py
import numpy as np
from scipy.constants import g
from scipy.interpolate import interp1d
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA, from_string
BASE_PATH = os.path.join(os.path.dirname(__file__), "kotha_2019_tables")
[docs]class KothaEtAl2019(GMPE):
"""
Implements the first complete version of the newly derived GMPE
for Shallow Crustal regions using the Engineering Strong Motion Flatfile.
(Working Title)
Kotha, S. R., Weatherill, G., Bindi, D., Cotton F. (2019) A Revised
Ground Motion Prediction Equation for Shallow Crustal Earthquakes in
Europe and the Middle-East
The GMPE is desiged for calibration of the stress parameter term
(a multiple of the fault-to-fault variability, tau_f) an attenuation
scaling term (c3) and a statistical uncertainty term (sigma_mu). The
statistical uncertainty is a scalar factor dependent on period, magnitude
and distance. These are read in from hdf5 upon instantiation and
interpolated to the necessary values.
In the core form of the GMPE no site term is included. This will be
added in the subclasses.
:param c3:
User supplied table for the coefficient c3 controlling the anelastic
attenuation as an instance of :class:
`openquake.hazardlib.gsim.base.CoeffsTable`. If absent, the value is
taken from the normal coefficients table.
:param sigma_mu_epsilon:
The number by which to multiply the epistemic uncertainty (sigma_mu)
for the adjustment of the mean ground motion.
"""
experimental = True
#: Supported tectonic region type is 'active shallow crust'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Set of :mod:`intensity measure types <openquake.hazardlib.imt>`
#: this GSIM can calculate. A set should contain classes from module
#: :mod:`openquake.hazardlib.imt`.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
PGV,
SA
])
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: Supported standard deviation types are inter-event, intra-event
#: and total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: Required site parameter is not set
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude and hypocentral depth
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth'))
#: Required distance measure is Rjb (eq. 1).
REQUIRES_DISTANCES = set(('rjb', ))
def __init__(self, sigma_mu_epsilon=0.0, c3=None):
"""
Instantiate setting the sigma_mu_epsilon and c3 terms
"""
super().__init__()
if isinstance(c3, dict):
# Inputing c3 as a dictionary sorted by the string representation
# of the IMT
c3in = {}
for c3key in c3:
c3in[from_string(c3key)] = {"c3": c3[c3key]}
self.c3 = CoeffsTable(sa_damping=5, table=c3in)
else:
self.c3 = c3
self.sigma_mu_epsilon = sigma_mu_epsilon
if self.sigma_mu_epsilon:
# Connect to hdf5 and load tables into memory
self.retreive_sigma_mu_data()
else:
# No adjustments, so skip this step
self.mags = None
self.dists = None
self.s_a = None
self.pga = None
self.pgv = None
self.periods = None
[docs] def retreive_sigma_mu_data(self):
"""
For the general form of the GMPE this retrieves the sigma mu
values from the hdf5 file using the "general" model, i.e. sigma mu
factors that are independent of the choice of region or depth
"""
fle = h5py.File(os.path.join(BASE_PATH,
"KothaEtAl2019_SigmaMu_Fixed.hdf5"), "r")
self.mags = fle["M"][:]
self.dists = fle["R"][:]
self.periods = fle["T"][:]
self.pga = fle["PGA"][:]
self.pgv = fle["PGV"][:]
self.s_a = fle["SA"][:]
fle.close()
[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[imt]
mean = (self.get_magnitude_scaling(C, rup.mag) +
self.get_distance_term(C, rup, dists.rjb, imt) +
self.get_site_amplification(C, sites))
# GMPE originally in cm/s/s - convert to g
if imt.name in "PGA SA":
mean -= np.log(100.0 * g)
stddevs = self.get_stddevs(C, dists.rjb.shape, stddev_types, sites)
if self.sigma_mu_epsilon:
# Apply the epistemic uncertainty factor (sigma_mu) multiplied by
# the number of standard deviations
sigma_mu = self.get_sigma_mu_adjustment(C, imt, rup, dists)
# Cap sigma_mu at 0.5 ln units
sigma_mu[sigma_mu > 0.5] = 0.5
# Sigma mu should not be less than the standard deviation of the
# fault-to-fault variability
sigma_mu[sigma_mu < C["tau_fault"]] = C["tau_fault"]
mean += (self.sigma_mu_epsilon * sigma_mu)
return mean, stddevs
[docs] def get_magnitude_scaling(self, C, mag):
"""
Returns the magnitude scaling term
"""
d_m = mag - self.CONSTANTS["Mh"]
if mag < self.CONSTANTS["Mh"]:
return C["e1"] + C["b1"] * d_m + C["b2"] * (d_m ** 2.0)
else:
return C["e1"] + C["b3"] * d_m
[docs] def get_distance_term(self, C, rup, rjb, imt):
"""
Returns the distance attenuation factor
"""
h = self._get_h(C, rup.hypo_depth)
rval = np.sqrt(rjb ** 2. + h ** 2.)
c3 = self.get_distance_coefficients(C, imt)
f_r = (C["c1"] + C["c2"] * (rup.mag - self.CONSTANTS["Mref"])) *\
np.log(rval / self.CONSTANTS["Rref"]) +\
c3 * (rval - self.CONSTANTS["Rref"])
return f_r
def _get_h(self, C, hypo_depth):
"""
Returns the depth-specific coefficient
"""
if hypo_depth <= 10.0:
return C["h_D10"]
elif hypo_depth > 20.0:
return C["h_D20"]
else:
return C["h_10D20"]
[docs] def get_distance_coefficients(self, C, imt):
"""
Returns the c3 term
"""
c3 = self.c3[imt]["c3"] if self.c3 else C["c3"]
return c3
[docs] def get_site_amplification(self, C, sites):
"""
In base model no site amplification is used
"""
return 0.0
[docs] def get_sigma_mu_adjustment(self, C, imt, rup, dists):
"""
Returns the sigma mu adjustment factor
"""
if imt.name in "PGA PGV":
# PGA and PGV are 2D arrays of dimension [nmags, ndists]
sigma_mu = getattr(self, imt.name.lower())
if rup.mag <= self.mags[0]:
sigma_mu_m = sigma_mu[0, :]
elif rup.mag >= self.mags[-1]:
sigma_mu_m = sigma_mu[-1, :]
else:
intpl1 = interp1d(self.mags, sigma_mu, axis=0)
sigma_mu_m = intpl1(rup.mag)
# Linear interpolation with distance
intpl2 = interp1d(self.dists, sigma_mu_m, bounds_error=False,
fill_value=(sigma_mu_m[0], sigma_mu_m[-1]))
return intpl2(dists.rjb)
# In the case of SA the array is of dimension [nmags, ndists, nperiods]
# Get values for given magnitude
if rup.mag <= self.mags[0]:
sigma_mu_m = self.s_a[0, :, :]
elif rup.mag >= self.mags[-1]:
sigma_mu_m = self.s_a[-1, :, :]
else:
intpl1 = interp1d(self.mags, self.s_a, axis=0)
sigma_mu_m = intpl1(rup.mag)
# Get values for period - N.B. ln T, linear sigma mu interpolation
if imt.period <= self.periods[0]:
sigma_mu_t = sigma_mu_m[:, 0]
elif imt.period >= self.periods[-1]:
sigma_mu_t = sigma_mu_m[:, -1]
else:
intpl2 = interp1d(np.log(self.periods), sigma_mu_m, axis=1)
sigma_mu_t = intpl2(np.log(imt.period))
intpl3 = interp1d(self.dists, sigma_mu_t, bounds_error=False,
fill_value=(sigma_mu_t[0], sigma_mu_t[-1]))
return intpl3(dists.rjb)
[docs] def get_stddevs(self, C, stddev_shape, stddev_types, sites):
"""
Returns the standard deviations
"""
stddevs = []
tau = C["tau_event"]
phi = np.sqrt(C["phi0"] ** 2.0 + C["phis2s"] ** 2.)
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(tau ** 2. + phi ** 2.) +
np.zeros(stddev_shape))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(phi + np.zeros(stddev_shape))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(tau + np.zeros(stddev_shape))
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt e1 b1 b2 b3 c1 h_D10 h_10D20 h_D20 c2 c3 tau_h tau_c3 phis2s tau_event tau_fault phi0 d0_obs d1_obs sigma_s_obs d0_inf d1_inf sigma_s_inf
pgv 1.892806328872520 1.997290013647580 0.086081063981519 0.630585733419827 -1.352927456741330 3.621177834846830 6.570188023667550 11.636086852028200 0.292226428741456 -0.003717368903319 3.350274740504120 0.001989175108629 0.597642034232805 0.372379668871244 0.311130314832717 0.483487360873615 3.59155588988794 -0.573104547503056 0.354252517655502 3.50154144252107 -0.549036348204835 0.471341743936194
pga 4.417284059645490 1.381281569279050 0.004327491747107 0.378789009712617 -1.521958246846950 5.248835811278450 8.165564473597410 10.207830496829000 0.304956691600404 -0.006384808664692 1.230792745760920 0.003322073844615 0.669106254869499 0.381917344130535 0.370122543171531 0.510861957895391 2.79725327727529 -0.447626700422651 0.480117350959533 2.86975218395504 -0.450758427681675 0.565557973373843
0.010 4.548444019710410 1.545413777369810 0.055777461826735 0.287004772074489 -1.518125079550980 5.196280657581540 8.103270060237860 10.539069934362600 0.298393283713967 -0.006458744312803 1.408668268220030 0.003249099924187 0.674745769793643 0.387148247525608 0.383687297188258 0.510104205329196 2.79727234832924 -0.447869656445290 0.481653781767443 2.87463675463566 -0.451742899490231 0.567276273220833
0.025 4.442580815397090 1.346091126371840 0.000511785809480 0.422339574539637 -1.586970951009750 5.399704970497420 8.298529100299890 10.834714579137600 0.304615839626772 -0.005879118382059 1.393095036321120 0.003276969789544 0.671679004630200 0.383176945383864 0.366298823896753 0.512392066661141 2.70308959325038 -0.432005769213633 0.487280586089154 2.79414874529075 -0.438730483722306 0.569356945466973
0.040 4.675805934816830 1.496300750855740 0.076016731610596 0.243275008695628 -1.728407882013360 5.942366776813880 8.587944926186650 12.624212787205000 0.319237677090743 -0.005120561634558 2.837493515680960 0.003112094247622 0.691848007494006 0.376564696325853 0.384505198625636 0.518461715489209 2.44415724128302 -0.390358911183250 0.527052093345632 2.73149628777198 -0.428908283902744 0.592284135200849
0.050 4.656248766515670 1.254970613755230 0.003614618720890 0.316737720903129 -1.794320830857420 6.503489728482530 9.136811109794560 12.569039314120400 0.332108140841410 -0.005264500214593 1.827537822442560 0.003353817406823 0.704483726226435 0.374527074391120 0.403501921390989 0.524129983454523 2.39487265788737 -0.382896939598838 0.545580900582058 2.69008768532356 -0.422278148438213 0.609760771097008
0.070 4.922575670299870 1.263395221116320 0.014010962989755 0.319746235272060 -1.826812962184560 7.416957296597530 10.05184974781670 12.829896514151700 0.342173772868787 -0.005657375107420 1.673134498670350 0.003756011346075 0.730696638333531 0.377132478863452 0.433435245514180 0.527258463232455 2.36043303535580 -0.380433120317511 0.558959254429671 2.69088202174411 -0.423030530282438 0.637249070963625
0.100 5.273573951455780 1.455230368535440 0.072738302170768 0.165303361562237 -1.718933300761690 7.767511226547350 10.32601427372340 13.151816895596300 0.309586419036125 -0.006883472019433 2.271207407275640 0.004231945903474 0.753507140006929 0.382040067526270 0.433812760529140 0.534721815465482 2.28643533414677 -0.368234009748755 0.591287812067563 2.65702415193391 -0.418380962130904 0.659444131894117
0.150 5.365005467478860 1.455572275342220 0.040440987249440 0.243034969330473 -1.430653323847180 5.810656994201750 9.082810077383200 11.337820953209100 0.247751883884461 -0.008379507529490 2.419548710426230 0.004285093038848 0.742264291850245 0.399169524678397 0.410545124538557 0.536676157950607 2.58767038578537 -0.415628772851415 0.578608595614738 2.66768751935281 -0.419695530569169 0.646231316632271
0.200 5.340843250207400 1.421317129241390 -0.008574793393420 0.404597294230414 -1.300571451166200 4.675853256994330 8.707712056336570 11.331373707888200 0.200900820815253 -0.008258443814965 2.474519037517560 0.004065520686124 0.725320656640016 0.410970785906127 0.384111554440299 0.532188765446470 3.06257295397241 -0.490955029234259 0.540015369367897 2.84959984752439 -0.448452245334260 0.621110826966698
0.250 5.379165191094910 1.613172422465060 0.030732401474054 0.282107490214437 -1.224456747634730 3.931649778228820 8.283466589346060 10.699022985920500 0.174457473156904 -0.008168225448742 2.934369251816590 0.003694223510441 0.702963159310018 0.412506846837313 0.373580297647849 0.526995694991015 3.13458492347708 -0.504668552535490 0.501353212589825 2.95547915669062 -0.465462087344715 0.594501521043147
0.300 5.290651826542550 1.677045706210000 0.028582516747067 0.300455509720834 -1.179087781402620 3.571988098279060 7.530686758925950 10.601807863073700 0.160489044877199 -0.007633705781879 2.944948091989140 0.003523170130238 0.691160893394519 0.409290395416361 0.361190381465491 0.521904513113003 3.24558518828961 -0.522520462500027 0.477618221616811 3.11399537945149 -0.490182911905075 0.576990047530632
0.350 5.143420445805400 1.676699374038290 0.011926131038970 0.413771449361342 -1.151384769209340 3.478098007259010 7.264029052679490 9.638426432589590 0.149835683999565 -0.006957073673618 2.726977604394550 0.003380818237915 0.677871583212350 0.404722333499924 0.349932304751709 0.517473487991425 3.44838796236805 -0.552467586074445 0.454490665715818 3.32660997337116 -0.523265793495923 0.558934733460938
0.400 5.007766105042600 1.654070453039360 -0.014767594472343 0.502752266070053 -1.120171296841220 3.316580856168640 7.014295416608370 8.942947523048470 0.142932983815086 -0.006621400220309 2.297576377223100 0.003224354754275 0.676342491986797 0.402216454290276 0.349594773894112 0.510214230044972 3.73614899367811 -0.597200285087204 0.446340645075208 3.49321148509485 -0.549187545850890 0.553365815976012
0.450 4.993309405388980 1.787861125523350 0.013327295813481 0.382735050831296 -1.116490216706990 3.303587351513180 6.914732372738140 8.748850430484320 0.138194933304793 -0.006096405733691 2.430095568240010 0.003154801713776 0.678495425690818 0.399307399487995 0.343276544713056 0.503982756931627 3.94978634376916 -0.630839152367926 0.444619048959004 3.66166095243848 -0.575601401138774 0.554477875004125
0.500 5.025808775293170 2.010879653962750 0.072935798481947 0.253212667760166 -1.125872461848280 3.313175921989680 6.705696316546080 8.781889076061700 0.133115624510051 -0.005479207002881 1.575567280567830 0.003026941234605 0.679453093268171 0.402086391093198 0.324698722709901 0.496744390517092 3.97043265095054 -0.633280800189855 0.442401729050217 3.80437373293752 -0.597770227095264 0.551767933300466
0.600 4.575054661557320 1.627559080374890 -0.081644115008946 0.636839453474050 -1.122896467461930 3.250388459820300 6.755141447727090 10.578310335521400 0.123781303419217 -0.004644786062988 1.762812620619740 0.002686696245752 0.680693821092247 0.398582471430753 0.326299644912384 0.485887400763896 4.11553965350644 -0.655519404806555 0.431767437492638 4.01195042750724 -0.630227822234957 0.549925656586413
0.700 4.552997806717560 1.855279432723890 -0.036656519663037 0.320315409452011 -1.124261988244940 3.164458715155760 6.795706851017660 14.428096427586800 0.116709781985408 -0.004025744863412 2.897309755112500 0.002564264366739 0.681285118343840 0.405350717442049 0.311798101479078 0.477975448246383 4.40373663774109 -0.700058288174968 0.419186105021081 4.12174760391623 -0.646775405781893 0.548180262000477
0.750 4.490071505295000 1.954274125293150 -0.003641660433376 0.456746317851063 -1.100945904099820 2.993445369118350 6.605231810094700 14.816521542859300 0.118164255034819 -0.004061356198934 4.344844406860950 0.002396351691290 0.675374259014311 0.399886897132088 0.308310368674288 0.474831748313580 4.41370691686027 -0.700929994258438 0.419235647299442 4.11858834742546 -0.646311647282336 0.544827942346524
0.800 4.346340135789670 1.903954443525600 -0.027210137253621 0.571405031282990 -1.091284189625060 3.011537576407330 6.383813030413980 8.654923981735060 0.117888128784975 -0.003879315832285 1.064916407668700 0.002262050918392 0.669964265091023 0.405011617726239 0.297779075583881 0.470675816183951 4.40023807557548 -0.698286286632014 0.420206179657632 4.15262278426163 -0.651443005295049 0.543149430752588
0.900 4.172884941038480 1.870903240776090 -0.059326413467110 0.641520889426695 -1.083165017606630 2.914691523196970 6.203853239158910 13.416728990608000 0.117605536642874 -0.003666723557583 2.969877409593050 0.002162505133793 0.682312548536914 0.401371185079930 0.305551357825079 0.461879366570655 4.54974665381206 -0.721274094012117 0.433447566803411 4.33437738669094 -0.679801540800839 0.549339600089621
1.000 4.273364795550890 2.284923556328090 0.065866868784990 0.390273018724367 -1.066847039367690 -2.770998201229750 5.860078215476920 13.460444813265200 0.120495994214884 -0.003428313609870 3.881503254169090 0.001961940063713 0.679308403598395 0.406075656060488 0.318741184949152 0.455552800346687 4.63320008058818 -0.733070104878305 0.435831282783962 4.39109255455187 -0.688465075188292 0.545809019593528
1.200 3.937942766920120 2.170455024448590 0.001174567307882 0.611504555404356 -1.066799402049050 -2.802467021249190 5.853186666416320 14.231560539244100 0.131385480451062 -0.002911204978252 5.399650832898010 0.001827548291076 0.672245643532270 0.402070918575962 0.309254551116353 0.444878350249610 4.66293055224909 -0.737895073569996 0.434028645187010 4.39765274799130 -0.689425377174240 0.543229115708139
1.400 3.772961844544640 2.291407004764750 0.019686183706859 0.639178281399829 -1.070485349817400 2.964269815258380 5.623451439084210 7.746278822950370 0.130566705424876 -0.002529697033308 0.849207406682328 0.001567754308089 0.662596356519541 0.407601922856431 0.292848034404669 0.436849421688952 4.50690099561210 -0.713882430127437 0.440012962336114 4.35234175521656 -0.682441565982256 0.540827372209902
1.600 3.514467366093290 2.294895809430900 0.010752267351047 0.713970090920851 -1.091228676769790 2.883405145840870 5.644671551941680 14.525659107086500 0.144029228752413 -0.002047277539427 5.089802482507260 0.001586628710920 0.664551801117703 0.410886432394217 0.300675754668513 0.431989239017968 4.42698771453499 -0.701598682161155 0.444141743600401 4.35714361415801 -0.682557084627090 0.539116843859117
1.800 3.558886245279490 2.666010152380630 0.115262687271212 0.497582334875118 -1.100660898745970 2.949559265826990 5.480402245803100 10.216862145575300 0.146617369543987 -0.001554451068759 1.296530314251750 0.001390149466717 0.665502891686339 0.389699175362844 0.287717357430583 0.428737629779977 4.38722282924947 -0.696767820891729 0.448128375603855 4.34980568924963 -0.681312244335941 0.534908929898277
2.000 3.183532894947410 2.388446315455500 0.018352451718499 0.584383533482738 -1.108358161998800 -2.911819519994510 5.278887669847590 15.668917064866600 0.150743827092867 -0.001580015449440 7.687533056277530 0.001354445228794 0.656519021204742 0.390879045937366 0.261303789411214 0.427120153573043 4.26618002948656 -0.677840863946992 0.445268405111334 4.36909584809318 -0.684254142482054 0.529187650914867
2.500 2.836907451195650 2.536546088155800 0.062398760604848 0.596079144473462 -1.105603366221790 -2.823586071191350 4.750273265887600 15.487892191774300 0.175239687999456 -0.001631228333605 5.461836301977410 0.001201195688135 0.646055736219785 0.379738530038140 0.223229075011747 0.425817651524798 4.22371310321513 -0.673186562665730 0.422435774484840 4.33349112967483 -0.678761193852883 0.519689843919031
3.000 2.517737034750380 2.546050164341940 0.055154674642950 0.809850456474428 -1.080067562920250 2.791528486447530 4.198987339784080 16.199213420987600 0.184128987340750 -0.001922721370983 5.495712825361990 0.001266687383427 0.644137229457818 0.381565976193432 0.242099243686895 0.422252639239821 4.09589755151420 -0.655102179588055 0.415188078320107 4.28612060333917 -0.671097390391303 0.516644494740873
3.500 2.119154537449590 2.396069299049670 0.008539272672874 1.164554654673330 -1.078957829171880 2.799516490028090 3.809647060408550 14.361952992707000 0.192610794489156 -0.002126518816230 2.988237308109300 0.001270039982803 0.619042168874467 0.366597795968384 0.248890074124623 0.421148406228811 3.87130345045571 -0.620935593452115 0.393657395953868 4.05518974023777 -0.635183933808111 0.501852480973462
4.000 1.847621951421810 2.360501647907130 -0.012290291175221 1.203181384723020 -1.085147369608560 2.850640140168700 3.753076646146860 7.572223679128170 0.212495563316293 -0.002160985939694 0.972813090643118 0.001160548266474 0.611445419916175 0.368313505931245 0.253499095223261 0.423003337400490 3.66750003456413 -0.588258931615559 0.377650627209691 3.88014398605592 -0.607581511885431 0.492187585551506
4.500 2.004721331888600 2.749583105839750 0.124920421668848 1.109962973543350 -1.106053570513110 3.052905831797360 4.057744203916230 4.310346595023010 0.222730247969709 -0.001860522670072 0.709961258389252 0.000000000000000 0.611455447150517 0.357487272025988 0.241635677822731 0.408704987873161 3.50840501651649 -0.565538752485990 0.409557470904523 4.00798424133467 -0.626644011126345 0.489116498441993
5.000 1.766244279359640 2.775644704909250 0.136811181908039 1.277024063081970 -1.134940922975580 3.156427441541180 4.182103070858070 4.099969082316580 0.247128194747863 -0.001550196672696 0.625986200151889 0.000000000000000 0.598171990718161 0.357769751705229 0.250782161006834 0.409277420621721 3.27278257182859 -0.529012351103819 0.397002875689376 3.84718134870989 -0.601713782510972 0.476960884877633
6.000 1.495644634092600 2.906956649834780 0.206605866198126 1.436150033009390 -1.155226946853440 2.732111686024190 5.157196005146210 5.134139700462980 0.261450980486218 -0.001439766119884 1.343568797412350 0.000000000000000 0.577497461758988 0.364322510724063 0.224152579183778 0.401597199934827 3.01673206668580 -0.489064156495419 0.379679274738408 3.58229829260865 -0.561049974091566 0.459592859585885
7.000 1.182821190754860 2.917667033954530 0.223647052589440 1.645537964856860 -1.228574871054330 2.970825808343180 5.783138212668300 5.347061845422780 0.289575079930824 -0.000867891160389 1.439390706721320 0.000000000000000 0.563819357916120 0.368571233598105 0.229328741533368 0.401052676368561 3.09654599365856 -0.503275832203786 0.363962303516824 3.44766788599524 -0.540181500989622 0.447668743764740
8.000 0.877936104327193 2.908933205097090 0.234947578468289 1.691937861016660 -1.271209905469500 3.052069542435400 6.188468047371990 6.198930745809970 0.312385151596051 -0.000600200472803 1.671791342658880 0.000892670164182 0.556359572194014 0.365797914105721 0.204945101304949 0.401323166589614 3.08002142877393 -0.501377187109764 0.359647250033555 3.38667681338371 -0.530743607500501 0.440968433335620
""")
CONSTANTS = {"Mref": 4.5, "Rref": 30., "Mh": 6.2}
[docs]class KothaEtAl2019SERA(KothaEtAl2019):
"""
Implementation of the Kotha et al. (2019) GMPE with the site
amplification components included. This form of the GMPE defines the
site in terms of a measured or inferred Vs30, with the total
aleatory variability adjusted accordingly.
"""
#: Required site parameter is not set
REQUIRES_SITES_PARAMETERS = set(("vs30", "vs30measured"))
[docs] def get_site_amplification(self, C, sites):
"""
Returns the linear site amplification term depending on whether the
Vs30 is observed of inferred
"""
ampl = np.zeros(sites.vs30.shape)
# For observed vs30 sites
ampl[sites.vs30measured] = (C["d0_obs"] + C["d1_obs"] *
np.log(sites.vs30[sites.vs30measured]))
# For inferred Vs30 sites
idx = np.logical_not(sites.vs30measured)
ampl[idx] = (C["d0_inf"] + C["d1_inf"] * np.log(sites.vs30[idx]))
return ampl
[docs] def get_stddevs(self, C, stddev_shape, stddev_types, sites):
"""
Returns the standard deviations, with different site standard
deviation for inferred vs. observed vs30 sites.
"""
stddevs = []
tau = C["tau_event"]
sigma_s = np.zeros(sites.vs30measured.shape, dtype=float)
sigma_s[sites.vs30measured] += C["sigma_s_obs"]
sigma_s[np.logical_not(sites.vs30measured)] += C["sigma_s_inf"]
phi = np.sqrt(C["phi0"] ** 2.0 + sigma_s ** 2.)
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(tau ** 2. + phi ** 2.) +
np.zeros(stddev_shape))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(phi + np.zeros(stddev_shape))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(tau + np.zeros(stddev_shape))
return stddevs