# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2023 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:`CauzziEtAl2014`,
:class:`CauzziEtAl2014NoSOF`,
:class:`CauzziEtAl2014FixedVs30`,
:class:`CauzziEtAl2014FixedVs30NoSOF`,
:class:`CauzziEtAl2014Eurocode8`,
:class:`CauzziEtAl2014Eurocode8NoSOF`,
:class:`CauzziEtAl2014Eurocode8scaled`
"""
import numpy as np
from scipy.constants import g
from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
def _compute_mean(clsname, sof, adjustment_factor, C, ctx, imt):
"""
Returns the mean ground motion acceleration and velocity
"""
if sof:
sof_term = _get_style_of_faulting_term(C, ctx.rake)
else:
sof_term = 0.
if clsname.endswith("Germany"):
# Point source MSR used - convert rhypo to rrup
rrup = rhypo_to_rrup(ctx.rhypo, ctx.mag)
# Finite rupture source used
rrup[ctx.width > 1E-3] = ctx.rrup[ctx.width > 1E-3]
else:
rrup = ctx.rrup
mean = (_get_magnitude_scaling_term(C, ctx.mag) +
_get_distance_scaling_term(C, ctx.mag, rrup) +
sof_term + _get_site_amplification_term(
clsname, sof, C, ctx.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 imt.string == "PGA":
mean = np.log((10 ** mean) * ((2 * np.pi / 0.01) ** 2) *
1e-2 / g)
elif imt.string[:2] == "SA":
mean = np.log((10 ** mean) * ((2 * np.pi / imt.period) ** 2) *
1e-2 / g)
else:
mean = np.log(10 ** mean)
return mean + adjustment_factor
def _get_distance_scaling_term(C, mag, rrup):
"""
Returns the distance scaling parameter
"""
return (C["r1"] + C["r2"] * mag) * np.log10(rrup + C["r3"])
def _get_magnitude_scaling_term(C, mag):
"""
Returns the magnitude term
"""
return C["c1"] + C["m1"] * mag + C["m2"] * (mag ** 2.)
_get_site_amplification_term = CallableDict()
@_get_site_amplification_term.add(
"CauzziEtAl2014", "CauzziEtAl2014NoSOF", "CauzziEtAl2014Armenia",
"CauzziEtAl2014RhypoGermany")
def _get_site_amplification_term_1(clsname, sof, C, vs30):
"""
Returns the site amplification scaling term assuming
period dependent reference vs30
"""
return C["bV"] * np.log10(vs30 / C["VA"])
@_get_site_amplification_term.add(
"CauzziEtAl2014FixedVs30", "CauzziEtAl2014FixedVs30NoSOF")
def _get_site_amplification_term_2(clsname, sof, C, vs30):
"""
Returns the site amplification scaling term assuming
period dependent reference vs30
"""
return C["bV800"] * np.log10(vs30 / 800.)
@_get_site_amplification_term.add("CauzziEtAl2014Eurocode8")
def _get_site_amplification_term_4(clsname, sof, C, vs30):
"""
Returns the site amplification term on the basis of Eurocode 8
site class
"""
s_b, s_c, s_d = _get_site_dummy_variables(sof, vs30)
return C["sB"] * s_b + C["sC"] * s_c + C["sD"] * s_d
@_get_site_amplification_term.add("CauzziEtAl2014Eurocode8NoSOF")
def _get_site_amplification_term_5(clsname, sof, C, vs30):
"""
Returns the site amplification term on the basis of Eurocode 8
site class
"""
s_b, s_c, s_d = _get_site_dummy_variables(sof, vs30)
return C["sB"] * s_b + C["sC"] * s_c + C["sD"] * s_d
@_get_site_amplification_term.add("CauzziEtAl2014Eurocode8scaled")
def _get_site_amplification_term_6(clsname, sof, C, vs30):
"""
Returns the site amplification term on the basis of Eurocode 8
site class
"""
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 C["sB"] * s_b + C["sC"] * s_c + C["sD"] * s_d
_get_site_dummy_variables = CallableDict()
@_get_site_dummy_variables.add(True)
def _get_site_dummy_variables_1(sof, 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
@_get_site_dummy_variables.add(False)
def _get_site_dummy_variables_2(sof, 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
_get_stddevs = CallableDict()
@_get_stddevs.add(True)
def _get_stddevs_1(sof, C):
"""
Return standard deviations assuming style-of-faulting is known
"""
return [np.log(10.0 ** C['sM']),
np.log(10.0 ** C["tM"]),
np.log(10.0 ** C['f'])]
@_get_stddevs.add(False)
def _get_stddevs_2(sof, C):
"""
Returns the standard deviation terms assuming no style-of-faulting
is known
"""
return [np.log(10.0 ** C['s']),
np.log(10.0 ** C["t"]),
np.log(10.0 ** C['f'])]
def _get_style_of_faulting_term(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
"""
res = np.full_like(rake, C['fSS'])
res[(rake > -150.0) & (rake <= -30.0)] = C['fN']
res[(rake > 30.0) & (rake <= 150.0)] = C['fR']
return res
[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 = {PGA, PGV, SA}
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
#: :attr:`~openquake.hazardlib.const.IMC.GEOMETRIC_MEAN`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation types are inter-event, intra-event and
#: total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT, const.StdDev.TOTAL}
#: Required site parameter is only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is Rrup,
REQUIRES_DISTANCES = {'rrup'}
#: The reference rock conditions. The definition of this parameter is
#: unclear in the paper so we assume a value of 800 m/s
DEFINED_FOR_REFERENCE_VELOCITY = 800.0
#: style of faulting term
sof = True
def __init__(self, adjustment_factor=1.0, **kwargs):
super().__init__(adjustment_factor=adjustment_factor, **kwargs)
self.adjustment_factor = np.log(adjustment_factor)
[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]
mean[m] = _compute_mean(
self.__class__.__name__, self.sof, self.adjustment_factor,
C, ctx, imt)
sig[m], tau[m], phi[m] = _get_stddevs(self.sof, C)
#: 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
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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
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9.1500 -3.6415684868140000 1.4832496750290600 -0.0882801776254173 -2.8316984719199600 0.2795706157440860 10.2292965524120000 0.0774127740445665 0.2054313832171680 0.3414856316940290 -0.4895528027000000 -0.3307385072999990 638.1316644967620000 -0.0383259229823866 -0.0369360409269914 0.0484516171928708 0.2393922545039400 0.2438834516974920 0.3417422852506880 0.2421211728061710 0.3404868776289550
9.2000 -3.6358618030125400 1.4806503766183400 -0.0880951372082101 -2.8313584177433000 0.2797124921374630 10.1831224953033000 0.0774343593906956 0.2051768377633560 0.3409281682670690 -0.4883293713999990 -0.3303773998999990 638.3054168111270000 -0.0382826188349576 -0.0370625470105356 0.0485450115802021 0.2391193626346570 0.2438527968513160 0.3415292902797860 0.2420836969158860 0.3402684027341760
9.2500 -3.6306578720600800 1.4782969192214200 -0.0879297532833681 -2.8310842221739700 0.2798305283546610 10.1386633260520000 0.0775605524907102 0.2049956139727700 0.3405222790283220 -0.4872095866999990 -0.3302475446000000 638.6315712994390000 -0.0381114855795094 -0.0372012360607918 0.0485973441461446 0.2388731886871020 0.2438147533507740 0.3413298027202470 0.2420418117766810 0.3400656391370380
9.3000 -3.6285131734070000 1.4767666345109300 -0.0878221281613636 -2.8302203227721400 0.2798692303064070 10.0895660088383000 0.0776395140424447 0.2048346537755090 0.3400668564641560 -0.4862067884999990 -0.3301435334999990 638.7415782733240000 -0.0378660975262286 -0.0373251358359453 0.0486064193354909 0.2386364124246430 0.2437692904447910 0.3411316524435410 0.2419955524202410 0.3398664218867200
9.3500 -3.6256188748134900 1.4751848179024900 -0.0877223903085246 -2.8298248359189200 0.2799692849142380 10.0438013343963000 0.0778209538599002 0.2047301823165290 0.3397316640919970 -0.4852416660000000 -0.3302405800000000 639.1501627649190000 -0.0374677809083872 -0.0374536957406505 0.0485573801786802 0.2384073926144210 0.2437168969682260 0.3409340269334050 0.2419464858804530 0.3396707035985100
9.4000 -3.6243625074887200 1.4739965848952700 -0.0876414297747248 -2.8287909257367600 0.2799609771275360 9.9997380408693000 0.0779686763238270 0.2046643268601000 0.3394323035667090 -0.4845466159999990 -0.3303758259999990 639.3680439436500000 -0.0369612331478237 -0.0375900670503463 0.0484711915534354 0.2381863894127830 0.2436683681926270 0.3407448161882370 0.2419038545583080 0.3394852440853140
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
""")
# NB: the implementation is really ugly and should be changed by using
# parametric GMPEs: we will do that if the need to add subclasses will arise
[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.
"""
sof = False # no style of faulting term
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
[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
"""
[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
"""
[docs]class CauzziEtAl2014Eurocode8(CauzziEtAl2014):
"""
Implemements the Cauzzi et al. (2014) GMPE for the case in which
the Eurocode 8 site classification is preferred
"""
[docs]class CauzziEtAl2014Eurocode8NoSOF(CauzziEtAl2014NoSOF):
"""
Implemements 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.
"""
[docs]def rhypo_to_rrup(rhypo, mag):
"""
Converts hypocentral distance to an equivalent rupture distance
dependent on the magnitude
"""
rrup = rhypo - (0.7108 + 2.496E-6 * (mag ** 7.982))
rrup[rrup < 3.0] = 3.0
return rrup
# Cauzzi et al. 2014 - Converted from Rhypo
[docs]class CauzziEtAl2014RhypoGermany(CauzziEtAl2014):
"""
Implements the Cauzzi et al. (2015) GMPE applying the rhypo to rrup
adjustment factor adopted for Germany
"""
REQUIRES_DISTANCES = {"rhypo", "rrup"}
REQUIRES_RUPTURE_PARAMETERS = {"rake", "mag", "width"}
[docs]class CauzziEtAl2014Eurocode8scaled(CauzziEtAl2014Eurocode8):
"""
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
"""
#: 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 0.483292714 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 -2.153913989 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
0.0500 -0.133056941 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
0.1000 0.720631637 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 0.457351183 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 -0.041706067 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
0.3000 -0.44693261 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
0.4000 -0.9682344 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
0.5000 -1.314364459 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
0.7500 -1.972769452 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
1.0000 -2.432723783 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
2.0000 -3.428939783 1.6562992065143400 -0.1154147661327820 -3.0442154569996200 0.2641813503629670 8.9746507855722500 0.1058745154124260 0.3256670883462820 0.5351158123025720 -0.7909590998000000 -0.6342277109999990 641.1223369683100000 -0.0162396506874878 -0.0019971914576055 0.0080969196977610 0.2906422190364900 0.2257008081025670 0.3679860789005580 0.2255881657370820 0.3679170015194690
3.0000 -3.663741045 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
4.0000 -3.529301652 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
""")