# coding: utf-8
# The Hazard Library
# Copyright (C) 2014, GEM Foundation
#
# This program 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.
#
# This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports :class:`CauzziEtAl2014`,
:class:`CauzziEtAl2014NoSOF`,
:class:`CauzziEtAl2014FixedVs30`,
:class:`CauzziEtAl2014FixedVs30NoSOF`,
:class:`CauzziEtAl2014Eurocode8`,
:class:`CauzziEtAl2014Eurocode8NoSOF`,
"""
from __future__ import division
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
[docs]class CauzziEtAl2014(GMPE):
"""
Implements GMPE developed by Carlo Cauzzi et al (2014) and published
as C.Cauzzi, E. Faccioli, M. Vanini and A. Bianchini (2014) "Updated
predictive equations for broadband (0.0 - 10.0 s) horizontal response
spectra and peak ground motions, based on a global dataset of digital
acceleration records", Bulletin of Earthquake Engineering, In Press
Spectral acceleration (SA) values are obtained from displacement response
spectrum (DSR) values (as provided by the original equations) using the
following formula ::
SA = DSR * (2 * π / T) ** 2
"""
#: Supported tectonic region type is active shallow crust,
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration, peak
#: ground acceleration and peak ground velocity.
#: The original paper provides coefficients for PGA and PGV, while SA
#: is obtained from displacement response spectrum values.
#: Coefficients for PGA are taken from the SA (0.01 s) spectral
#: acceleration, as indicated in Page 11 (at the time of writing)
#: of Cauzzi et al. (2014)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
PGV,
SA
])
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
#: :attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
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.INTER_EVENT,
const.StdDev.INTRA_EVENT,
const.StdDev.TOTAL
])
#: Required site parameter is only Vs30
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude and rake
REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag'))
#: Required distance measure is Rrup,
REQUIRES_DISTANCES = set(('rrup', ))
[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.
"""
# extract dictionaries of coefficients specific to required
# intensity measure type
C = self.COEFFS[imt]
mean = self._compute_mean(C, rup, dists, sites, imt)
stddevs = self._get_stddevs(C, stddev_types, sites.vs30.shape[0])
return mean, stddevs
def _compute_mean(self, C, rup, dists, sites, imt):
"""
Returns the mean ground motion acceleration and velocity
"""
mean = (self._get_magnitude_scaling_term(C, rup.mag) +
self._get_distance_scaling_term(C, rup.mag, dists.rrup) +
self._get_style_of_faulting_term(C, rup.rake) +
self._get_site_amplification_term(C, sites.vs30))
# convert from cm/s**2 to g for SA and from cm/s**2 to g for PGA (PGV
# is already in cm/s) and also convert from base 10 to base e.
if isinstance(imt, PGA):
mean = np.log((10 ** mean) * ((2 * np.pi / 0.01) ** 2) *
1e-2 / g)
elif isinstance(imt, SA):
mean = np.log((10 ** mean) * ((2 * np.pi / imt.period) ** 2) *
1e-2 / g)
else:
mean = np.log(10 ** mean)
return mean
def _get_magnitude_scaling_term(self, C, mag):
"""
Returns the magnitude term
"""
return C["c1"] + (C["m1"] * mag) + (C["m2"] * (mag ** 2.))
def _get_distance_scaling_term(self, C, mag, rrup):
"""
Returns the distance scaling parameter
"""
return (C["r1"] + C["r2"] * mag) * np.log10(rrup + C["r3"])
def _get_style_of_faulting_term(self, C, rake):
"""
Returns the style of faulting term. Cauzzi et al. determind SOF from
the plunge of the B-, T- and P-axes. For consistency with existing
GMPEs the Wells & Coppersmith model is preferred
"""
if rake > -150.0 and rake <= -30.0:
return C['fN']
elif rake > 30.0 and rake <= 150.0:
return C['fR']
else:
return C['fSS']
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification scaling term assuming
period dependent reference vs30
"""
return C["bV"] * np.log10(vs30 / C["VA"])
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return total standard deviation.
"""
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(np.log(10.0 ** C['sM']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0 ** C['f']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0 ** C["tM"]) + np.zeros(num_sites))
return stddevs
#: Coefficient table constructed from the electronic suplements of the
#: original paper.
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt c1 m1 m2 r1 r2 r3 sB sC sD bV bV800 VA fN fR fSS f t s tM sM
pgv 0.4422159946365680 0.5482239378818140 -0.0319470258028777 -2.8457788432226700 0.2406737047414070 6.51696666287798000 0.1919277313361110 0.3706196443240230 0.4978018189249720 -0.6909580227999990 -0.7596804404000000 883.9565406477700000 -0.1433313027208760 0.0184633160924233 0.0049897699311183 0.2398935826956730 0.2213004346208430 0.3263783286033860 0.2149404298227920 0.3220998664588330
pga -2.1961743955816300 0.5237450060972680 -0.0609447663010394 -3.8019035608295600 0.3550808121411740 11.6415555876916000 0.2106985279596590 0.2825106921224770 0.2828846140789600 -0.3100704816000000 -0.7024376883999990 2319.1859784562300000 -0.0241122431339601 0.0724633666482452 -0.0563165754085399 0.2589229720745850 0.2214506097241730 0.3407073201666570 0.2162221044760760 0.3373323345485870
0.0100 -2.1961743955816300 0.5237450060972680 -0.0609447663010394 -3.8019035608295600 0.3550808121411740 11.6415555876916000 0.2106985279596590 0.2825106921224770 0.2828846140789600 -0.3100704816000000 -0.7024376883999990 2319.1859784562300000 -0.0241122431339601 0.0724633666482452 -0.0563165754085399 0.2589229720745850 0.2214506097241730 0.3407073201666570 0.2162221044760760 0.3373323345485870
0.0200 -1.8195694621090300 0.6453679917780000 -0.0718828302259198 -3.8644883929436800 0.3593203519694770 12.1350058517031000 0.1992376827391620 0.2657559899035650 0.2597832779404480 -0.2838417797000000 -0.6697416278000000 2528.8050326671200000 -0.0272261357768130 0.0770853044555010 -0.0589959439154124 0.2592700212170700 0.2266408762153660 0.3443646768667910 0.2208310066257620 0.3405690493706790
0.0300 -1.2943572408433100 0.6982707545157320 -0.0795637931948720 -4.0443482492067200 0.3765163250150630 13.3154555674385000 0.1781152657707780 0.2315977870956060 0.2152815315755380 -0.2288226422000000 -0.6191416576999990 3228.4186287294800000 -0.0333340581611655 0.0835931466396944 -0.0620510202333671 0.2610359421517940 0.2329378875769420 0.3498568601069340 0.2262184621898820 0.3454193910750090
0.0400 -0.6931089735055480 0.7088746113257160 -0.0846090922165347 -4.2569567103123300 0.3973949524463510 14.9701297686778000 0.1812772493016900 0.2182921854255120 0.1831111109272540 -0.1573206416000000 -0.6076234879999990 8228.7311143995100000 -0.0383834128731151 0.0898513499539263 -0.0655039981465477 0.2655226521597100 0.2370812514738440 0.3559631983932190 0.2293557959689310 0.3508651592199890
0.0500 -0.1738965355678180 0.7038280147755070 -0.0875507720994941 -4.4155335972196800 0.4140306595178590 15.9634085011888000 0.1678531023791990 0.1863342553869610 0.1392855607298930 -0.1000000000000000 -0.5639501998999990 30552.3271673005000000 -0.0389955855635790 0.0960304396771990 -0.0706779148995298 0.2702569776994650 0.2423624069839720 0.3630129065395790 0.2337736891265200 0.3573359367920780
0.0600 0.2069820440679000 0.6906315133559440 -0.0888413835088005 -4.4921203206778700 0.4232967413275050 16.1995006962009000 0.1627597795917690 0.1676876852934890 0.1025963949386600 -0.1000000000000000 -0.5367391490999990 23999.0695317075000000 -0.0490906833424132 0.1014786096166360 -0.0714347704520967 0.2750551534173430 0.2452399150958750 0.3685077385587310 0.2354962432697930 0.3620964208820960
0.0700 0.5608903992017920 0.6756111304642140 -0.0888630574702343 -4.5440277265296000 0.4259196396385800 17.3789888842896000 0.1654527289615880 0.1595821580576020 0.0862878935870393 -0.1000000000000000 -0.5266083805000000 20327.5550092185000000 -0.0514168691984178 0.1046974117607580 -0.0734422969499682 0.2799503455014960 0.2489917590200640 0.3746586339673930 0.2388079459053130 0.3679693342846950
0.0800 0.7587338187758670 0.6654944435687730 -0.0879358050549968 -4.5316608540212100 0.4201856029560480 18.1449146140712000 0.2082896980661270 0.1963833825796230 0.1173006295737050 -0.1000000000000000 -0.6008677443000000 37180.0713615876000000 -0.0435691980080517 0.1025092491607880 -0.0752680566199420 0.2859658855181830 0.2463439179170010 0.3774411392189470 0.2367345282757910 0.3712407905364930
0.0900 0.7846617840834190 0.6646697953340180 -0.0863250891406979 -4.4431082348763900 0.4096459868804770 17.7940601032257000 0.2058086667038910 0.2005503414374950 0.1239225551215690 -0.1000000000000000 -0.5999306542000000 36947.8787712051000000 -0.0386068513354472 0.1002656772083840 -0.0754602300716578 0.2879669013021380 0.2455100824949440 0.3784179393900740 0.2363877833587920 0.3725642499849370
0.1000 0.6759351202982480 0.6701555114371590 -0.0842487133409999 -4.2989668796524600 0.3950150942756780 16.9499399186483000 0.1982256814552770 0.2004113577343430 0.1312995606293180 -0.1000000000000000 -0.5923724273999990 36597.5600451842000000 -0.0282989830364419 0.1005680531402610 -0.0799511338270659 0.2864871213393960 0.2433368095307030 0.3758825262843640 0.2343281863791130 0.3701142656330040
0.1500 0.4060442725277190 0.6331119438041180 -0.0719075361587948 -3.8697055665013900 0.3527209416036150 13.7553799942078000 0.2489114740764020 0.3018776519585660 0.2531944049628660 -0.2273218226000000 -0.7549461000999990 5440.3520640067600000 -0.0299967463616727 0.0962871690940792 -0.0762552422410023 0.2888548904585920 0.2369264158171150 0.3735923905191180 0.2282717557908330 0.3681645586333300
0.2000 -0.0964722849285886 0.6394154973768270 -0.0625617809919999 -3.4154331729506900 0.3010051287415760 11.4534631595437000 0.2821393446741870 0.4058929876762180 0.3690896542349010 -0.4384492105000000 -0.8944358918000000 1898.2857019816500000 -0.0036711341998802 0.0693398950336865 -0.0633905167734821 0.2932537473600140 0.2159716768759310 0.3641998428792800 0.2112464445303770 0.3614177924057090
0.2500 -0.3647383426795800 0.6464747603497000 -0.0578247658996581 -3.1964135977713500 0.2821632069794590 9.3622805399371000 0.2473181283189340 0.4087140621326480 0.4091275508533770 -0.5647295578000000 -0.8869576743000000 1202.6438872651600000 -0.0230481052501677 0.0635985592512166 -0.0517929263524518 0.2957833156803400 0.2005738694875840 0.3573760581741280 0.1960766398604580 0.3548715521619380
0.3000 -0.5066096034428090 0.6651087078884250 -0.0560927957029996 -3.0938863341046000 0.2735167424921670 8.2935173490201800 0.2096502844403170 0.4001251672249500 0.4335528490826920 -0.6554113151999990 -0.8545657526000000 967.9255537188150000 -0.0179995073864090 0.0508746350031907 -0.0417662944939413 0.2955895319193470 0.1990806049250280 0.3563793745962490 0.1961542457250350 0.3547529555849480
0.3500 -0.6649758303983760 0.6953229230929930 -0.0557864397714597 -3.0349384847947700 0.2671679125064100 7.6913250281925500 0.2023161205394590 0.4213786462865890 0.4808046291639440 -0.7428322161999990 -0.8762700561999990 873.3816688525000000 -0.0055734214033697 0.0466580942068334 -0.0422068301406186 0.2982216260863880 0.2050086373684360 0.3618904249372630 0.2027190392808950 0.3605983182886170
0.4000 -1.0245292872263400 0.7477063980675440 -0.0562692503039990 -2.8852884017037800 0.2536783288165920 6.2119923952061800 0.1858234788604210 0.4107333337437640 0.5209946684961200 -0.8100884283999990 -0.8530330874999990 794.5532205269830000 0.0004098177393169 0.0403886753646120 -0.0384916849988285 0.2987789982376510 0.2068578206071190 0.3633992951757350 0.2051740007093480 0.3624434581489560
0.4500 -1.1767192815454400 0.7807854544753780 -0.0576268771260726 -2.8427465328831800 0.2513716341911510 5.6484108448966700 0.1887026468902940 0.4164505033363750 0.5807879191359790 -0.8751821459999990 -0.8642899934000000 759.8399393759310000 0.0142197714791134 0.0307891929593598 -0.0345417763728089 0.2980455169408630 0.2077050898342350 0.3632802423909040 0.2066635500615080 0.3626857497787470
0.5000 -1.3699721103726600 0.8260335951960020 -0.0600971406249981 -2.7937608332104700 0.2483537730430820 5.2021129207912500 0.1912072326769610 0.4163804535941900 0.6163803445766500 -0.9166134093000000 -0.8761241065999990 747.1063408592170000 0.0086757291814616 0.0281315838618958 -0.0297855596041406 0.2988253255683690 0.2171380197001870 0.3693852931565640 0.2163378482566530 0.3689154913924880
0.5500 -1.5532301153734600 0.8841219121467910 -0.0636142514828666 -2.7774746094333300 0.2461269298729300 5.2748945458277300 0.1922552801830820 0.4208041398937580 0.6473190646386160 -0.9489890487000000 -0.8873310084000000 734.2611220214530000 0.0079885694661098 0.0262605964386996 -0.0276217316684702 0.2988468611615510 0.2262163167887810 0.3748109769038170 0.2255424149235550 0.3744046305211260
0.6000 -1.7510694008742700 0.9456512032228760 -0.0676680143359787 -2.7659990406711700 0.2459840593699260 5.2326502260400600 0.1856646121052040 0.4151367349613850 0.6685439427938120 -0.9849329436000000 -0.8818026484000000 707.0886231073480000 0.0074237017603430 0.0214264218419423 -0.0228007233673257 0.2969715874045810 0.2312084370851160 0.3763634747221610 0.2307626428710610 0.3760897779393020
0.6500 -1.8812203651728900 0.9989155250987470 -0.0714815223937251 -2.7822077114825400 0.2481313717858710 5.1530276954427200 0.1694624830668270 0.4049886708458540 0.6814504542040380 -1.0153146583999900 -0.8594841094999990 681.4614028632290000 0.0196350915362537 0.0150526924795911 -0.0215740715394286 0.2954635012276740 0.2351953967474790 0.3776447473604260 0.2348427194465870 0.3774252024372300
0.7000 -2.0011372675364000 1.0414823426186300 -0.0743785413870095 -2.8015816681340200 0.2515222494019510 5.1214455547007300 0.1675787426166320 0.4084745747915290 0.6970629308604510 -1.0382766045000000 -0.8628249864999990 673.9691869217830000 0.0259814084850892 0.0078403558745567 -0.0173402456257839 0.2960570452959170 0.2315424218284400 0.3758479309182480 0.2312259898442240 0.3756530745898280
0.7500 -2.0314990724971100 1.0612712694853100 -0.0761444939880500 -2.8411938303340100 0.2583666046875160 5.0513970104537200 0.1680957619203300 0.4032102189640850 0.7080554315362520 -1.0313556675000000 -0.8579717241000000 675.6979435204260000 0.0239285639574445 0.0074392636316948 -0.0161682493304947 0.2951575001067500 0.2297001913951280 0.3740055184034380 0.2294277631124650 0.3738382649703680
0.8000 -2.0713348083169800 1.0808387377773600 -0.0771826900479910 -2.8493436285427500 0.2594995074375930 5.0928181363661800 0.1544249375549970 0.3844974525043310 0.7007764887596430 -1.0231311698000000 -0.8263667377000000 657.2061757191460000 0.0214029074524496 0.0059539323088165 -0.0138202326157295 0.2924385987558100 0.2300565388177360 0.3720837877347760 0.2298456978854890 0.3719534633240150
0.8500 -2.1262894469442700 1.1018607109753000 -0.0783302036376399 -2.8588995970631400 0.2606572708674180 5.0935967372020100 0.1504639323164540 0.3792467896733620 0.6969408900855260 -1.0144829571000000 -0.8137829287000000 653.8125318549530000 0.0211071089179620 0.0019008327668466 -0.0099488373254348 0.2928306239015010 0.2309607956817200 0.3729512882890680 0.2307840014488140 0.3728418292242290
0.9000 -2.2073925801959200 1.1318798449661200 -0.0803255749490028 -2.8708066901482300 0.2616586646777760 5.1233267618852900 0.1544558393365580 0.3837285215652260 0.7012236860739990 -1.0093585997000000 -0.8210169819999990 662.2439869415740000 0.0289033402423253 -0.0019777781552522 -0.0093910224696682 0.2946269771092460 0.2326264459950670 0.3753932857908200 0.2322986984058910 0.3751902729570740
0.9500 -2.3618782822744800 1.1773372149747300 -0.0831133136219246 -2.8589190798699000 0.2591714809709110 5.1245152218844200 0.1606585521223750 0.3919467205487660 0.7031862226528190 -1.0029855543999900 -0.8356389507999990 676.6634212470730000 0.0322919482685976 -0.0043031378218605 -0.0085106024606202 0.2959927052620510 0.2310434003198280 0.3754899924095130 0.2306211043763800 0.3752302964209160
1.0000 -2.4878726728670000 1.2134822214871800 -0.0854280000001306 -2.8543804213112900 0.2593699405690310 4.9780849514747200 0.1576721986608320 0.3903326170865970 0.6932630179184690 -0.9891875651000000 -0.8248044635000000 678.6122701764790000 0.0344742509193550 -0.0054363568289916 -0.0082972422158440 0.2963176996743180 0.2307500744544380 0.3755659409491340 0.2302608656402460 0.3752655664801600
1.0500 -2.6077715643895400 1.2585971052394800 -0.0891555463418651 -2.8698128821985400 0.2620344315381600 5.0106995281376200 0.1568834769642220 0.3926119120922580 0.6859752493739490 -0.9787207632000000 -0.8182870278999990 683.9014863863440000 0.0342851595332001 -0.0084217050339768 -0.0054727622220529 0.2956778853817590 0.2309807392831370 0.3752032966587760 0.2304571871861140 0.3748812172269560
1.1000 -2.6283843967759800 1.2724304040636900 -0.0902954540190852 -2.8957258830060600 0.2658130031005880 5.0680549323866900 0.1552026620595820 0.3911807820188090 0.6792311574060850 -0.9656582968000000 -0.8078533354000000 685.9310034655940000 0.0343732130091374 -0.0110760496482985 -0.0031534311291972 0.2949665179443070 0.2350632307671690 0.3771736591636390 0.2344939964929200 0.3768191623304360
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2.9500 -3.7293477782697800 1.7305044988754600 -0.1157771908946510 -2.9864543650849900 0.2508656441106190 11.7706242218151000 0.1087673659644000 0.2992866185509130 0.5023343957707720 -0.7190851235999990 -0.5619106802000000 643.8430695390050000 -0.0418387212028657 0.0114385205458388 0.0057047398189249 0.2811940369283110 0.2320915251748830 0.3646046659904990 0.2312488305299750 0.3640688231990220
3.0000 -3.7181242535349100 1.7276931468404900 -0.1155813789892250 -2.9923117217806700 0.2523813577739830 11.8386025178292000 0.1081958140488820 0.2968493026283440 0.4983702292088530 -0.7127096177999990 -0.5547507065000000 643.3004613025160000 -0.0434663752687055 0.0115341667660334 0.0062500594261708 0.2812581479022440 0.2324512752973370 0.3648831883613700 0.2315528559466120 0.3643115025063480
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4.0000 -3.5879174492308300 1.6890940080884600 -0.1128841877050190 -3.1224660460706600 0.2822792909686670 12.7543160967594000 0.1119890714433590 0.2817361688665730 0.4534378584333170 -0.6428214690000000 -0.4939849281000000 651.4850608555060000 -0.0583039796710700 0.0092717900996661 0.0145442858770594 0.2713069027359440 0.2407315750359230 0.3627108031082710 0.2392999325376520 0.3617622053016260
4.0500 -3.5763924962613400 1.6868729155391200 -0.1127051537283960 -3.1284169355448200 0.2833667271003130 12.8327594914900000 0.1093760327290160 0.2782208210569330 0.4487487914174280 -0.6387628990999990 -0.4868682186000000 646.5514392717970000 -0.0589747287756861 0.0095363361233895 0.0145877595061200 0.2708009977914730 0.2410222502114330 0.3625257308134700 0.2395545293854020 0.3615515909990150
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9.4500 -3.6252296417523400 1.4734590078938600 -0.0876033217895421 -2.8272924974842200 0.2798661246911100 9.9568486646732500 0.0779673334390103 0.2045033623618200 0.3389628023810330 -0.4839306506000000 -0.3302964102000000 639.2690767054230000 -0.0364576834275160 -0.0377048505377346 0.0483671689776835 0.2379847663807150 0.2436345469237430 0.3405797138468780 0.2418771381549220 0.3393247691980330
9.5000 -3.6291890753648300 1.4740755286446200 -0.0876536115044512 -2.8257298517925400 0.2797180741694120 9.9176348490441000 0.0778646135692573 0.2042469463890010 0.3383567831442550 -0.4833098198999990 -0.3299349122999990 638.9393968115410000 -0.0360094055217468 -0.0378268634922470 0.0482916609998345 0.2377938320589950 0.2436370915964900 0.3404481443140760 0.2418846731002860 0.3391962583020840
9.5500 -3.6337178261922700 1.4747344076730900 -0.0876994165450255 -2.8238293717526200 0.2795154439863610 9.8762867582252200 0.0778935614381431 0.2040196173013390 0.3378878217732090 -0.4826367426000000 -0.3297270065999990 638.8379816021620000 -0.0355937969740863 -0.0379432680192283 0.0482241132657414 0.2375845091330840 0.2436639206360030 0.3403211794756780 0.2419159062574670 0.3390718282021970
9.6000 -3.6372920186273100 1.4750027616986600 -0.0877156829119312 -2.8220326243203100 0.2793515953660900 9.8329346847442500 0.0780269918113046 0.2038442541730860 0.3375404661522670 -0.4820215192000000 -0.3296752041000000 638.9863066040760000 -0.0351487918627335 -0.0380594977772842 0.0481446815238407 0.2373929478567240 0.2436564015824890 0.3401820890702980 0.2419132110620430 0.3389357068508040
9.6500 -3.6367948684118700 1.4742636589705600 -0.0876736231252098 -2.8214265714996900 0.2793685132820200 9.7924789130203500 0.0782053274252555 0.2037778824268180 0.3372390668492160 -0.4814860798999990 -0.3297891102000000 639.3612080601100000 -0.0346375357671435 -0.0381940456533048 0.0480544639188358 0.2371821835733990 0.2436178284835270 0.3400074036836180 0.2418796687918110 0.3387641692674740
9.7000 -3.6334548250800900 1.4726632353229400 -0.0875733072615184 -2.8215704529991900 0.2795224877396360 9.7505101759597900 0.0784877222346124 0.2037844236399530 0.3369955057265060 -0.4808777315000000 -0.3300690017999990 640.0415310612710000 -0.0341481526578314 -0.0383016311484454 0.0479496318233520 0.2369603650516700 0.2435020991748550 0.3397697557287610 0.2417693290206470 0.3385300918094500
9.7500 -3.6278862713021700 1.4705904486300700 -0.0874562913467633 -2.8226770880444000 0.2798372238118730 9.7090645858519900 0.0787597819413020 0.2037594985799430 0.3367005457769100 -0.4802290482000000 -0.3303649006000000 640.7337323417640000 -0.0337597796762549 -0.0383814737720275 0.0478613048148427 0.2367264661639160 0.2433884787054420 0.3395252145997480 0.2416599902436130 0.3382882951965650
9.8000 -3.6219089832604400 1.4683874874746500 -0.0873327347322782 -2.8239198402529100 0.2801860702763330 9.6657189764286600 0.0790526515238753 0.2037099468178050 0.3364818228030130 -0.4796036269999990 -0.3306238406000000 641.2944362338770000 -0.0332430776964065 -0.0384847678284701 0.0477405688480982 0.2364998862831830 0.2433323484556730 0.3393270222321110 0.2416101447882870 0.3380941559337810
9.8500 -3.6141066294235500 1.4657340654784900 -0.0871812501686083 -2.8256844419057100 0.2806116869267060 9.6262800923935100 0.0794070061916134 0.2037263971456380 0.3362471697536570 -0.4789140136999990 -0.3308819422000000 641.9790142517690000 -0.0326936020777195 -0.0386379526119478 0.0476506466152012 0.2363060001928540 0.2432864522815560 0.3391589945599130 0.2415679302597400 0.3379283809583320
9.9000 -3.6046110470587000 1.4625537483932500 -0.0869909066222028 -2.8275892122588000 0.2810579452208420 9.5888786116330800 0.0798387153955572 0.2038659047951920 0.3361687670176440 -0.4783942108000000 -0.3313416531000000 642.7801845789930000 -0.0320028415491399 -0.0388303475596501 0.0475378734149687 0.2361403438202960 0.2432438818702880 0.3390130499654760 0.2415298062245280 0.3377853005600240
9.9500 -3.5947824200752900 1.4592781904090000 -0.0867955772967101 -2.8295373839007700 0.2815176089652910 9.5508587467113700 0.0802364187522683 0.2039584653400550 0.3360978547766230 -0.4778683249999990 -0.3317447512999990 643.6959838189770000 -0.0312406042225414 -0.0390147022607702 0.0473891211033721 0.2360009544070160 0.2431903585115490 0.3388775604167350 0.2414825704864920 0.3376540867956230
10.000 -3.5847384302061900 1.4558870236650600 -0.0865869101137698 -2.8314179611693300 0.2819614748639540 9.5125955757678000 0.0806523182496776 0.2040163247484210 0.3361158872481720 -0.4773499893000000 -0.3321858028999990 644.7099922203470000 -0.0304518098784769 -0.0391893111651246 0.0472212949777613 0.2358942564213900 0.2431253208902690 0.3387565820328770 0.2414245587622760 0.3375380242078810
""")
[docs]class CauzziEtAl2014NoSOF(CauzziEtAl2014):
"""
Returns the Cauzzi et al (GMPE) for the case when no style-of-faulting is
input. This modifies both the expected ground motion as well as the
inter-event (and thus total) standard deviations.
"""
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag',))
def _compute_mean(self, C, rup, dists, sites, imt):
"""
Returns the mean ground motion acceleration and velocity
"""
mean = (self._get_magnitude_scaling_term(C, rup.mag) +
self._get_distance_scaling_term(C, rup.mag, dists.rrup) +
self._get_site_amplification_term(C, sites.vs30))
# convert from cm/s**2 to g for SA and from m/s**2 to g for PGA (PGV
# is already in cm/s) and also convert from base 10 to base e.
if isinstance(imt, PGA):
mean = np.log((10 ** mean) * ((2 * np.pi / 0.01) ** 2) *
1e-2 / g)
elif isinstance(imt, SA):
mean = np.log((10 ** mean) * ((2 * np.pi / imt.period) ** 2) *
1e-2 / g)
else:
mean = np.log(10 ** mean)
return mean
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Returns the standard deviation terms assuming no style-of-faulting
is known
"""
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(np.log(10.0 ** C['s']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0 ** C['f']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0 ** C["t"]) + np.zeros(num_sites))
return stddevs
[docs]class CauzziEtAl2014FixedVs30(CauzziEtAl2014):
"""
Implements the Cauzzi et al (2014) model for the case in which
the reference Vs30 in the site amplification term is fixed at 800 m/s
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification scaling term assuming
period dependent reference vs30
"""
return C["bV800"] * np.log10(vs30 / 800.)
[docs]class CauzziEtAl2014FixedVs30NoSOF(CauzziEtAl2014NoSOF):
"""
Implements the Cauzzi et al (2014) model for the case in which
the reference Vs30 in the site amplification term is fixed at 800 m/s
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification scaling term assuming the reference
Vs30 is fixed at 800 m/s
"""
return C["bV800"] * np.log10(vs30 / 800.)
[docs]class CauzziEtAl2014Eurocode8(CauzziEtAl2014):
"""
Implmements the Cauzzi et al. (2014) GMPE for the case in which
the Eurocode 8 site classification is preferred
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification term on the basis of Eurocode 8
site class
"""
s_b, s_c, s_d = self._get_site_dummy_variables(vs30)
return (C["sB"] * s_b) + (C["sC"] * s_c) + (C["sD"] * s_d)
def _get_site_dummy_variables(self, vs30):
"""
Returns the Eurocode 8 site class dummy variable
"""
s_b = np.zeros_like(vs30)
s_c = np.zeros_like(vs30)
s_d = np.zeros_like(vs30)
s_b[np.logical_and(vs30 >= 360., vs30 < 800.)] = 1.0
s_c[np.logical_and(vs30 >= 180., vs30 < 360.)] = 1.0
s_d[vs30 < 180] = 1.0
return s_b, s_c, s_d
[docs]class CauzziEtAl2014Eurocode8NoSOF(CauzziEtAl2014NoSOF):
"""
Implmements the Cauzzi et al. (2014) GMPE for the case in which
the Eurocode 8 site classification is preferred and style of faulting
is not specified.
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification term on the basis of Eurocode 8
site class
"""
s_b, s_c, s_d = self._get_site_dummy_variables(vs30)
return (C["sB"] * s_b) + (C["sC"] * s_c) + (C["sD"] * s_d)
def _get_site_dummy_variables(self, vs30):
"""
Returns the Eurocode 8 site class dummy variable
"""
s_b = np.zeros_like(vs30)
s_c = np.zeros_like(vs30)
s_d = np.zeros_like(vs30)
s_b[np.logical_and(vs30 >= 360., vs30 < 800.)] = 1.0
s_c[np.logical_and(vs30 >= 180., vs30 < 360.)] = 1.0
s_d[vs30 < 180.] = 1.0
return s_b, s_c, s_d