# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2023 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:`DerrasEtAl2014`
"""
import numpy as np
from scipy.constants import g
from openquake.hazardlib import const
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib.imt import PGA, PGV, SA
# Constants used to normalise the input parameters
CONSTANTS = {
"minMw": 3.6,
"maxMw": 7.6,
"logMinR": np.log10(0.1),
"logMaxR": np.log10(547.0),
"minD": 0.0,
"maxD": 25.0,
"logMinVs30": np.log10(92.0),
"logMaxVs30": np.log10(1597.7),
"minFM": 1.0,
"maxFM": 4.0}
[docs]def rhypo_to_rjb(rhypo, mag):
"""
Converts hypocentral distance to an equivalent Joyner-Boore distance
dependent on the magnitude
"""
epsilon = rhypo - (4.853 + 1.347E-6 * mag ** 8.163)
rjb = np.zeros_like(rhypo)
idx = epsilon >= 3.
rjb[idx] = np.sqrt((epsilon[idx] ** 2.) - 9.0)
rjb[rjb < 0.0] = 0.0
return rjb
def _get_normalised_term(pval, pmax, pmin):
"""
Normalisation of a variable between its minimum and maximum using:
2.0 * ((p - p_min) / (p_max - p_min)) - 1
N.B. This is given as 0.5 * (...) - 1 in the paper, but the Electronic
Supplement implements it as 2.0 * (...) - 1
"""
return 2.0 * (pval - pmin) / (pmax - pmin) - 1
def _get_sof_dummy_variable(rake):
"""
Authors use a style of faulting dummy variable of 1 for normal
faulting, 2 for reverse faulting and 3 for strike-slip
"""
res = np.full_like(rake, 4.0) # strike slip
res[(rake > 45.0) & (rake < 135.0)] = 3.0 # reverse
res[(rake < -45.) & (rake > -135.)] = 1.0 # normal
return res
[docs]def get_pn(region, ctx, sof):
"""
Normalise the input parameters within their upper and lower
defined range.
:returns: an array of shape (N, 5) with rjb, magn, vs30, depth, sof
"""
p_n = np.zeros((len(ctx), 5))
rjb = np.copy(ctx.rjb)
if region == 'germany':
rjb[ctx.width <= 1E-3] = rhypo_to_rjb(
ctx.rhypo, ctx.mag)[ctx.width <= 1E-3]
rjb[rjb < 0.1] = 0.1 # must be clipped at 0.1 km
p_n[:, 0] = _get_normalised_term(
np.log10(rjb), CONSTANTS["logMaxR"], CONSTANTS["logMinR"])
p_n[:, 1] = _get_normalised_term(
ctx.mag, CONSTANTS["maxMw"], CONSTANTS["minMw"])
p_n[:, 2] = _get_normalised_term(
np.log10(ctx.vs30), CONSTANTS["logMaxVs30"], CONSTANTS["logMinVs30"])
p_n[:, 3] = _get_normalised_term(
ctx.hypo_depth, CONSTANTS["maxD"], CONSTANTS["minD"])
p_n[:, 4] = _get_normalised_term(
sof, CONSTANTS["maxFM"], CONSTANTS["minFM"])
return p_n # must be clipped at 0.1 km
[docs]def get_mean(region, W_1, B_1, C, ctx):
"""
Returns the mean ground motion in terms of log10 m/s/s, implementing
equation 2 (page 502)
"""
w_2 = np.array([C["W_21"], C["W_22"], C["W_23"], C["W_24"], C["W_25"]])
p_n = get_pn(region, ctx, _get_sof_dummy_variable(ctx.rake))
mean = np.zeros_like(ctx.rhypo if region == "germany" else ctx.rjb)
for i, p_n_i in enumerate(p_n):
mean[i] = (w_2 @ np.tanh(W_1 @ p_n_i + B_1) + C["B_2"] + 1.0) * (
C["tmax"] - C["tmin"]) / 2 + C["tmin"]
return mean
[docs]class DerrasEtAl2014(GMPE):
"""
Implements GMPE developed by:
B. Derras, P. Y. Bard, F. Cotton (2014) "Toward fully data driven ground-
motion prediction models for Europe", Bulletin of Earthquake Engineering
12, 495-516
The GMPE is derived from an artifical neural network approach, and
therefore does not assume the form of source, path and site scaling that is
conventionally adopted by GMPEs. Instead the influence of each variable
is modelled via a hyperbolic tangent-sigmoid function which is then applied
to the vector of normalised predictor variables. As a consequence the
expected ground motion for each site is derived from a set of matrix
products from the respective weighting and bias vectors. This means that
vectorisation by ctx cannot be achieved and a loop is implemented
instead.
"""
region = "base"
#: The supported tectonic region type is active shallow crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: The supported intensity measure types are PGA, PGV, and SA
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: The supported intensity measure component is 'average horizontal',
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: The supported standard deviations are total, inter and intra event
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: The required site parameter is vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: The required rupture parameters are rake and magnitude
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag', 'hypo_depth'}
#: The required distance parameter is 'Joyner-Boore' distance
REQUIRES_DISTANCES = {'rjb'}
adjustment_factor = 0.
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
# Get the mean
mean[m] = get_mean(self.region, self.W_1, self.B_1, C, ctx)
if imt.string == "PGV":
# Convert from log10 m/s to ln cm/s
mean[m] = np.log(10.0 ** mean[m] * 100.)
else:
# convert from log10 m/s/s to ln g
mean[m] = np.log(10.0 ** mean[m] / g)
mean[m] += self.adjustment_factor
# Get the standard deviations, originally given
# in terms of log_10, so converting to log_e
t = C["tau"]
p = C["phi"]
sig[m] = np.log(10.0 ** np.sqrt(t ** 2 + p ** 2))
tau[m] = np.log(10.0 ** t),
phi[m] = np.log(10.0 ** p)
# Coefficients for the normalised output parameters and the standard
# deviations. The former are taken from the Electronic Supplement to the
# paper, whilst the latter are reported in Table 4
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt tmin tmax W_21 W_22 W_23 W_24 W_25 B_2 tau phi
pgv -3.8494850021680100 -0.0609239111303057 -0.5108267761681320 0.0705547785487647 0.2209141747955480 0.1688158389158400 0.1709281636238190 -0.0764727446960991 0.149 0.258
pga -2.9793036574208900 0.9810183503579470 -0.5410141503620630 0.2542513268001230 0.1097776172273200 0.0759590949968710 -0.0203475717695006 -0.1434930784597300 0.155 0.267
0.010 -2.9851967249308700 0.9914516597246590 -0.5397735372214730 0.2543012574125800 0.1079740373017020 0.0748819979307182 -0.0215854294792677 -0.1412511667390830 0.155 0.268
0.020 -2.9860592771710800 1.0077124420319700 -0.5393759310902680 0.2489420439884360 0.0994466712435390 0.0819871365119616 -0.0176628358022071 -0.1402921001720010 0.157 0.270
0.030 -2.9841758145362700 1.0894952395988900 -0.5372084125784670 0.2404412781206790 0.0831456774341980 0.0874217720987058 -0.0180534593115691 -0.1424462376090170 0.160 0.276
0.040 -2.9825522761997800 1.1566621151436100 -0.5206342580190630 0.2294225918588260 0.0640819890269353 0.0877235647991578 -0.0269902106014438 -0.1694035452552550 0.162 0.279
0.050 -2.9566377219788700 1.1570953988072200 -0.5361435294571330 0.2379322017094610 0.0529587474813025 0.0798504289034170 -0.0405055241606587 -0.1686057780902590 0.163 0.281
0.075 -2.9459804563422900 1.2607331074608400 -0.5546280636130240 0.2717556008480520 0.0503566319333317 0.0555940736542207 -0.0760453347003470 -0.1548592158007060 0.165 0.284
0.100 -2.9363076345808300 1.4108142877985600 -0.5322665166770080 0.2914468968945670 0.0646170592452679 0.0552707941106321 -0.0964503498877211 -0.1690197091113510 0.168 0.290
0.110 -2.9322166355719500 1.4577277923071400 -0.5215128792512610 0.2965867096510700 0.0695760247079559 0.0562737115252725 -0.0990624353396091 -0.1766136272223460 0.170 0.293
0.120 -2.9305311375291000 1.4449914592215900 -0.5198772004016020 0.3011890551316260 0.0743266524551252 0.0548447531722862 -0.1029658495094730 -0.1704198073752260 0.170 0.292
0.130 -2.9285425963598900 1.4530620363660300 -0.5148987743195460 0.3037547597744620 0.0817723836736415 0.0550681905859763 -0.1023106677399450 -0.1690129653555490 0.169 0.292
0.140 -2.9196673126642800 1.3850373642004000 -0.5162158939482600 0.3134397947980450 0.0919389106853358 0.0523805390604297 -0.1023906820870020 -0.1639289532015240 0.170 0.293
0.150 -2.9116971310363600 1.4717692347530400 -0.4979794995850170 0.3170187266665320 0.1021521946332690 0.0498359134240515 -0.0981672896924820 -0.1740083544141590 0.169 0.292
0.160 -2.8705568997525400 1.4895420183953000 -0.4931767106638240 0.3270078628983330 0.1141829496237820 0.0492091819199796 -0.0948725836214985 -0.1944783861258280 0.168 0.290
0.170 -2.8593355700991500 1.4908884937335900 -0.4857478781120660 0.3312535985763490 0.1272056140815920 0.0464184725116303 -0.0917363411984680 -0.2008014717185950 0.168 0.289
0.180 -2.8730587645958800 1.4866172870411900 -0.4781912516799790 0.3353814666780460 0.1373250655602460 0.0442295221716087 -0.0884393991088352 -0.2031412936236190 0.167 0.288
0.190 -2.8500590289332900 1.5037499302991000 -0.4725778368822180 0.3353557358116270 0.1441404667224620 0.0447290643462311 -0.0830593580179204 -0.2121347949463220 0.165 0.285
0.200 -2.8346730052712600 1.5353949145918900 -0.4606756389203650 0.3316296218871790 0.1481014005941910 0.0513471795325157 -0.0744742378559087 -0.2147884447706200 0.164 0.284
0.220 -2.7816474516543800 1.4090364464987300 -0.4554012863696480 0.3453620188396050 0.1684854523654020 0.0571549142765452 -0.0644918601474274 -0.2141824270627850 0.164 0.284
0.240 -2.7587127627028800 1.2613190491473700 -0.4562901401401190 0.3599075311538000 0.1916373800357890 0.0581183907349576 -0.0551954667062526 -0.2139326390536270 0.164 0.282
0.260 -2.7672142992978700 1.2328800873137700 -0.4489428577012490 0.3520377121866010 0.2060114119614530 0.0619618613915453 -0.0446763458089277 -0.2120082925765110 0.163 0.281
0.280 -2.7539129775240000 1.2673005587893700 -0.4370333386072840 0.3405350070398710 0.2147075590644740 0.0647924028017897 -0.0312576308790298 -0.2270374840457480 0.161 0.279
0.300 -2.6852493291163700 1.2694556822676200 -0.4499739611099390 0.3435506072145680 0.2320243598599740 0.0662676034963602 -0.0217727943584929 -0.2467388587050040 0.161 0.279
0.320 -2.6991805763642700 1.2484271058697100 -0.4359142869138620 0.3278454583887470 0.2374133062955710 0.0688195968326906 -0.0112937781310018 -0.2479505796888810 0.163 0.282
0.340 -2.6570613555195600 1.2616874302266000 -0.4246578404042180 0.3214088653882970 0.2477315961162920 0.0776129389334972 0.0023523038064737 -0.2518272001246020 0.164 0.284
0.360 -2.7437796145718100 1.2454934926617400 -0.4156780409664940 0.3147539089045510 0.2559901586728200 0.0818650155768611 0.0151819981706302 -0.2128795651353130 0.165 0.285
0.380 -2.7195497918478700 1.2125588720053700 -0.4153142558477670 0.3132625302105240 0.2667362278641250 0.0900050273237833 0.0273797732431594 -0.2155122777564500 0.166 0.286
0.400 -2.6678719453367700 1.2067376317183300 -0.4148393323716700 0.3135090138545670 0.2763358576796840 0.1011428576097660 0.0395314004057325 -0.2328088293018920 0.165 0.285
0.420 -2.6190431813951900 1.1839787015772600 -0.4180389717159100 0.3041648885898690 0.2794266748853570 0.1095410125090980 0.0555732927493092 -0.2426143478909290 0.165 0.284
0.440 -2.6670814113367600 1.1882067311600000 -0.4122233327403940 0.2941850234308620 0.2801896101028070 0.1082438904742000 0.0657208292330138 -0.2307431723671490 0.164 0.283
0.460 -2.7152952527243300 1.1875342933433100 -0.4057328308481130 0.2871560332561040 0.2831389560681230 0.1088576268241710 0.0745893379996742 -0.2196578428856080 0.164 0.283
0.480 -2.7449377737603000 1.1950170564423600 -0.4042442949321190 0.2826540614689630 0.2896798342337830 0.1106937563488640 0.0820474670933300 -0.2103972308776420 0.164 0.284
0.500 -2.7916168576169200 1.1628672472270300 -0.3983495545101600 0.2751342456016150 0.2934269446244130 0.1130998496578200 0.0914288908624079 -0.1977953081959260 0.164 0.283
0.550 -2.9085176331735700 1.1492944969331100 -0.3829335031319720 0.2534509479512370 0.2975054555430770 0.1220898010344560 0.1158878365781790 -0.1605302161157090 0.165 0.285
0.600 -2.9527892439411500 1.2262661309843900 -0.3733494878295400 0.2402565458756540 0.3033626561390710 0.1369612964952120 0.1390215245267430 -0.1408229861049840 0.166 0.286
0.650 -3.0026215277061900 1.1741707545783800 -0.3737297590137460 0.2286575527083400 0.3127942905381040 0.1470137503552750 0.1606968958306870 -0.1078386841695510 0.166 0.287
0.700 -3.0907155152427200 1.1282247021099500 -0.3595747879091110 0.2138390648396750 0.3131143596433960 0.1511687087496880 0.1780505303916640 -0.0940148618240067 0.166 0.287
0.750 -3.1861000329639700 1.0529909418260700 -0.3457845093591480 0.1971871390764250 0.3112853868777880 0.1587308671541900 0.1930663079353090 -0.0738953365430371 0.167 0.287
0.800 -3.2428377142230400 1.0356641472530100 -0.3410377613378580 0.1815362600786750 0.3150054375339770 0.1662013073727660 0.2064007448169790 -0.0579937199240750 0.166 0.287
0.850 -3.3098183909070300 1.0066746524126100 -0.3362283844654920 0.1719300754280320 0.3206377441169860 0.1704889996865340 0.2148224986765460 -0.0422841140092537 0.165 0.285
0.900 -3.3478678630973000 1.0223667326774400 -0.3310855303059200 0.1613174280558760 0.3224420373283380 0.1734924296476220 0.2223668830003590 -0.0436922077271728 0.166 0.286
0.950 -3.3763632924771200 0.9939469522031180 -0.3286709399402540 0.1498864022427240 0.3233898520052460 0.1764115362533880 0.2290134059343970 -0.0279284754279632 0.167 0.288
1.000 -3.4115407372712100 0.9665514895815880 -0.3230171734247490 0.1375672564720860 0.3230700604901910 0.1808357107147800 0.2309413468142540 -0.0054011463982554 0.168 0.290
1.100 -3.4993495334897900 0.8871267401798590 -0.3180802493404970 0.1243289706983620 0.3317851615514970 0.1880067507057070 0.2388240852699050 0.0164308501469957 0.170 0.293
1.200 -3.5986781202665600 0.7864526839073110 -0.3142209228842820 0.1158450868508410 0.3428200429190670 0.1962523122822420 0.2468832550954440 0.0564369809281568 0.172 0.297
1.300 -3.6999711861320200 0.7733709022499610 -0.3105851723096060 0.1011155080198590 0.3454176627463390 0.2023311989700740 0.2517464908783650 0.0764154979483396 0.174 0.299
1.400 -3.7879350245402200 0.7491360583715300 -0.3081864702345780 0.0840234064510466 0.3410894807211710 0.2007676727452840 0.2503944944640020 0.0800052849758061 0.177 0.305
1.500 -3.8584851451030700 0.7801030153435410 -0.3066860473938940 0.0747038101272826 0.3420608999207350 0.2021422385782360 0.2455427938771910 0.0740356502837967 0.179 0.308
1.600 -3.9197357230741200 0.7357733127234250 -0.3138768827368040 0.0710335065847289 0.3551929423792120 0.2044504163715720 0.2446083868540210 0.0929987701096936 0.180 0.310
1.700 -3.9865291860204900 0.6429990500216410 -0.3146885420448420 0.0615551069292049 0.3561899834395030 0.2057362565875580 0.2427472311463730 0.0980909150382213 0.181 0.313
1.800 -4.0370347010657600 0.6109513810330780 -0.3159626742658760 0.0498236128258896 0.3544717670256240 0.2017909436242210 0.2369306389801100 0.0949462342019402 0.183 0.316
1.900 -4.0846735931012900 0.5982242299658990 -0.3139279332770400 0.0423509609886955 0.3537603183234680 0.1991631458487430 0.2339710370234500 0.0870020981022919 0.185 0.319
2.000 -4.1236685284395200 0.5873171870931590 -0.3117335324254940 0.0380015978725541 0.3538673603704110 0.2001053693535210 0.2330666561399190 0.0806339322918566 0.184 0.319
2.200 -4.2387778832468400 0.4948813686240000 -0.3206657494638550 0.0175043984865415 0.3550235841806770 0.2001083120780390 0.2327556274375540 0.0915109633943688 0.186 0.320
2.400 -4.3439113217801100 0.4378318961619270 -0.3217988425844910 0.0031765916842267 0.3523017159503150 0.2048163038665100 0.2333086765062030 0.0949570801231493 0.186 0.320
2.600 -4.4256986725969500 0.4195511027963140 -0.3222257216502840 -0.0046596561936244 0.3534079953257340 0.2073879114325200 0.2293888385211810 0.0952204306583157 0.187 0.323
2.800 -4.4700290559690200 0.4277699005477710 -0.3220627029522440 -0.0158911129901433 0.3472459157261390 0.2090023880852250 0.2285790428580730 0.0865046630560831 0.188 0.324
3.000 -4.5317431287605500 0.4550671374027660 -0.3237549464388110 -0.0228296340930483 0.3457464811150070 0.2086171933285430 0.2290736376985430 0.0809483142583118 0.189 0.326
3.200 -4.6003297252732100 0.4662604822144270 -0.3260851512560800 -0.0251581680254629 0.3460812057425470 0.2060000808467140 0.2280369607329540 0.0696040680327187 0.190 0.327
3.400 -4.6449413174440900 0.4756561952288580 -0.3263224567869750 -0.0280776334302466 0.3442566677875700 0.2027136653718320 0.2226307270185910 0.0597105130623805 0.190 0.327
3.600 -4.6946699184550600 0.4736398903735540 -0.3287919421496010 -0.0330294887363268 0.3436469221704870 0.2000334235962920 0.2199215942475770 0.0511768464840134 0.189 0.326
3.800 -4.7508447231052000 0.4676956353810650 -0.3309666276314150 -0.0382820403055363 0.3435683224798710 0.2014574493098730 0.2197797508897330 0.0536843640889908 0.188 0.325
4.000 -4.7992997296092300 0.4447267414263530 -0.3319919140676440 -0.0418376481536162 0.3440063128328000 0.2035147583228230 0.2201758793657570 0.0561693756880409 0.188 0.324
""")
# Synaptic weights between input parameters and the hidden layer, as
# taken from the Electronic Supplement
W_1 = np.array([
[2.6478916349996700, -1.0702179603728100, 0.1740877575500600, 0.0921912871948344, -0.0137636792052785],
[-1.9086754364970900, -0.5350173685445370, -0.7051416226841650, 0.1676115828115410, -0.0266104896709684],
[0.2035421429167090, 1.7805576356286200, -0.0804945913340041, 0.0135963560304775, 0.0615082092899090],
[-0.6927374979706600, 0.4415052319560030, 0.7755799725513130, -0.0317177329335344, -0.1630657104941780],
[0.0161628210842544, 0.2181413386066750, -1.6060994470735100, -0.0416362555063091, 0.0260579832482612]])
# Bias vector of the hidden layer, as taken from the Electronic Supplement
B_1 = np.array([-1.2712324878693900,
1.5126110282013300,
0.5910890088019860,
-0.1266226880549210,
-0.4157212218401920])
# Derras et al 2014
[docs]class DerrasEtAl2014RhypoGermany(DerrasEtAl2014):
"""
Re-calibration of the Derras et al. (2014) GMPE taking hypocentral
distance as an input and converting to Rjb
"""
region = "germany"
#: The required distance parameter is hypocentral distance
REQUIRES_DISTANCES = {'rjb', 'rhypo'}
REQUIRES_RUPTURE_PARAMETERS = {"rake", "mag", "hypo_depth", "width"}
def __init__(self, adjustment_factor=1.0):
self.adjustment_factor = np.log(adjustment_factor)
