# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2019 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.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
[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 sites cannot be achieved and a loop is implemented
instead.
"""
#: 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 = set([
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 = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: The required site parameter is vs30
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: The required rupture parameters are rake and magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag', 'hypo_depth'))
#: The required distance parameter is 'Joyner-Boore' distance
REQUIRES_DISTANCES = set(('rjb', ))
[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.
"""
C = self.COEFFS[imt]
# Get the mean
mean = self.get_mean(C, rup, sites, dists)
if imt.name == "PGV":
# Convert from log10 m/s to ln cm/s
mean = np.log((10.0 ** mean) * 100.)
else:
# convert from log10 m/s/s to ln g
mean = np.log((10.0 ** mean) / g)
# Get the standard deviations
stddevs = self.get_stddevs(C, mean.shape, stddev_types)
return mean, stddevs
[docs] def get_mean(self, C, rup, sites, dists):
"""
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 = self._get_sof_dummy_variable(rup.rake)
# Get the normalised coefficients
p_n = self.get_pn(rup, sites, dists, sof)
mean = np.zeros_like(dists.rjb)
# Need to loop over sites - 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(self.W_1, p_n_i) + self.B_1))
mean[idx] = (0.5 * (mean_i + C["B_2"] + 1.0) *
(C["tmax"] - C["tmin"])) + C["tmin"]
return mean
[docs] def get_stddevs(self, C, n_sites, stddev_types):
"""
Returns the standard deviations - originally given
in terms of log_10, so converting to log_e
"""
tau = C["tau"] + np.zeros(n_sites)
phi = C["phi"] + np.zeros(n_sites)
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigma = np.log(10.0 ** (np.sqrt(tau ** 2. + phi ** 2.)))
stddevs.append(sigma)
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0 ** phi))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0 ** tau))
return stddevs
[docs] def get_pn(self, rup, sites, dists, 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(dists.rjb)
rjb[rjb < 0.1] = 0.1
p_n.append(self._get_normalised_term(np.log10(rjb),
self.CONSTANTS["logMaxR"],
self.CONSTANTS["logMinR"]))
# Magnitude
p_n.append(self._get_normalised_term(rup.mag,
self.CONSTANTS["maxMw"],
self.CONSTANTS["minMw"]))
# Vs30
p_n.append(self._get_normalised_term(np.log10(sites.vs30),
self.CONSTANTS["logMaxVs30"],
self.CONSTANTS["logMinVs30"]))
# Depth
p_n.append(self._get_normalised_term(rup.hypo_depth,
self.CONSTANTS["maxD"],
self.CONSTANTS["minD"]))
# Style of Faulting
p_n.append(self._get_normalised_term(sof,
self.CONSTANTS["maxFM"],
self.CONSTANTS["minFM"]))
return p_n
@staticmethod
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(self, 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
# 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}
# 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])