# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2017 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:`KothaEtAl2016`,
:class:`KothaEtAl2016Italy`,
:class:`KothaEtAl2016Turkey`,
:class:`KothaEtAl2016Others`,
"""
from __future__ import division
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 KothaEtAl2016(GMPE):
"""
Implements unregionalised form of the European GMPE of:
Kotha, S. R., Bindi, D. and Cotton, F. (2016) "Partially non-ergodic
region specific GMPE for Europe and the Middle-East", Bull. Earthquake Eng.
14: 1245 - 1263
"""
#: 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.AVERAGE_HORIZONTAL
#: 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 only Vs30
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude only (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = set(('mag',))
#: Required distance measure is Rjb (eq. 1).
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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
mean = (self._get_magnitude_term(C, rup.mag) +
self._get_distance_term(C, dists.rjb, rup.mag) +
self._get_site_term(C, sites.vs30))
# Units of GMPE are in terms of m/s (corrected in an Erratum)
# Convert to g
if isinstance(imt, (PGA, SA)):
mean = np.log(np.exp(mean) / g)
else:
# For PGV convert from m/s to cm/s/s
mean = np.log(np.exp(mean) * 100.)
# Get standard deviations
stddevs = self._get_stddevs(C, stddev_types, dists.rjb.shape)
return mean, stddevs
def _get_magnitude_term(self, C, mag):
"""
Returns the magnitude scaling term - equation 3
"""
if mag >= self.CONSTS["Mh"]:
return C["e1"] + C["b3"] * (mag - self.CONSTS["Mh"])
else:
return C["e1"] + (C["b1"] * (mag - self.CONSTS["Mh"])) +\
(C["b2"] * (mag - self.CONSTS["Mh"]) ** 2.)
def _get_distance_term(self, C, rjb, mag):
"""
Returns the general distance scaling term - equation 2
"""
c_3 = self._get_anelastic_coeff(C)
rval = np.sqrt(rjb ** 2. + C["h"] ** 2.)
return (C["c1"] + C["c2"] * (mag - self.CONSTS["Mref"])) *\
np.log(rval / self.CONSTS["Rref"]) +\
c_3 * (rval - self.CONSTS["Rref"])
def _get_anelastic_coeff(self, C):
"""
This function is a regionalisable parameter - will be modified in
other classes
"""
return C["c3"]
def _get_site_term(self, C, vs30):
"""
Returns only a linear site amplification term
"""
dg1, dg2 = self._get_regional_site_term(C)
return (C["g1"] + dg1) + (C["g2"] + dg2) * np.log(vs30)
def _get_regional_site_term(self, C):
"""
Region specific site term - modified in subclasses
"""
return 0., 0.
def _get_stddevs(self, C, stddev_types, stddev_shape):
"""
Returns a total standard deviation
Intra-event standard deviation should be treated here as
sqrt(phi0 ** 2. + phiS2S ** 2.)
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(C['sigma'] + np.zeros(stddev_shape))
elif stddev_type == const.StdDev.INTRA_EVENT:
phi = np.sqrt(C['phi0'] ** 2. + C["phiS2S"] ** 2.)
stddevs.append(phi + np.zeros(stddev_shape))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['tau'] + np.zeros(stddev_shape))
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""
imt e1 b1 b2 b3 c1 c2 c3 h g1 g2 tau phi0 sigma phiS2S sigma Dc3IT Dc3OTH Dc3TR SE(Dc3IT) SE(Dc3OTH) SE(Dc3TR) tau_c3 Dg1IT Dg1OTH Dg1TR Dg2IT Dg2OTH Dg2TR SE(Dg2IT) SE(Dg2OTH) SE(Dg2TR) SE(Dg1IT) SE(Dg1OTH) SE(Dg1TR) tau_g1 tau_g2
pgv 0.773448532300000 0.48295609180000 -0.1013899388000000 -0.0211759777000000 -1.197557080000000 0.229140238700000 -0.0000830116515161252 5.84530471620000 2.1875716805 -0.3643741495 0.348763395300000 0.495980939200000 0.768173253600000 0.3137247297 0.682683091907392 -0.0018916416 0.0014236266 0.00050081190000000000 0.0007689578 0.0007372030 0.0003534052 0.0015388227 -0.2959264052 -1.0821939285 1.3782664393 0.0507702961 0.1856654408 -0.2364608034 0.0491199945 0.0393998898 0.0598580222 0.2863072456 0.2296513693 0.3488963189 1.0673423315 0.1831174421
pga 2.981853543700000 -0.36324783770000 -0.1947968611000000 -0.4057967936000000 -1.230785202700000 0.271868892300000 -0.0039450559000000000 6.38988189290000 1.4069433075 -0.2342417112 0.349815625100000 0.450631096100000 0.723682628400000 0.3304253082 0.659257340221143 -0.0032597832 0.0032648044 -0.00000439588422080639 0.0007949687 0.0007572335 0.0003354350 0.0027446152 -0.3602648470 -0.6776115954 1.0380588295 0.0632138563 0.1188970925 -0.1821429513 0.0453351292 0.0371438274 0.0550867309 0.2583714144 0.2116880096 0.3139471920 0.7911010240 0.1388105096
0.01 3.002028294200000 -0.36603926960000 -0.1933119745000000 -0.4119542683000000 -1.235690007800000 0.271682730700000 -0.0038461541000000000 6.42510376690000 1.3986480324 -0.2328051104 0.347165581200000 0.452282136000000 0.723328345000000 0.3303191705 0.658933855340932 -0.0033370251 0.0034089753 -0.00007218609764977390 0.0007973964 0.0007591361 0.0003359461 0.0028333710 -0.3506434045 -0.6627804988 1.0133951420 0.0616159653 0.1164655026 -0.1780764139 0.0449108580 0.0368500864 0.0544677112 0.2555781783 0.2097060349 0.3099642047 0.7735091224 0.1359230224
0.02 3.063886757900000 -0.36766026720000 -0.1924547062000000 -0.4254010617000000 -1.250786612600000 0.272735132100000 -0.0037520606000000000 6.33634383160000 1.3823143357 -0.2300559740 0.350503318700000 0.454352863500000 0.727649531600000 0.3321209893 0.663018440561026 -0.0034295045 0.0034948203 -0.00006496111175672410 0.0008030409 0.0007645627 0.0003378673 0.0029052359 -0.3794085084 -0.6551011990 1.0344459042 0.0668475713 0.1154215664 -0.1822578963 0.0446512509 0.0366716719 0.0540808095 0.2534282729 0.2081383681 0.3069478650 0.7842928661 0.1381837051
0.03 3.128272124600000 -0.37766990480000 -0.1828190988000000 -0.4404575362000000 -1.267446341900000 0.277810808500000 -0.0037139223000000000 6.10844028110000 1.3123984433 -0.2184227802 0.348022252800000 0.461449929300000 0.733244620400000 0.3358990123 0.668493584231799 -0.0035636966 0.0036420721 -0.00007836964492686870 0.0008121313 0.0007726011 0.0003414672 0.0030158759 -0.3760026560 -0.6518269885 1.0284122276 0.0664490638 0.1151941186 -0.1817461394 0.0444499669 0.0365805780 0.0536542632 0.2515205628 0.2069915533 0.3036031596 0.7793626014 0.1377328466
0.04 3.222582777700000 -0.41376738240000 -0.1677810024000000 -0.4870244514000000 -1.298602166200000 0.290559314500000 -0.0037685605000000000 6.09639971500000 1.2438501532 -0.2070306129 0.350246760300000 0.462720624500000 0.737868184500000 0.3420262907 0.673620926759492 -0.0037184552 0.0037076830 0.00001077989698630680 0.0008179932 0.0007779008 0.0003431692 0.0031051599 -0.4086767835 -0.6061297199 1.0141156623 0.0722579789 0.1071695538 -0.1793053854 0.0449985578 0.0370833760 0.0542035116 0.2545029094 0.2097362128 0.3065643009 0.7672503000 0.1356572192
0.05 3.304178248500000 -0.47788152330000 -0.1649466600000000 -0.4971193313000000 -1.321405889500000 0.300993708300000 -0.0038844433000000000 6.08554732440000 1.1628198018 -0.1935756212 0.352007488000000 0.469497842200000 0.747156032600000 0.3500096696 0.683260026821434 -0.0037426325 0.0037770187 -0.00004936490788013450 0.0008286535 0.0007876888 0.0003476605 0.0031459981 -0.4388084783 -0.5624400618 1.0013027801 0.0776274032 0.0994984454 -0.1771354439 0.0457485413 0.0377599215 0.0549788737 0.2586051702 0.2134474815 0.3107819522 0.7573332636 0.1339760226
0.10 3.757380187000000 -0.66592977070000 -0.2318502043000000 -0.3411866240000000 -1.342289257800000 0.294832659500000 -0.0052217844000000000 7.65818369340000 0.9621640992 -0.1599922852 0.375213723700000 0.458697009700000 0.767187184100000 0.3926235601 0.710873789857342 -0.0033038247 0.0034685939 -0.00016344130000000000 0.0008352332 0.0007944174 0.0003493079 0.0028533136 -0.3438530779 -0.3902824195 0.7344036178 0.0613743936 0.0696615750 -0.1310838255 0.0465827158 0.0392612561 0.0542367588 0.2609819712 0.2199631313 0.3038641262 0.5828255648 0.1040286332
0.15 3.876807696300000 -0.40425693250000 -0.2261910581000000 -0.2136343142000000 -1.212346856100000 0.243493138400000 -0.0069330665000000000 7.46776957670000 1.0657502041 -0.1767076596 0.362042816800000 0.462663925500000 0.766551393000000 0.3986259534 0.709954618183167 -0.0037064561 0.0033757771 0.00033171860000000000 0.0008392461 0.0007963701 0.0003501197 0.0029834549 -0.0720626778 -0.3408500604 0.4129748107 0.0131744619 0.0623140426 -0.0754998526 0.0386790408 0.0337127252 0.0426361232 0.2115695611 0.1844044328 0.2332143117 0.3764511925 0.0688226214
0.20 3.577881511200000 -0.21664790570000 -0.2311220336000000 -0.1218093828000000 -1.047628389900000 0.206603903500000 -0.0079215285000000000 6.02971016370000 1.2073326171 -0.2002961687 0.364286000900000 0.471936638500000 0.758349340400000 0.3591951303 0.696024153921133 -0.0040165930 0.0034804929 0.00053670130000000000 0.0008387612 0.0007980689 0.0003516328 0.0031620497 -0.0939285934 -0.4029169502 0.4969280815 0.0168231126 0.0721645770 -0.0890024725 0.0401650673 0.0343146106 0.0459219043 0.2242538804 0.1915889877 0.2563960659 0.4366201866 0.0782010065
0.22 3.554159735200000 -0.13572756200000 -0.2227849851000000 -0.1593324182000000 -1.024568232100000 0.198069574500000 -0.0079264169000000000 5.74696722800000 1.2316009842 -0.2043595571 0.361439062600000 0.478081315400000 0.756786799300000 0.3494363741 0.693762005050663 -0.0039890262 0.0032325563 0.00075722680000000000 0.0008377962 0.0007977073 0.0003529894 0.0030770306 -0.0456347874 -0.4319962538 0.4775105277 0.0081640110 0.0772836335 -0.0854260848 0.0394605921 0.0336556915 0.0452366702 0.2205748773 0.1881269290 0.2528617143 0.4341252333 0.0776645055
0.24 3.519064278100000 -0.03875387410000 -0.2167649237000000 -0.1425607585000000 -0.994800641900000 0.182569615500000 -0.0078087913000000000 5.29971658150000 1.3376724978 -0.2221397257 0.356764818600000 0.487045377200000 0.762979475800000 0.3501790221 0.697939598218566 -0.0040530554 0.0032176004 0.00083850820000000000 0.0008461091 0.0008049311 0.0003569722 0.0031073939 -0.0542403686 -0.5268685888 0.5811083064 0.0096338060 0.0935788241 -0.1032125144 0.0422650715 0.0356048354 0.0493652374 0.2379613015 0.2004627623 0.2779367386 0.5139479410 0.0912839460
0.26 3.436487773900000 0.00114579390000 -0.2249264473000000 -0.0544726476000000 -0.962135179400000 0.172871054200000 -0.0078078030000000000 4.97093936500000 1.3801871329 -0.2293432182 0.352807356200000 0.490437123900000 0.763485796300000 0.3470662166 0.696747129016816 -0.0039675618 0.0030756579 0.00087943080000000000 0.0008455532 0.0008042332 0.0003577044 0.0030226402 -0.0789499330 -0.5647868695 0.6435153239 0.0139121404 0.0995237608 -0.1133968734 0.0440472752 0.0368290486 0.0520517438 0.2499636515 0.2090009755 0.2953881685 0.5579736493 0.0983231711
0.28 3.456222770200000 0.02231717340000 -0.2333002469000000 -0.0424403462000000 -0.970863683900000 0.169389862600000 -0.0073579578000000000 5.14990701910000 1.3937843451 -0.2317740783 0.354103535600000 0.494847931000000 0.764421014300000 0.3383217678 0.696222239882294 -0.0038723231 0.0030429743 0.00082938150000000000 0.0008466378 0.0008058952 0.0003593187 0.0029686300 -0.0911159427 -0.6086917288 0.7001198087 0.0159022845 0.1062337938 -0.1221905550 0.0454849837 0.0377130721 0.0542469412 0.2606170364 0.2160860250 0.3108207496 0.5999975931 0.1047164185
0.30 3.481818236900000 0.10654454620000 -0.2263029865000000 -0.0418281324000000 -0.965917002300000 0.158837774800000 -0.0070098395000000000 5.12275065080000 1.4622066803 -0.2432367391 0.357390830500000 0.503136438200000 0.770257956200000 0.3307087198 0.700173363190729 -0.0039142966 0.0030844598 0.00082776590000000000 0.0008546790 0.0008141274 0.0003634575 0.0030019765 -0.1090753990 -0.6602785449 0.7691648086 0.0189743823 0.1148597910 -0.1338012719 0.0458502489 0.0377700352 0.0550473475 0.2635729648 0.2171233612 0.3164430495 0.6473255559 0.1126065334
0.40 3.339757657000000 0.24296283960000 -0.2334327888000000 0.0102283108000000 -0.947306205300000 0.142390669200000 -0.0053852194000000000 4.75045583620000 1.7790031706 -0.2958875974 0.365850750100000 0.539648610200000 0.802382185800000 0.3180151259 0.725397142357700 -0.0036590364 0.0029637587 0.00069609560000000000 0.0008867237 0.0008460309 0.0003818721 0.0028462458 -0.2060016249 -0.7772232532 0.9831940942 0.0358496692 0.1352571688 -0.1711014808 0.0454041705 0.0370287168 0.0553070333 0.2609043014 0.2127767424 0.3178087550 0.7806178770 0.1358479220
0.50 3.219837802700000 0.39216036780000 -0.1914544569000000 -0.2359285381000000 -0.946322046300000 0.163132167400000 -0.0049716692000000000 4.57971323480000 2.2361131713 -0.3725141419 0.381894169900000 0.527901989700000 0.824754120400000 0.3423108752 0.736002991171244 -0.0034264172 0.0023351975 0.00109047200000000000 0.0008919438 0.0008501866 0.0003841530 0.0025850208 -0.2935031361 -1.1131510245 1.4059797286 0.0504603184 0.1913777001 -0.2417220673 0.0528703908 0.0425162790 0.0645209093 0.3075213550 0.2472965214 0.3752867560 1.0959372117 0.1884182275
0.75 2.997758622400000 0.66707938240000 -0.1692240497000000 -0.1778438233000000 -0.971905099600000 0.144334560000000 -0.0019729159000000000 4.68546622730000 2.9310863050 -0.4881588484 0.381587399500000 0.540956069100000 0.875412014200000 0.3864606506 0.766546963085415 -0.0022862902 0.0017519797 0.00051726090000000000 0.0008795037 0.0008419852 0.0003947747 0.0018436549 -0.3291736229 -1.5012660807 1.8306239869 0.0565863119 0.2580738699 -0.3146918609 0.0603104284 0.0483603549 0.0739467101 0.3508375353 0.2813216252 0.4301624481 1.4261185165 0.2451556918
1.00 2.880339129900000 0.83747004290000 -0.1760783794000000 -0.1140374266000000 -0.989736511300000 0.128254469600000 -0.0009371899000000000 5.39161396920000 3.3475667959 -0.5576263173 0.369212497000000 0.522741073400000 0.890838358600000 0.4238718296 0.767621928874371 -0.0022565242 0.0018614242 0.00039449330000000000 0.0008841281 0.0008584518 0.0003905709 0.0018605520 -0.6034333548 -1.5807558710 2.1837482879 0.1034337848 0.2709554604 -0.3743136646 0.0671916459 0.0550942859 0.0820732834 0.3919964879 0.3214204134 0.4788160549 1.6455985014 0.2820700577
1.50 2.311866313225240 1.12737122148565 -0.1272466291291850 -0.0940345619541096 -0.948072199937748 0.139283453079961 0.0000000000000000000 4.55349651778848 3.3947735776 -0.5657772605 0.364604388787861 0.534479589233590 0.908806163164938 0.4461378758 0.785903172060027 0.0000000000 0.0000000000 0.00000000000000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000 -0.7196136960 -1.3091708781 2.0281602604 0.1226701212 0.2231699468 -0.3457336433 0.0730655711 0.0654034180 0.0861148101 0.4286209646 0.3836728530 0.5051710731 1.5204384299 0.2591840142
2.00 1.683732160380830 1.07923789414851 -0.1585659860388930 -0.2222592171080100 -0.911350017918323 0.161551084815657 0.0000000000000000000 4.30885604793099 3.3368325700 -0.5559975026 0.360101073292530 0.553135237617236 0.928121466837282 0.4626038673 0.805998580719113 0.0000000000 0.0000000000 0.00000000000000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000 -0.9520555035 -1.0089947716 1.9617675069 0.1621764158 0.1718756470 -0.3341742386 0.0764161941 0.0713315014 0.0885767609 0.4486007278 0.4187510752 0.5199892491 1.4632685429 0.2492582069
3.00 1.057210789386420 1.47429408384738 -0.0388245283242518 0.0523996894533524 -0.855363161926190 0.160267276499267 0.0000000000000000000 4.36484245411132 2.9635284908 -0.4929821183 0.432637575150368 0.519351721688414 0.898236393544161 0.4147276555 0.793032477575311 0.0000000000 0.0000000000 0.00000000000000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000 -0.3942891131 -0.8311703475 1.2255274878 0.0687001767 0.1448215226 -0.2135335522 0.0617506639 0.0679966526 0.0725989097 0.3544039575 0.3902513962 0.4166650091 0.9662071056 0.1683500676
4.00 0.754623572916101 1.77516800185502 0.0354551542781731 0.3019618968747080 -0.851637113897711 0.142613630697184 0.0000000000000000000 4.98982430836339 2.7071399686 -0.4506558103 0.429309829925598 0.507127364074350 0.871578899526473 0.3965493583 0.773780645294185 0.0000000000 0.0000000000 0.00000000000000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000 -0.3410199107 -0.7911405077 1.0206892052 0.0596115284 0.1382960265 -0.1784218738 0.0579631847 0.0674698178 0.0677166702 0.3315959389 0.3859794328 0.3873916767 0.8531916829 0.1491418665
""")
CONSTS = {"Mh": 6.75,
"Mref": 5.5,
"Rref": 1.0}
[docs]class KothaEtAl2016Italy(KothaEtAl2016):
"""
Regional varient of the Kotha et al. (2016) GMPE for the Italy case
"""
def _get_anelastic_coeff(self, C):
"""
Returns the anelastic adjustment for the Italy case
"""
return C["c3"] + C["Dc3IT"]
def _get_regional_site_term(self, C):
"""
Region specific site term for the Italy case
"""
return C["Dg1IT"], C["Dg2IT"]
[docs]class KothaEtAl2016Turkey(KothaEtAl2016):
"""
Regional varient of the Kotha et al. (2016) GMPE for the Turkey case
"""
def _get_anelastic_coeff(self, C):
"""
Returns the anelastic adjustment for the Turkey case
"""
return C["c3"] + C["Dc3TR"]
def _get_regional_site_term(self, C):
"""
Region specific site term for the Turkey case
"""
return C["Dg1TR"], C["Dg2TR"]
[docs]class KothaEtAl2016Other(KothaEtAl2016):
"""
Regional varient of the Kotha et al. (2016) GMPE for the "Other" case
"""
def _get_anelastic_coeff(self, C):
"""
Returns the anelastic adjustment for the Other case
"""
return C["c3"] + C["Dc3OTH"]
def _get_regional_site_term(self, C):
"""
Region specific site term for the Other case
"""
return C["Dg1OTH"], C["Dg2OTH"]