# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2025 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:`RamadanEtAl2023shallow`,
:class:`RamadanEtAl2023deep`
"""
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
def _compute_distance(rval2, mval, C, kind):
"""
Compute the distance function
"""
if kind == 'shallow': # equation (2) focal depth h ≤ 5km
h1 = 1
mref = 4.8
rval = np.sqrt(rval2 ** 2 + h1 ** 2)
return C['c1'] * np.log10(rval) + C['c2'] * (mval - mref) * np.log10(rval)
elif kind == 'deep': # equation (2) focal depth h > 5km
h2 = 5
mref = 4.8
rval = np.sqrt(rval2 ** 2 + h2 ** 2)
return C['c3'] * np.log10(rval) + C['c4'] * (mval - mref) * np.log10(rval) + C['c5'] * rval
raise ValueError(kind)
def _compute_magnitude(ctx, C):
"""
Compute the magnitude function, equation (9):
"""
return C['a'] + C['b'] * ctx.mag
def _get_site_amplification(ctx, C):
"""
Compute the site amplification function given by FS = eiSi, for
i = 1,2,3 where Si are the coefficients determined through regression
analysis, and ei are dummy variables (0 or 1) used to denote the
different EC8 site classes.
"""
ssb, ssc = _get_site_type_dummy_variables(ctx)
return (C['sB'] * ssb) + (C['sC'] * ssc)
def _get_site_type_dummy_variables(ctx):
"""
Get site type dummy variables, which classified the ctx into
different site classes based on the shear wave velocity in the
upper 30 m (Vs30) according to the EC8 (CEN 2003):
class A: Vs30 > 800 m/s
class B: Vs30 = 360 - 800 m/s
class C: Vs30 = 180 - 360 m/s
class D: Vs30 < 180 m/s
"""
ssb = np.zeros(len(ctx.vs30))
ssc = np.zeros(len(ctx.vs30))
# Class C; Vs30 < 360 m/s.
idx = (ctx.vs30 < 360.0)
ssc[idx] = 1.0
# Class B; 360 m/s <= Vs30 <= 800 m/s.
idx = (ctx.vs30 >= 360.0) & (ctx.vs30 < 800.0)
ssb[idx] = 1.0
return ssb, ssc
[docs]class RamadanEtAl2023shallow(GMPE):
"""
Implements GMPE developed by Fadel Ramadan, Giovanni Lanzano,
Sara Sgobba(2023) and submitted as "Vertical seismic ground shaking
in the volcanic areas of Italy: prediction equations and PSHA
examples" Soil Dynamics and Earthquake Engineering.
GMPE derives from earthquakes in the volcanic areas in Italy in the
magnitude range 3<ML<5 for hypocentral distances <200 km, and for
rock (EC8-A), stiff soil (EC8-B) and soft soil (EC8-C and EC8-D).
The GMPE distinguishes between shallow volcano-tectonic events
related to flank movements (focal depths <5km) and deeper events
occurring due to regional tectonics (focal depths >5km), considering
two different attenuations with distances.
Test tables are generated from a spreadsheet provided by the authors,
and modified according to OQ format (e.g. conversion from cm/s2 to fractions of g).
"""
kind = 'shallow'
#: Supported tectonic region type is 'volcanic'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC
#: Supported intensity measure types are PGA and SA
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation types are inter-event, intra-event
#: and total, page 1904
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameter is Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameter is magnitude.
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is Rhypo.
REQUIRES_DISTANCES = {'rhypo'}
[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]
imean = (_compute_magnitude(ctx, C) +
_compute_distance(ctx.rhypo, ctx.mag, C, self.kind) +
_get_site_amplification(ctx, C))
sigma = np.sqrt(C['tau'] ** 2 + C['phiS2S'] ** 2 + C['phi0'] ** 2)
phi1 = np.sqrt(C['phiS2S'] ** 2 + C['phi0'] ** 2)
istddevs = [sigma, C['tau'], phi1]
# Convert units to g, but only for PGA and SA (not PGV)
if imt.string.startswith(("SA", "PGA")):
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
else: # PGV:
mean[m] = np.log(10.0 ** imean)
# Return stddevs in terms of natural log scaling
sig[m], tau[m], phi[m] = np.log(10.0 ** np.array(istddevs))
# Sigma values in log10
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT a b c1 c2 c3 c4 c5 sB sC tau phiS2S phi0
pga 1.55618537121447 0.333127019670588 -1.80215414835785 0.489760712316293 -1.42712891076597 0.239145223726140 -0.00602954775925354 0.0849029979895893 0.282416332926826 0.158531365456166 0.257849237110302 0.218785421619145
pgv -0.823562722532021 0.564120018641826 -1.58123328827974 0.441957343546818 -1.46869782526347 0.183819014687225 -0.00403706069494924 0.0945375867733048 0.322649894866542 0.111794474452390 0.211984139742539 0.206490964065672
0.025 1.49253698552105 0.352967194440596 -1.81888669781098 0.471134151636350 -1.43537358277680 0.224666216398449 -0.00613337549791585 0.0834547514388841 0.282665251490508 0.159163212679202 0.259722649999760 0.220391148299680
0.04 1.52340332752832 0.361871888850407 -1.85382633747974 0.458191682579385 -1.45413965073425 0.209652046551918 -0.00639937786401334 0.0830638006960337 0.276150212985115 0.161792084380257 0.267659802456287 0.222448414991693
0.05 1.75744248291679 0.322679690570580 -1.87252022766518 0.472080216109852 -1.44452049977985 0.232457295206867 -0.00673689508235783 0.0831537428823732 0.276562816318349 0.166082115086053 0.279566071614903 0.226233335467767
0.07 2.08046466870254 0.282436248671939 -1.91811861340609 0.502764064718793 -1.44089936515435 0.239745404503315 -0.00746552737970068 0.0740041541213114 0.254347538274426 0.174186527179915 0.303201685267428 0.236899062221400
0.1 2.45681831357234 0.230907025091366 -1.95901494275549 0.512196416318455 -1.46205356217297 0.249510764460614 -0.00740236678773967 0.0576485824118061 0.238164224896399 0.188993160819513 0.319502820196321 0.228700008209447
0.15 2.24865135177356 0.277280653590315 -1.92844844845104 0.491864429571195 -1.44263611764468 0.242359474440766 -0.00676221727244252 0.0680899175555899 0.286250284328353 0.196952391896027 0.314668416708834 0.212813532660202
0.2 2.22043131874787 0.270484910271471 -1.87226996871060 0.489877541228117 -1.38337537850874 0.303340401633281 -0.00600393124906965 0.0685675737645497 0.272760687479625 0.196284277494126 0.297032901819520 0.209877257966932
0.25 1.95581165398751 0.327129086323127 -1.83910375068622 0.472960933373851 -1.39302439699428 0.304137928691265 -0.00524611966536042 0.0478728458295583 0.265992590549930 0.179984468395150 0.275997895277545 0.207321060780223
0.3 1.42431662712508 0.431944949795483 -1.80927005855343 0.425933895078030 -1.42183279228429 0.248170995060576 -0.00464975180040887 0.0720783022268137 0.295973680900923 0.175166048198337 0.265638238463579 0.203124052631301
0.35 0.884771023520400 0.530664005427965 -1.78786659520169 0.362881923971613 -1.41858019810732 0.208508315158859 -0.00423277696319091 0.0807968112301128 0.336413817551598 0.169529448183916 0.253726515988399 0.202751455044725
0.4 0.222439087794256 0.664427249126763 -1.75574727097258 0.327997697482776 -1.45357207447374 0.145053194031687 -0.00374929506269615 0.0791803129042107 0.323909607077676 0.170223652754985 0.251382148741827 0.202228804455864
0.45 -0.106591185232871 0.733473681805610 -1.75097840195585 0.312238649588824 -1.48701019107858 0.117419261771302 -0.00372291011823571 0.0849372979970515 0.345958743479481 0.166147265851321 0.240736911729139 0.204033174865472
0.5 -0.394421489452377 0.794913276519799 -1.75346355169159 0.297518262576494 -1.55096939165345 0.0788125816669681 -0.00326004672501193 0.100146371242976 0.362481285185161 0.162184272467937 0.239613994547163 0.202495177415152
0.6 -0.922431523795676 0.893058198307089 -1.72149659618465 0.267752931739568 -1.60988405542445 0.0237484929141557 -0.00265390788202489 0.113352566674329 0.364715905170319 0.154396611910407 0.228178431597656 0.199131124937892
0.7 -1.16808929914921 0.914427714772381 -1.65127901771088 0.277600912537678 -1.57529302690550 0.0440915742626641 -0.00245301007475515 0.105596974722736 0.378268883346709 0.136609106267637 0.225356247819452 0.196092678463843
0.75 -1.20948521581307 0.909196614632457 -1.62964624738193 0.280153311968537 -1.54787551975125 0.0593757897377989 -0.00268726977455889 0.112908921209560 0.387017647857062 0.137447009288124 0.227027403579023 0.193986201635664
0.8 -1.32318315558831 0.926904244937200 -1.63373900799406 0.269700719478004 -1.56858551221175 0.0464701245884586 -0.00247986952574131 0.114331899672671 0.396661181437359 0.135646006255393 0.224632479033389 0.193162293096130
0.9 -1.73220917714665 0.998511774413288 -1.62360119788188 0.248482215548637 -1.61509622490725 -0.00647563651684085 -0.00198840726829246 0.118111820448627 0.396999622781568 0.138511952999162 0.224475216438308 0.186858785306930
1 -1.80451544136929 0.982426394812571 -1.55679895121856 0.280083948255974 -1.58448845970044 0.0165662335740864 -0.00152007913762867 0.116496865872729 0.404821604363572 0.135700611920302 0.223354669239213 0.188225274144191
1.2 -1.85081177797649 0.970031827480477 -1.52627648006118 0.314763490837677 -1.62683913588997 0.0301595084001054 -0.000973042918937311 0.116028668352795 0.385957378262433 0.143878161090144 0.225447510173698 0.183863209485497
1.4 -2.38362660206301 1.05669923695560 -1.49333514610674 0.276966474763392 -1.65061564043184 -0.0329747839564720 -0.00109710019383801 0.112912558107300 0.372785390403438 0.164691435660162 0.219331048490733 0.183329733237713
1.6 -2.56581357086797 1.07937570786662 -1.50661062095013 0.270270869291938 -1.68559912815205 -0.0358238518718565 -0.000907026176122039 0.124556863309157 0.337398138959883 0.172227226552177 0.221367656548737 0.180483033550181
1.8 -2.36952674585974 1.00945767185484 -1.47990326180364 0.298055398377998 -1.65511755247358 0.0229035541171763 -0.000934846475767444 0.131261875702567 0.334852812306200 0.171252298361838 0.221092956104580 0.177306530466935
2 -2.48427003595501 1.01926348928219 -1.48122119382967 0.288038119505369 -1.68523813686047 0.0200224453494581 -0.000599813430603246 0.141640892753419 0.352429899822908 0.172896494539844 0.218744066163145 0.180679264411675
2.5 -2.89877349526432 1.06588601799483 -1.46453443207766 0.265221518594409 -1.69338397500374 -0.0123192801582618 -0.000763898919690631 0.136856874332350 0.334727303520607 0.184559572843780 0.211840025855318 0.183542648565007
3 -3.08143026118988 1.05866733022687 -1.40459806340918 0.288115449943811 -1.67509341185465 -0.0269135749422416 -0.000765220896671696 0.124800435640156 0.347319875530159 0.211080495731782 0.216403996426047 0.180633880187356
3.5 -2.56254071996106 0.903208091846693 -1.34679417451881 0.333130675949184 -1.64898490559263 0.0228896994254513 -0.000720456223244940 0.108687633727651 0.324463700238912 0.219784970042884 0.213480876769815 0.179554056937201
4 -2.41308409477241 0.829857499033524 -1.29669956348625 0.343961866390586 -1.58691523488863 0.0761699406002622 -0.000976132354147058 0.105069651442751 0.305393680944419 0.215451753324127 0.214141751748811 0.180830008362151
4.5 -2.32382052146498 0.788251349268690 -1.28127572136419 0.332517569816050 -1.58303513714938 0.0799342609560004 -0.000818314116145689 0.0888456188143767 0.319913231037914 0.205295970667863 0.201922366573869 0.180593068947733
5 -2.08916683359711 0.706980205347767 -1.25383987171694 0.375546573314401 -1.55672239022568 0.119864070018554 -0.000851691016895212 0.0833328790711912 0.296661208256126 0.202877060713245 0.202136519727228 0.180076594155831
""")
[docs]class RamadanEtAl2023deep(RamadanEtAl2023shallow):
kind = 'deep'
