Source code for openquake.hazardlib.gsim.ji_karimzadeh_azores_island_2025
# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2025 GEM Foundation
#
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# (at your option) any later version.
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# GNU Affero General Public License for more details.
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import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
[docs]class JiEtAl2025Azores(GMPE):
"""
Implements the Ground Motion Model for the Azores Plateau (Portugal)
developed by Ji et al. (2025) based on Simulated Scenario Earthquake Records.
The model is formulated for shallow seismic events on bedrock sites
(Vs30=760 m/s to 1000 m/s).
Reference:
Ji Kun, Shaghayegh Karimzadeh, Saman Yaghmaei Sabegh, Ruibin Hou,
Carvalho Alexandra, & Lourenço Paulo B.. (2025).
Ground motion model using simulated scenario earthquake records in Azores
Plateau (Portugal) at bedrock.
Soil Dynamics & Earthquake Engineering, 197, 109521.
https://doi.org/10.1016/j.soildyn.2025.109521
"""
# Tectonic region type: assumed active shallow crust;
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
# Supported intensity measures: PGA, PGV, 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: total, inter-event, intra-event
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT,
}
# No Vs30 required (bedrock model)
REQUIRES_SITES_PARAMETERS = set()
# Required rupture parameters: magnitude, hypocentral depth
REQUIRES_RUPTURE_PARAMETERS = {"mag", "hypo_depth"}
# Required distance metric: Rjb
REQUIRES_DISTANCES = {"rjb"}
[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.
"""
# Magnitude hinge points
Mh1 = 5.5
Mh2 = 6.5
# Pseudo-depth constant used in distance term
h_const = 3.0
for m, imt in enumerate(imts):
# Load coefficients linked to current IMT
C = self.COEFFS[imt]
# --- 1. Magnitude Scaling (fmag) ---
# if M < 5.5: c2*M + c1
# if 5.5 <= M < 6.5: c3*(M-5.5) + c2*M + c1
# if M >= 6.5: c4*(M-6.5) + c3*(M-5.5) + c2*M + c1
# Base term (common for all magnitudes)
f_mag = C["c2"] * ctx.mag + C["c1"]
# First hinge (M >= 5.5)
f_mag += np.where(ctx.mag >= Mh1, C["c3"] * (ctx.mag - Mh1), 0.0)
# Second hinge (M >= 6.5)
f_mag += np.where(ctx.mag >= Mh2, C["c4"] * (ctx.mag - Mh2), 0.0)
# --- 2. Distance Scaling (fdis) ---
# fdis = (c5 + c6*(M-4.5)) * log(sqrt(R^2 + 3^2)) + c7 * sqrt(R^2 + Fdepth^2)
# Geometric spreading coefficient
slope_geo = C["c5"] + C["c6"] * (ctx.mag - 4.5)
# Geometric spreading distance (3 km pseudo-depth is fixed)
r_geo = np.sqrt(ctx.rjb ** 2 + h_const ** 2)
term_geo = slope_geo * np.log(r_geo)
# Anelastic attenuation term using approximate slant distance
r_hypo_approx = np.sqrt(ctx.rjb ** 2 + ctx.hypo_depth ** 2)
term_anel = C["c7"] * r_hypo_approx
f_dis = term_geo + term_anel
# --- 3. Mean prediction (ln Y) ---
mean[m] = f_mag + f_dis
# --- 4. Standard deviations ---
tau[m] = C["tau"]
phi[m] = C["phi"]
sig[m] = np.sqrt(tau[m] ** 2 + phi[m] ** 2)
# Coefficient table
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 tau phi
pga -4.96708915535545 0.672223287840007 -0.276989292236236 0.0583578621101360 -1.07179692732781 0.172437369807980 -0.0102983602817697 0.236980120274175 0.202708693071518
0.02 -4.91691136987474 0.665702406219193 -0.273901584620427 0.0605481616658419 -1.07384627961283 0.172794337932387 -0.0103167792062967 0.236666343148387 0.204048780957233
0.03 -4.84247071527072 0.656045052943396 -0.269387503570062 0.0637514784760505 -1.07714391865245 0.173385064807256 -0.0103416786253443 0.236203175453200 0.206085682198788
0.05 -4.45275315986674 0.606083224567131 -0.246370388614185 0.0809638304065941 -1.09416637329090 0.176511239134107 -0.0105100858868651 0.233685750300577 0.222456958903459
0.07 -3.90989892704072 0.538881967914159 -0.204327632286716 0.0995181413974921 -1.10101241863761 0.175736108930232 -0.0111333976121632 0.231187002176798 0.247539792076154
0.10 -3.49914531858119 0.498695613156141 -0.164041779914646 0.124546505405421 -1.06629887025290 0.162838097061777 -0.0123511061344311 0.233553349532433 0.269695319566990
0.15 -3.67348114648977 0.549187116624378 -0.156086462359079 0.134667468127294 -0.980415861824312 0.135457334203018 -0.0134260701538668 0.246913754195626 0.265836997352510
0.20 -4.10864446144088 0.628873650363124 -0.192966570576910 0.105548087379453 -0.934983215744768 0.121653783506467 -0.0132111798738809 0.258114275682896 0.246928738497212
0.25 -4.64482340318867 0.717842975729968 -0.239245767027184 0.0651073654174402 -0.906829593473443 0.113080158525795 -0.0126667763853252 0.266968621663372 0.228940816005745
0.30 -5.28257457320302 0.819143571002498 -0.300910403188959 0.0587456536959487 -0.880402182552481 0.107009276627017 -0.0122763510040605 0.274687684359960 0.213929103917908
0.35 -6.02152052624861 0.937338845778299 -0.376004509278418 0.0317596092298837 -0.857363974587456 0.100782016812873 -0.0118689104958076 0.284254976498577 0.201202250962606
0.40 -6.66549023454421 1.03952030692445 -0.442330566774180 0.0146673627378387 -0.850006054688467 0.0978647125161091 -0.0113097521558465 0.291433660541297 0.191067066722068
0.45 -7.28218091506534 1.13740137002579 -0.508944125647674 -0.0238083594104635 -0.850969239627741 0.0979542540656805 -0.0107360514461984 0.297197771526406 0.182862123380182
0.50 -7.93428573560860 1.24010022319132 -0.575018903630375 -0.0502044021087550 -0.846507362263441 0.0959969379819393 -0.0102499795018604 0.302612100290133 0.176204970669932
0.60 -9.23413155490809 1.44135986348444 -0.694648821509520 -0.132349841730783 -0.825671684823805 0.0917769077069652 -0.00972057708163194 0.314617837085380 0.164567266286304
0.70 -10.4125065894592 1.62241030605266 -0.792591989468677 -0.203513090173950 -0.810179344624905 0.0873459944989140 -0.00920818873012090 0.324868795928303 0.155706803625198
0.80 -11.4453648185030 1.77889114331285 -0.876639342886565 -0.279205434676468 -0.803740322759807 0.0878443206257868 -0.00880985954996364 0.331605869197641 0.148982477692131
1.0 -13.2362994875980 2.04373068911682 -0.986491725618872 -0.420380600575133 -0.789381409273985 0.0844125861503426 -0.00793418504865400 0.345743966865382 0.136307103672930
1.2 -14.6136068664800 2.23747462034880 -1.03237584676630 -0.562563541931038 -0.776611962218868 0.0812229193351992 -0.00726086985087434 0.355989586022079 0.124440075160368
1.5 -16.0795885581007 2.42842315723775 -1.04366211115078 -0.725170260681383 -0.772335684911641 0.0836960716206892 -0.00630440163561198 0.368150858891495 0.111468233004069
2.0 -17.5070035971010 2.57756165408822 -0.956026569513148 -0.873242813885683 -0.777730534887090 0.0918622817211007 -0.00469142115446361 0.384725951835023 0.103789691706469
2.5 -18.4113176221174 2.64997760869579 -0.862446196989016 -0.881527588732902 -0.788854448235472 0.0995646573169405 -0.00333285447705191 0.395228339156854 0.101102383653251
3.0 -18.7690990609193 2.63671859844353 -0.737764218719865 -0.819530406582306 -0.802873793348393 0.109303960206381 -0.00248789839985708 0.399257643516076 0.101271043694488
4.0 -18.8048676186723 2.52038298090437 -0.516102686272828 -0.601695335234970 -0.842687684867223 0.130973662786576 -0.00122650853926933 0.400096989113447 0.104030327193461
pgv -3.32010242991311 1.12745819943232 -0.373893613834902 -0.112943647344538 -1.07977779174574 0.233118785856743 -0.00657639934690607 0.275714874417806 0.123356264698372
""")
