Source code for openquake.hazardlib.gsim.derras_2014

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2022 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.
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# GNU Affero General Public License for more details.
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# You should have received a copy of the GNU Affero General Public License
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"""
Module exports :class:`DerrasEtAl2014`
"""
import numpy as np
from scipy.constants import g

from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
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 """ if (rake > 45.0) and (rake < 135.0): # Reverse faulting return 3.0 elif (rake < -45.0) and (rake > -135.0): # Normal faulting return 1.0 else: # Strike slip return 4.0 get_pn = CallableDict() # overridden in germany_2008
[docs]@get_pn.add("base") def get_pn_base(region, ctx, sof): """ Normalise the input parameters within their upper and lower defined range """ # List must be in following order p_n = [] # Rjb # Note that Rjb must be clipped at 0.1 km rjb = np.copy(ctx.rjb) rjb[rjb < 0.1] = 0.1 p_n.append(_get_normalised_term(np.log10(rjb), CONSTANTS["logMaxR"], CONSTANTS["logMinR"])) # Magnitude p_n.append(_get_normalised_term(ctx.mag, CONSTANTS["maxMw"], CONSTANTS["minMw"])) # Vs30 p_n.append(_get_normalised_term(np.log10(ctx.vs30), CONSTANTS["logMaxVs30"], CONSTANTS["logMinVs30"])) # Depth p_n.append(_get_normalised_term(ctx.hypo_depth, CONSTANTS["maxD"], CONSTANTS["minD"])) # Style of Faulting p_n.append(_get_normalised_term(sof, CONSTANTS["maxFM"], CONSTANTS["minFM"])) return p_n
[docs]@get_pn.add("germany") def get_pn_germany(region, ctx, sof): """ Normalise the input parameters within their upper and lower defined range """ # List must be in following order p_n = [] # Rjb # Note that Rjb must be clipped at 0.1 km if ctx.width > 1.0E-3: rjb = np.copy(ctx.rjb) else: rjb = rhypo_to_rjb(ctx.rhypo, ctx.mag) rjb[rjb < 0.1] = 0.1 p_n.append(_get_normalised_term(np.log10(rjb), CONSTANTS["logMaxR"], CONSTANTS["logMinR"])) # Magnitude p_n.append(_get_normalised_term(ctx.mag, CONSTANTS["maxMw"], CONSTANTS["minMw"])) # Vs30 p_n.append(_get_normalised_term(np.log10(ctx.vs30), CONSTANTS["logMaxVs30"], CONSTANTS["logMinVs30"])) # Depth p_n.append(_get_normalised_term(ctx.hypo_depth, CONSTANTS["maxD"], CONSTANTS["minD"])) # Style of Faulting p_n.append(_get_normalised_term(sof, CONSTANTS["maxFM"], CONSTANTS["minFM"])) return p_n
[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) """ # W2 needs to be a 1 by 5 matrix (not a vector w_2 = np.array([ [C["W_21"], C["W_22"], C["W_23"], C["W_24"], C["W_25"]]]) # Gets the style of faulting dummy variable sof = _get_sof_dummy_variable(ctx.rake) # Get the normalised coefficients p_n = get_pn(region, ctx, sof) mean = np.zeros_like(ctx.rhypo if region == "germany" else ctx.rjb) # Need to loop over ctx - maybe this can be improved in future? # ndenumerate is used to allow for application to 2-D arrays for idx, rval in np.ndenumerate(p_n[0]): # Place normalised coefficients into a single array p_n_i = np.array([rval, p_n[1], p_n[2][idx], p_n[3], p_n[4]]) # Executes the main ANN model mean_i = np.dot(w_2, np.tanh(np.dot(W_1, p_n_i) + B_1)) mean[idx] = (0.5 * (mean_i + C["B_2"] + 1.0) * (C["tmax"] - C["tmin"])) + 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.AVERAGE_HORIZONTAL #: 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, 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, **kwargs): super().__init__(adjustment_factor=adjustment_factor, **kwargs) self.adjustment_factor = np.log(adjustment_factor)