# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2025 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:`LanzanoEtAl2019`.
"""
import numpy as np
from scipy.constants import g
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib.gsim import utils
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
def _get_stddevs(C):
"""
Return standard deviations as defined in table 1.
"""
return [np.sqrt(C['tau'] ** 2 + C['phi_S2S'] ** 2 + C['phi_0'] ** 2),
C['tau'],
np.sqrt(C['phi_S2S'] ** 2 + C['phi_0'] ** 2)]
def _compute_distance(ctx, dist_type, C):
"""
Compute the third term of the equation 1:
FD(Mw,R) = [c1(Mw-Mref) + c2] * log10(R) + c3(R) (eq 4)
Mref, h, Mh are in matrix C
"""
dist = getattr(ctx, dist_type)
R = np.sqrt(dist ** 2 + C['h'] ** 2)
return ((C['c1'] * (ctx.mag - C['Mref']) + C['c2']) * np.log10(R) +
C['c3']*R)
def _compute_magnitude(ctx, C):
"""
Compute the second term of the equation 1:
b1 * (Mw-Mh) for M<=Mh
b2 * (Mw-Mh) otherwise
"""
dmag = ctx.mag - C["Mh"]
return np.where(
ctx.mag <= C["Mh"], C['a'] + C['b1'] * dmag, C['a'] + C['b2'] * dmag)
def _site_amplification(ctx, C):
"""
Compute the fourth term of the equation 1 :
The functional form Fs in Eq. (1) represents the site amplification and
it is given by FS = klog10(V0/800), where V0 = Vs30 when Vs30 <= 1500
and V0=1500 otherwise
"""
return C['k'] * np.log10(np.clip(ctx.vs30, -np.inf, 1500.0) / 800.0)
def _gen2ref_rock_scaling(C, vs30, kappa0, imt):
"""
Computes the generic-to reference rock scaling factor as presented
in:
Lanzano, G., C. Felicetta, F. Pacor, D. Spallarossa, and P. Traversa
(2022). Generic-To-Reference Rock Scaling Factors for Seismic Ground Motion
in Italy, Bull. Seismol. Soc. Am. 112, 1583–1606, doi: 10.1785/0120210063
The coefficients are from table S2. They allow to scale the grond motion to
a reference rock from a generic site.
kappa0 is in meter.
"""
return C['a'] + C['b'] * np.log10(vs30/800.0) + C['c'] * kappa0
def _ness_correction(ctx, dist_type, C):
"""
Compute near-source correction C in Eq. 4 of Sgobba, S., Felicetta,
C., Lanzano, G., Ramadan, F., D’Amico, M., & Pacor, F. (2021).
NESS2. 0: An updated version of the worldwide dataset for calibrating
and adjusting ground‐motion models in near source.
Bulletin of the Seismological Society of America, 111(5), 2358-2378.
"""
dist = getattr(ctx, dist_type)
R = np.sqrt(dist ** 2 + C['hR'] ** 2)
SS, _NF, TF = utils.get_fault_type_dummy_variables(ctx)
return np.where(ctx.mag <= C['MrefR'], C['aR'] + C['bR'] * (ctx.mag - C['MrefR']) +
C['cR'] * np.log10(R) + C['f1R'] * SS + C['f2R'] * TF,
C['aR'] + C['cR'] * np.log10(R) + C['f1R'] * SS + C['f2R'] * TF)
def _get_mechanism(ctx, C):
"""
Compute the part of the second term of the equation 1 (FM(SoF)):
Get fault type dummy variables
"""
SS, _NF, TF = utils.get_fault_type_dummy_variables(ctx)
return C['f1'] * SS + C['f2'] * TF
[docs]class LanzanoEtAl2019_RJB_OMO(GMPE):
"""
Implements GMPE developed by G.Lanzano, L.Luzi, F.Pacor, L.Luzi,
C.Felicetta, R.Puglia, S. Sgobba, M. D'Amico and published as "A Revised
Ground-Motion Prediction Model for Shallow Crustal Earthquakes in Italy",
Bull Seismol. Soc. Am., DOI 10.1785/0120180210
SA are given up to 10 s.
The horizontal component of motion corresponds to RotD50, i.e. the median
of the distribution of the intensity measures, obtained from the
combination of the two horizontal components across all nonredundant
azimuths (Boore, 2010).
"""
#: Supported tectonic region type is 'active shallow crust' because the
#: equations have been derived from data from Italian database ITACA, as
#: explained in the 'Introduction'.
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 = {PGA, PGV, SA}
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.RotD50`
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: 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 only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is R Joyner-Boore distance (eq. 1).
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.
"""
dist_type = 'rjb' if "RJB" in self.__class__.__name__ else 'rrup'
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imean = (_compute_magnitude(ctx, C) +
_compute_distance(ctx, dist_type, C) +
_site_amplification(ctx, C) +
_get_mechanism(ctx, C))
istddevs = _get_stddevs(C)
# 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))
# mean_LogNaturale = np.log((10 ** mean) * 1e-2 / g)
#: Coefficients from SA PGA and PGV from esupp Table S2
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT a b1 b2 c1 c2 c3 k f1 f2 tau phi_S2S phi_0 Mh Mref h
pga 3.4210464090 0.1939540900 -0.0219827770 0.2871492910 -1.4056354760 -0.0029112640 -0.3945759700 0.0859837430 0.0105002390 0.1559878330 0.2205815790 0.2000991410 5.5000000000 5.3239727140 6.9237429440
pgv 2.0774292740 0.3486332380 0.1359129150 0.2840909830 -1.4565164760 -0.0005727360 -0.5927640710 0.0410782350 -0.0123124280 0.1388529950 0.1641479240 0.1938530300 5.7000000000 5.0155451980 5.9310213910
0.010 3.4245483320 0.1925159840 -0.0226504290 0.2875277900 -1.4065574040 -0.0029092280 -0.3936344950 0.0859882130 0.0104732970 0.1561741750 0.2207225690 0.2001331220 5.5000000000 5.3265568770 6.9261983550
0.025 3.4831620980 0.1745072330 -0.0303191060 0.2917712270 -1.4243608230 -0.0028437300 -0.3808661290 0.0869007960 0.0121168920 0.1585446770 0.2231805710 0.2008657270 5.5000000000 5.3726995880 6.9273792970
0.040 3.6506006610 0.1159102530 -0.0646660020 0.3111117150 -1.4695119300 -0.0027310440 -0.3429284420 0.0870477700 0.0161177530 0.1644920090 0.2324602390 0.2038917110 5.5000000000 5.4968889680 6.9815887950
0.050 3.7315797180 0.0938111470 -0.0847276080 0.3184743710 -1.4684793000 -0.0029101640 -0.3201326870 0.0900141460 0.0129486380 0.1679197090 0.2388540270 0.2068943560 5.5000000000 5.5554373580 7.1218137630
0.070 3.8298265420 0.0775399420 -0.1074506180 0.3219830820 -1.4693089940 -0.0034922110 -0.2775266740 0.1027835460 0.0229271220 0.1761561100 0.2512937930 0.2101610770 5.5000000000 5.5053847230 7.2904858360
0.100 3.8042169810 0.1360109680 -0.0692203330 0.2908601720 -1.4016627520 -0.0043005780 -0.2686743880 0.1147824540 0.0248269350 0.1787478720 0.2637458450 0.2113961580 5.5000000000 5.3797044570 7.2742555760
0.150 3.6500641550 0.2565050720 0.0271400960 0.2339551240 -1.3111751160 -0.0047018230 -0.3207560810 0.1109474740 0.0198659050 0.1666766970 0.2596149390 0.2113112910 5.5000000000 5.0965762810 6.6927744070
0.200 3.5441076850 0.3561477800 0.0934922750 0.1983575680 -1.2809085750 -0.0045122270 -0.3768139640 0.0942130060 0.0116640180 0.1611613280 0.2493593750 0.2085199270 5.5000000000 4.8016422440 6.1273995880
0.250 3.4904108560 0.4258794620 0.1431007860 0.1768779550 -1.2710203890 -0.0038947210 -0.4275803190 0.0803226570 0.0097630190 0.1541437520 0.2349586720 0.2074459640 5.5000000000 4.7851094040 6.0907948160
0.300 3.4415379890 0.4717747480 0.1926037060 0.1614915210 -1.2949801370 -0.0032193060 -0.4770515440 0.0776675640 0.0061077540 0.1465825190 0.2248859230 0.2059316980 5.5000000000 4.7167541960 5.9795025500
0.350 3.3446630670 0.5062658120 0.2151211470 0.1564621150 -1.3178170520 -0.0029990590 -0.5306569440 0.0728397670 0.0026993430 0.1410870920 0.2175844480 0.2080023630 5.5000000000 4.3812120300 5.8130994320
0.400 3.2550575400 0.5331242140 0.2421620470 0.1502822370 -1.2806103220 -0.0027428760 -0.5562808430 0.0661760590 0.0011870680 0.1351999940 0.2142019330 0.2045660900 5.5000000000 4.4598958150 5.8073330520
0.450 3.3642504070 0.5364578580 0.1855438960 0.1489823740 -1.3018257500 -0.0022889740 -0.5950316360 0.0648499220 0.0049044230 0.1282711800 0.2116409250 0.2038392300 5.8000000000 4.4733992810 5.9505143630
0.500 3.3608504670 0.5595158750 0.2002091480 0.1445889550 -1.3577631940 -0.0018214290 -0.6175021300 0.0643336580 0.0049344710 0.1292553150 0.2101486370 0.2021378460 5.8000000000 4.3061718270 6.0827633150
0.600 3.3138586220 0.6159734570 0.2429526950 0.1308776180 -1.3751116050 -0.0011783100 -0.6515274580 0.0517509190 -0.0106807380 0.1388319340 0.2085483340 0.2012532670 5.8000000000 4.2621864430 6.0960486570
0.700 3.2215424560 0.6410331910 0.2631217720 0.1310231460 -1.3777586170 -0.0008288090 -0.6770253130 0.0348343350 -0.0138034390 0.1487445760 0.2078712150 0.1990177160 5.8000000000 4.2242791970 5.8705686780
0.750 3.1945748660 0.6615384790 0.2753805270 0.1279582150 -1.3816587680 -0.0006332620 -0.6770002780 0.0325604250 -0.0106144310 0.1493281120 0.2061474600 0.1985444200 5.8000000000 4.2193032080 5.9399226070
0.800 3.1477172010 0.6744754580 0.2843168320 0.1274454970 -1.3805238730 -0.0005387910 -0.6807607950 0.0301501140 -0.0093150580 0.1488858080 0.2059923330 0.1975251810 5.8000000000 4.1788159560 5.9158308810
0.900 3.0438692320 0.6960808380 0.2908389870 0.1307696640 -1.3712299710 -0.0003650810 -0.6901600210 0.0243867030 -0.0057274610 0.1510220880 0.2088059530 0.1964681960 5.8000000000 4.1280019240 5.6499915110
1.000 2.9329562820 0.7162569260 0.2992085610 0.1330221520 -1.3581003000 -0.0003481280 -0.7010380780 0.0187836090 -0.0026838270 0.1498799880 0.2099740670 0.1952706350 5.8000000000 4.0068764960 5.4265347610
1.200 2.7969754630 0.7522683610 0.3148914470 0.1356882390 -1.3418915980 -0.0001946160 -0.7211447760 0.0156692770 -0.0123682580 0.1475708640 0.2085469600 0.1935369570 5.8000000000 4.0000000000 5.2114400990
1.400 2.6681627290 0.7789439750 0.3310958850 0.1374053210 -1.3265422970 -0.0001071290 -0.7304122120 0.0122846810 -0.0159220670 0.1480430620 0.2089391760 0.1905401100 5.8000000000 4.0000000000 5.0911883420
1.600 2.5723270160 0.7847328080 0.3394239090 0.1454225100 -1.3308582950 0.0000000000 -0.7386216010 0.0034499080 -0.0231247190 0.1468224080 0.2119887010 0.1888323370 5.8000000000 4.0644421250 5.1206266020
1.800 2.4933386330 0.7900020080 0.3305433860 0.1542283440 -1.3289912520 0.0000000000 -0.7538191680 -0.0079587620 -0.0354487870 0.1517555390 0.2125975420 0.1861583190 5.8000000000 4.1264090540 5.2737078390
2.000 2.4060176790 0.7777348120 0.3199509080 0.1684793150 -1.3282655150 0.0000000000 -0.7472001440 -0.0111369970 -0.0375300390 0.1533446260 0.2112262090 0.1855430060 5.8000000000 4.2174770140 5.3910987520
2.500 2.2251396500 0.7789914250 0.3280727550 0.1827792890 -1.3593977940 0.0000000000 -0.7332744950 -0.0298755170 -0.0447073420 0.1581459890 0.2057405400 0.1873131960 5.8000000000 4.0841192840 5.2885431340
3.000 2.0653645110 0.7855377910 0.3585874760 0.1917372820 -1.3622291610 -0.0000725000 -0.6907295050 -0.0523142100 -0.0534721760 0.1730562270 0.2046940180 0.1856376420 5.8000000000 4.0000000000 5.0089807590
3.500 1.9413692760 0.8006822910 0.3924715050 0.2003105480 -1.3459808710 -0.0003295060 -0.6572701800 -0.0831135690 -0.0497671120 0.1694808560 0.2000002880 0.1858647730 5.8000000000 4.0000000000 5.2239249130
4.000 1.8088893770 0.7742293710 0.3863288840 0.2209746660 -1.3605497440 -0.0004514760 -0.6361325920 -0.0850828750 -0.0481922640 0.1729190890 0.1933427470 0.1876984700 5.8000000000 4.0000000000 5.1428287170
4.500 1.7067047740 0.7606577820 0.3932273220 0.2318655310 -1.3607064390 -0.0005424670 -0.6212289540 -0.0851787910 -0.0420861940 0.1750836140 0.1912528510 0.1875258320 5.8000000000 4.0000000000 4.9944908560
5.000 1.5674508510 0.7351540960 0.4075899440 0.2444741770 -1.3443973430 -0.0006142880 -0.5996128590 -0.0740372190 -0.0294935120 0.1724655580 0.1849939070 0.1920775290 5.8000000000 4.0995166500 4.9182635170
6.000 1.8015664050 0.6866068140 0.2400330900 0.2681399590 -1.4273047180 -0.0004079660 -0.5582643820 -0.0530155580 -0.0281879710 0.1608258320 0.1827343650 0.1868738640 6.3000000000 4.0725997780 5.6196373890
7.000 1.6596668010 0.6688108030 0.2910039860 0.2736804460 -1.4575752030 -0.0002092330 -0.5293913010 -0.0164879330 -0.0063757230 0.1639920950 0.1793061350 0.1785781870 6.3000000000 4.0597872070 5.3393074950
8.000 1.5146417080 0.6053146580 0.2927231020 0.3021009530 -1.4528220690 -0.0001882700 -0.5054615800 0.0012388470 -0.0011382590 0.1605307940 0.1737530120 0.1769475170 6.3000000000 4.2884159230 5.4984545260
9.000 1.4186859130 0.5413850170 0.2751627760 0.3283351620 -1.4351308790 0.0000000000 -0.5015172920 0.0083605610 0.0036314410 0.1593645820 0.1666775610 0.1771272580 6.3000000000 4.5884949620 6.0000000000
10.000 1.3142120360 0.4897308100 0.2536297690 0.3484436940 -1.4421713740 0.0000000000 -0.4867303450 0.0170019340 0.0044164240 0.1580884750 0.1616666450 0.1776399420 6.3000000000 4.6826704140 6.2391199410
""")
COEFFS_SITE = CoeffsTable(sa_damping=5, table="""
IMT a b c
PGA 0.107 -0.394 -11.775
0.01 0.107 -0.394 -11.775
0.025 0.137 -0.381 -12.812
0.04 0.168 -0.343 -14.276
0.05 0.182 -0.320 -15.012
0.07 0.180 -0.278 -15.428
0.10 0.162 -0.269 -15.014
0.15 0.119 -0.321 -13.081
0.20 0.084 -0.377 -11.228
0.25 0.057 -0.428 -9.620
0.30 0.042 -0.477 -8.360
0.35 0.030 -0.531 -7.276
0.40 0.018 -0.557 -6.266
0.45 0.009 -0.595 -5.563
0.50 0.002 -0.617 -5.174
0.60 -0.006 -0.651 -4.621
0.70 -0.010 -0.677 -4.184
0.75 -0.010 -0.677 -3.968
0.80 -0.009 -0.681 -3.756
0.90 -0.007 -0.690 -3.473
1.00 -0.008 -0.701 -3.298
1.20 -0.010 -0.721 -2.947
1.40 -0.012 -0.730 -2.630
1.60 -0.015 -0.739 -2.337
1.80 -0.021 -0.754 -2.054
2.00 -0.024 -0.747 -1.685
2.50 -0.026 -0.733 -0.954
3.00 -0.024 -0.691 -0.632
3.50 -0.020 -0.657 -0.499
4.00 -0.016 -0.636 -0.444
4.50 -0.016 -0.621 -0.437
5.00 -0.022 -0.600 -0.349
6.00 -0.034 -0.558 -0.409
7.00 -0.043 -0.529 -0.519
8.00 -0.048 -0.505 -0.601
9.00 -0.052 -0.502 -0.493
10.0 -0.055 -0.487 -0.414
""")
[docs]class LanzanoEtAl2019_RUP_OMO(LanzanoEtAl2019_RJB_OMO):
"""
Implements GMPE developed by G.Lanzano, L.Luzi, F.Pacor, L.Luzi,
C.Felicetta, R.Puglia, S. Sgobba, M. D'Amico and published as "A Revised
Ground-Motion Prediction Model for Shallow Crustal Earthquakes in Italy",
Bull Seismol. Soc. Am., DOI 10.1785/0120180210
SA are given up to 10 s.
The prediction is valid for RotD50, which is the median of the
distribution of the intensity measures, obtained from the combination
of the two horizontal components across all nonredundant azimuths
(Boore, 2010).
"""
#: Supported tectonic region type is 'active shallow crust' because the
#: equations have been derived from data from Italian database ITACA, as
#: explained in the 'Introduction'.
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 = {PGA, PGV, SA}
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.RotD50`
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: 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 only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is Rrup (eq. 1).
REQUIRES_DISTANCES = {'rrup'}
#: Coefficients from SA PGA and PGV from esupp Table S2
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT a b1 b2 c1 c2 c3 k f1 f2 tau phi_S2S phi_0 Mh Mref h
pga 3.8476009130 0.0774422740 -0.1419991420 0.3478652700 -1.5533187520 -0.0018762870 -0.3804756380 0.0981863920 0.0312839980 0.1614849070 0.2214693590 0.2009857770 5.5000000000 5.7161225870 6.6412174580
pgv 2.3828051810 0.2389279260 0.0261097410 0.3406251950 -1.5178700950 0.0000000000 -0.5766806200 0.0496574190 0.0048867220 0.1377338650 0.1657577940 0.1947190870 5.7000000000 5.4986237650 5.2603202210
0.010 3.8506248160 0.0758687500 -0.1428322710 0.3483279440 -1.5537399740 -0.0018758340 -0.3795182780 0.0982026160 0.0312888740 0.1617017580 0.2216042230 0.2010196680 5.5000000000 5.7182953400 6.6339536220
0.025 3.9192103880 0.0557696980 -0.1527646590 0.3537205430 -1.5755362770 -0.0017839260 -0.3665232370 0.0994148360 0.0335230700 0.1648739390 0.2239781630 0.2017348520 5.5000000000 5.7583429090 6.6418028640
0.040 4.1174892770 -0.0090338610 -0.1935502850 0.3762847240 -1.6561808690 -0.0015888760 -0.3280283020 0.1003977920 0.0391489610 0.1728423350 0.2330030290 0.2047022980 5.5000000000 5.7989637460 6.7563889150
0.050 4.2100749050 -0.0339492180 -0.2162534440 0.3850707690 -1.6588279250 -0.0017350640 -0.3051389660 0.1038403080 0.0364310640 0.1769569220 0.2393492360 0.2072790280 5.5000000000 5.8513503470 6.9511244450
0.070 4.3116802080 -0.0505614890 -0.2390930110 0.3886131870 -1.6360072930 -0.0023201630 -0.2625774900 0.1169554080 0.0468045100 0.1850495830 0.2515478690 0.2106976190 5.5000000000 5.8718716570 7.2254468560
0.100 4.2619091410 0.0155135150 -0.1931111810 0.3536108950 -1.5607240070 -0.0031932490 -0.2541922120 0.1287730480 0.0481946680 0.1870755970 0.2641319770 0.2116384010 5.5000000000 5.7816875540 7.1942049600
0.150 4.0281333720 0.1490530750 -0.0842910460 0.2904596360 -1.4558853220 -0.0038111280 -0.3065865390 0.1234294560 0.0409920340 0.1747944550 0.2597923620 0.2119010310 5.5000000000 5.5070413070 6.0448362270
0.200 3.9581561800 0.2581085140 -0.0067616210 0.2493181400 -1.4304030950 -0.0035049250 -0.3631567460 0.1054336950 0.0308675300 0.1663095650 0.2500575700 0.2094881320 5.5000000000 5.4083470680 6.0814859680
0.250 3.8975164920 0.3349956980 0.0504825640 0.2239371150 -1.4165129430 -0.0028978730 -0.4143360740 0.0906817050 0.0279033120 0.1577890900 0.2357231150 0.2084723930 5.5000000000 5.4514190000 6.0143888830
0.300 3.8389631040 0.3840688150 0.1030589990 0.2069719800 -1.4440780970 -0.0022541340 -0.4636965900 0.0874129150 0.0234314860 0.1496049650 0.2259333260 0.2073687490 5.5000000000 5.3968851350 5.8135245350
0.350 3.7427724390 0.4229320630 0.1304612770 0.1993820250 -1.4408251060 -0.0020338970 -0.5174986310 0.0820839430 0.0191395270 0.1437104080 0.2185074890 0.2098701290 5.5000000000 5.2806552370 5.8177492120
0.400 3.6333013750 0.4525776370 0.1603621910 0.1917091960 -1.4190236990 -0.0018301470 -0.5434295700 0.0748159970 0.0169681240 0.1358758520 0.2149494900 0.2064883230 5.5000000000 5.2222009260 5.6501186180
0.450 3.7154781180 0.4556396130 0.1097027610 0.1893950510 -1.4373487560 -0.0013790170 -0.5822090800 0.0724614960 0.0200828160 0.1287203560 0.2124451610 0.2057455270 5.8000000000 5.2478823960 5.7811054530
0.500 3.7225644930 0.4791000150 0.1250270520 0.1847593340 -1.4792888180 -0.0008746350 -0.6048678230 0.0719131380 0.0201771040 0.1286518970 0.2113216850 0.2036659890 5.8000000000 5.2517779510 5.9416879950
0.600 3.6682670680 0.5366335520 0.1687213280 0.1707059500 -1.5049666160 -0.0002411380 -0.6392187290 0.0588865330 0.0046486850 0.1365657160 0.2100293700 0.2024728710 5.8000000000 5.2219439350 5.7575653430
0.700 3.5476098040 0.5605925270 0.1871321630 0.1717388940 -1.4920154380 0.0000000000 -0.6643250560 0.0414345280 0.0015640500 0.1444444740 0.2094865120 0.2002723840 5.8000000000 5.1693165540 5.2232086450
0.750 3.4860153280 0.5835516220 0.2009753460 0.1676162740 -1.4705858310 0.0000000000 -0.6633662960 0.0390747580 0.0045913530 0.1444192940 0.2075499490 0.1999247850 5.8000000000 5.1608011770 5.2390714490
0.800 3.4153176700 0.5963140190 0.2090305350 0.1674214930 -1.4563908280 0.0000000000 -0.6668025460 0.0364159000 0.0057644770 0.1435650390 0.2072863380 0.1990343260 5.8000000000 5.1084013460 5.0192508660
0.900 3.2837755070 0.6203647060 0.2174322510 0.1695628290 -1.4268589930 0.0000000000 -0.6750760810 0.0302972660 0.0092171050 0.1439597930 0.2100453700 0.1980967980 5.8000000000 5.0273018570 4.6888779800
1.000 3.1646298450 0.6394268750 0.2244466880 0.1725257020 -1.4104378560 0.0000000000 -0.6858604010 0.0243862220 0.0120110190 0.1425963490 0.2117095410 0.1964539980 5.8000000000 4.9152918370 4.2786484540
1.200 3.0000699100 0.6752604010 0.2398000250 0.1754340770 -1.3847402050 0.0000000000 -0.7049869270 0.0203886700 0.0020858610 0.1376747050 0.2106367700 0.1947050440 5.8000000000 4.8219418190 3.8902573240
1.400 2.8548239110 0.7016598380 0.2555322610 0.1774234610 -1.3693052940 0.0000000000 -0.7139420780 0.0169071570 -0.0016271820 0.1352870520 0.2110771360 0.1914515130 5.8000000000 4.7438528440 3.6282580540
1.600 2.7452884200 0.7087902600 0.2642955350 0.1848978730 -1.3616920690 0.0000000000 -0.7215074520 0.0083121970 -0.0083006310 0.1331921300 0.2141947700 0.1895359950 5.8000000000 4.7549230280 3.7025291230
1.800 2.6642129620 0.7154152980 0.2560921110 0.1931546230 -1.3507839540 0.0000000000 -0.7371011570 -0.0017321440 -0.0190618180 0.1382147940 0.2147123860 0.1868917710 5.8000000000 4.8130574510 3.9589480220
2.000 2.5756862730 0.7028435510 0.2447144810 0.2076118600 -1.3471065740 0.0000000000 -0.7307501910 -0.0050040160 -0.0212358510 0.1397875260 0.2129299180 0.1864771670 5.8000000000 4.8506617380 4.1479373910
2.500 2.3963959400 0.7033050700 0.2518818530 0.2222780470 -1.3743185070 0.0000000000 -0.7168917870 -0.0246343480 -0.0290936910 0.1437343890 0.2068222070 0.1887206470 5.8000000000 4.7203537770 4.1181389600
3.000 2.2442760420 0.7064408310 0.2805790070 0.2323944870 -1.3938825540 0.0000000000 -0.6755767110 -0.0449346600 -0.0392006000 0.1579916440 0.2051285540 0.1872462500 5.8000000000 4.5967141280 3.6676358910
3.500 2.1509457620 0.7197140890 0.3144950490 0.2408879210 -1.3056875070 0.0000000000 -0.6454403000 -0.0712686810 -0.0377413380 0.1574415450 0.2005062730 0.1876227070 5.8000000000 5.0000000000 3.9746700550
4.000 2.0269129410 0.6873092210 0.3037401830 0.2643086690 -1.3612857890 0.0000000000 -0.6250815320 -0.0736555330 -0.0363730290 0.1610380970 0.1940097180 0.1895939010 5.8000000000 4.8167431120 3.5842582520
4.500 1.9350799290 0.6687716310 0.3061467880 0.2778468310 -1.3144751280 0.0000000000 -0.6110294070 -0.0740593630 -0.0294989060 0.1623295570 0.1927623170 0.1893881480 5.8000000000 5.0000000000 3.2644687160
5.000 1.8090192480 0.6410330200 0.3183807710 0.2915021780 -1.3209096320 0.0000000000 -0.5897990580 -0.0632488020 -0.0172750890 0.1600134890 0.1872621910 0.1941054980 5.8000000000 5.0000000000 3.3548060430
6.000 1.9455190300 0.5901995040 0.1564201050 0.3140022010 -1.3375771520 0.0000000000 -0.5478118740 -0.0424599370 -0.0125854850 0.1509581730 0.1838901820 0.1900203310 6.3000000000 5.0000000000 3.9006202840
7.000 1.7832223090 0.5733237300 0.2019467610 0.3199016260 -1.3374591120 0.0000000000 -0.5197861950 -0.0045757050 0.0111162730 0.1555189840 0.1794302890 0.1819988840 6.3000000000 5.0000000000 3.7233318770
8.000 1.6472982850 0.5073993280 0.2006409390 0.3494261080 -1.4463813400 0.0000000000 -0.4956266160 0.0136222610 0.0172305930 0.1529394340 0.1736945870 0.1803254150 6.3000000000 4.8103931580 4.3526246000
9.000 1.5105710010 0.4450324910 0.1830610430 0.3751346350 -1.4367324130 0.0000000000 -0.4912014160 0.0208945970 0.0217267490 0.1529569490 0.1662440990 0.1804191720 6.3000000000 4.9295888090 4.5509858920
10.000 1.3966806560 0.3900867860 0.1589602600 0.3968394420 -1.4232531770 0.0000000000 -0.4765713040 0.0296164880 0.0222468600 0.1525077910 0.1614679730 0.1808181160 6.3000000000 5.0403227000 4.5998115120
""")
[docs]class LanzanoEtAl2019_RJB_OMOscaled(LanzanoEtAl2019_RJB_OMO):
"""
Implements GMPE developed by G.Lanzano, L.Luzi, F.Pacor, L.Luzi,
C.Felicetta, R.Puglia, S. Sgobba, M. D'Amico and published as "A Revised
Ground-Motion Prediction Model for Shallow Crustal Earthquakes in Italy",
Bull Seismol. Soc. Am., DOI 10.1785/0120180210
SA are given up to 10 s.
The prediction is valid for RotD50, which is the median of the
distribution of the intensity measures, obtained from the combination
of the two horizontal components across all nonredundant azimuths
(Boore, 2010).
Application of a scaling factor that converts the prediction of
LanzanoEtAl2019_RJB_OMO, valid for RotD50, to the corresponding
prediction for the Maximum value.
"""
#: Coefficient table constructed from the electronic suplements of the
#: original paper.
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT a b1 b2 c1 c2 c3 k f1 f2 tau phi_S2S phi_0 Mh Mref h
pga 3.4597007 0.1939541 -0.0219828 0.2871493 -1.4056355 -0.0029113 -0.3945760 0.0859837 0.0105002 0.1559878 0.2205816 0.2000991 5.5000000 5.3239727 6.9237429
pgv 2.1195033 0.3486332 0.1359129 0.2840910 -1.4565165 -0.0005727 -0.5927641 0.0410782 -0.0123124 0.1388530 0.1641479 0.1938530 5.7000000 5.0155452 5.9310214
0.05 3.7703201 0.0938111 -0.0847276 0.3184744 -1.4684793 -0.0029102 -0.3201327 0.0900141 0.0129486 0.1679197 0.2388540 0.2068944 5.5000000 5.5554374 7.1218138
0.10 3.8445966 0.1360110 -0.0692203 0.2908602 -1.4016628 -0.0043006 -0.2686744 0.1147825 0.0248269 0.1787479 0.2637458 0.2113962 5.5000000 5.3797045 7.2742556
0.15 3.6932915 0.2565051 0.0271401 0.2339551 -1.3111751 -0.0047018 -0.3207561 0.1109475 0.0198659 0.1666767 0.2596149 0.2113113 5.5000000 5.0965763 6.6927744
0.20 3.5896393 0.3561478 0.0934923 0.1983576 -1.2809086 -0.0045122 -0.3768140 0.0942130 0.0116640 0.1611613 0.2493594 0.2085199 5.5000000 4.8016422 6.1273996
0.30 3.4885390 0.4717747 0.1926037 0.1614915 -1.2949801 -0.0032193 -0.4770515 0.0776676 0.0061078 0.1465825 0.2248859 0.2059317 5.5000000 4.7167542 5.9795026
0.40 3.3047378 0.5331242 0.2421620 0.1502822 -1.2806103 -0.0027429 -0.5562808 0.0661761 0.0011871 0.1352000 0.2142019 0.2045661 5.5000000 4.4598958 5.8073331
0.50 3.4107980 0.5595159 0.2002091 0.1445890 -1.3577632 -0.0018214 -0.6175021 0.0643337 0.0049345 0.1292553 0.2101486 0.2021378 5.8000000 4.3061718 6.0827633
0.75 3.2462015 0.6615385 0.2753805 0.1279582 -1.3816588 -0.0006333 -0.6770003 0.0325604 -0.0106144 0.1493281 0.2061475 0.1985444 5.8000000 4.2193032 5.9399226
1.00 2.9835849 0.7162569 0.2992086 0.1330222 -1.3581003 -0.0003481 -0.7010381 0.0187836 -0.0026838 0.1498800 0.2099741 0.1952706 5.8000000 4.0068765 5.4265348
2.00 2.4561293 0.7777348 0.3199509 0.1684793 -1.3282655 0.0000000 -0.7472001 -0.0111370 -0.0375300 0.1533446 0.2112262 0.1855430 5.8000000 4.2174770 5.3910988
3.00 2.1181011 0.7855378 0.3585875 0.1917373 -1.3622292 -0.0000725 -0.6907295 -0.0523142 -0.0534722 0.1730562 0.2046940 0.1856376 5.8000000 4.0000000 5.0089808
4.00 1.8623784 0.7742294 0.3863289 0.2209747 -1.3605497 -0.0004515 -0.6361326 -0.0850829 -0.0481923 0.1729191 0.1933427 0.1876985 5.8000000 4.0000000 5.1428287
""")
[docs]class LanzanoEtAl2019_RJB_OMO_RefRock(GMPE):
"""
Implements GMPE developed by G.Lanzano, L.Luzi, F.Pacor, L.Luzi,
C.Felicetta, R.Puglia, S. Sgobba, M. D'Amico and published as "A Revised
Ground-Motion Prediction Model for Shallow Crustal Earthquakes in Italy",
Bull Seismol. Soc. Am., DOI 10.1785/0120180210
SA are given up to 10 s.
The horizontal component of motion corresponds to RotD50, i.e. the median
of the distribution of the intensity measures, obtained from the
combination of the two horizontal components across all nonredundant
azimuths (Boore, 2010).
In this version we scale the ground-motion to reference rock conditions
using the findings of Lanzano et al. (2020) "Generic-To-Reference Rock
Scaling Factors for Seismic Ground Motion in Italy", BSSA, 112(3),
https://doi.org/10.1785/0120210063
"""
#: Supported tectonic region type is 'active shallow crust' because the
#: equations have been derived from data from Italian database ITACA, as
#: explained in the 'Introduction'.
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 = {PGA, SA}
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.RotD50`
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: 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 only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30', 'kappa0'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is R Joyner-Boore distance (eq. 1).
REQUIRES_DISTANCES = {'rjb'}
COEFFS = LanzanoEtAl2019_RJB_OMO.COEFFS
COEFFS_SITE = LanzanoEtAl2019_RJB_OMO.COEFFS_SITE
def __init__(self, kappa0=None):
"""
Instantiate the model. When the kappa0 value is provided when
initializing the class, this overrides the kappa0 value assigned to
the site.
"""
self.kappa0 = kappa0
[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.
"""
if self.kappa0 is not None:
ctx = ctx.copy()
ctx.kappa0 = self.kappa0
[dist_type] = self.REQUIRES_DISTANCES
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imean = (_compute_magnitude(ctx, C) +
_compute_distance(ctx, dist_type, C) +
_site_amplification(ctx, C) +
_get_mechanism(ctx, C))
istddevs = _get_stddevs(C)
# Return stddevs in terms of natural log scaling
sig[m], tau[m], phi[m] = np.log(10.0 ** np.array(istddevs))
# Apply correction to reference according to Lanzano et al.
# (2022; BSSA)
SCOF = self.COEFFS_SITE[imt]
adjustment = _gen2ref_rock_scaling(SCOF, ctx.vs30, ctx.kappa0, imt)
imean += adjustment
# Convert units to g, but only for PGA and SA (not PGV):
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
[docs]class LanzanoEtAl2019_RJB_OMO_NESS2(GMPE):
"""
Implements GMPE developed by G.Lanzano, L.Luzi, F.Pacor, L.Luzi,
C.Felicetta, R.Puglia, S. Sgobba, M. D'Amico and published as "A Revised
Ground-Motion Prediction Model for Shallow Crustal Earthquakes in Italy",
Bull Seismol. Soc. Am., DOI 10.1785/0120180210
SA are given up to 10 s.
The horizontal component of motion corresponds to RotD50, i.e. the median
of the distribution of the intensity measures, obtained from the
combination of the two horizontal components across all nonredundant
azimuths (Boore, 2010).
In this version we add a near-source correction as calibrated in
Sgobba, S., Felicetta, C., Lanzano, G., Ramadan, F., D’Amico, M.,
& Pacor, F. (2021). NESS2. 0: An updated version of the worldwide
dataset for calibrating and adjusting ground‐motion models in near source.
Bulletin of the Seismological Society of America, 111(5), 2358-2378.
"""
#: Supported tectonic region type is 'active shallow crust' because the
#: equations have been derived from data from Italian database ITACA, as
#: explained in the 'Introduction'.
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 = {PGA, SA}
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.RotD50`
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: 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 only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is R Joyner-Boore distance (eq. 1).
REQUIRES_DISTANCES = {'rjb'}
COEFFS = LanzanoEtAl2019_RJB_OMO.COEFFS
[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.
"""
[dist_type] = self.REQUIRES_DISTANCES
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imean = (_compute_magnitude(ctx, C) +
_compute_distance(ctx, dist_type, C) +
_site_amplification(ctx, C) +
_get_mechanism(ctx, C))
istddevs = _get_stddevs(C)
# Return stddevs in terms of natural log scaling
sig[m], tau[m], phi[m] = np.log(10.0 ** np.array(istddevs))
# Apply correction to reference according to Sgobba et al (2021)
COEFF_R = self.COEFFS_R[imt]
adjustment = _ness_correction(ctx, dist_type, COEFF_R)
adjustment[adjustment < 0] = 0
imean += adjustment
# 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:
mean[m] = np.log(10.0 ** imean)
COEFFS_R = CoeffsTable(sa_damping=5, table="""
IMT aR bR cR f1R f2R hR MrefR
pga 0.787478215 0.088770426 -0.413768294 -0.06026392 0.033858525 47.74672921 6.7
pgv 0.8592549 0.071563232 -0.491301268 0.026774225 0.069196361 41.20192962 6.7
0.010 0.787175425 0.08896066 -0.413534 -0.06028122 0.03365462 47.75602121 6.7
0.025 0.764491242 0.093130958 -0.396257625 -0.069223728 0.023615346 48.9614708 6.7
0.040 0.726355304 0.115782012 -0.366697331 -0.074779741 0.013805846 51.15058401 6.7
0.050 0.612054704 0.122639338 -0.299314474 -0.084376271 0.0110746 49.05470755 6.7
0.070 0.400708515 0.108985501 -0.182716111 -0.087470327 0.014284547 45.72288419 6.7
0.100 0.15499496 0.095270453 -0.039327593 -0.099731305 0.018751436 40.91092673 6.7
0.150 -0.00844227 0.055307361 0.054636175 -0.097962926 0.032572387 41.2447101 6.7
0.200 0.009087855 0.057109969 0.043497701 -0.114999243 0.021501432 38.36526231 6.7
0.250 -0.00226902 0.055972206 0.049428586 -0.119321061 0.016406682 40.70320281 6.7
0.300 0.133512633 0.053620918 -0.030034406 -0.12000329 0.018602122 39.49920779 6.7
0.350 0.168517781 0.046429228 -0.052704492 -0.115711083 0.018465044 38.75956761 6.7
0.400 0.274226221 0.039948329 -0.121628272 -0.099248914 0.040560722 41.50434408 6.7
0.450 0.3981889 0.036947038 -0.203091887 -0.071998627 0.065723723 47.32999832 6.7
0.500 0.64992861 0.046333218 -0.338630857 -0.049621838 0.081624352 58.44922068 6.7
0.600 1.131029598 0.025283514 -0.578953165 -0.02155919 0.086655937 78.36451744 6.7
0.700 1.153825076 0.013173396 -0.591675895 -0.007083008 0.083557283 81.12064206 6.7
0.750 1.035871545 -0.001472946 -0.540809171 0.004759027 0.077596681 77.74202337 6.7
0.800 1.024820433 -0.001170074 -0.539405242 0.008952563 0.069284856 74.31852489 6.7
0.900 1.960532101 0.023226485 -0.972275599 0.017006082 0.065846277 96.96619773 6.7
1.000 2.010631147 0.027242195 -1.017890523 0.032711631 0.060514594 86.4514989 6.7
1.200 2.388754809 0.048935181 -1.234235642 0.059185841 0.061690355 80.93239898 6.7
1.400 1.646513458 0.081121474 -0.898090616 0.065535469 0.078703437 60.67359062 6.7
1.600 1.331164843 0.099387448 -0.754064859 0.092138178 0.123430272 51.23511146 6.7
1.800 1.19457951 0.084516446 -0.685088996 0.111323616 0.142764607 51.02063196 6.7
2.000 0.97064787 0.077383157 -0.561095606 0.108652508 0.138837329 48.15759882 6.7
2.500 0.541663899 0.0854089 -0.340575056 0.143613017 0.146084029 37.91884921 6.7
3.000 0.528462362 0.102182005 -0.333805253 0.143023908 0.141003536 39.51910168 6.7
3.500 0.635235933 0.105833915 -0.383912684 0.110313089 0.064950541 35.5783488 6.7
4.000 0.499658821 0.118334308 -0.310867658 0.130591575 0.064005226 32.29346011 6.7
4.500 0.661570957 0.128856871 -0.403179297 0.137230924 0.04353781 34.30312303 6.7
5.000 0.969181154 0.129530859 -0.584060571 0.146503294 0.026093139 38.41884159 6.7
6.000 1.147797426 0.080843293 -0.688890512 0.168970647 0.025350344 43.92034279 6.7
7.000 1.101971251 0.053294728 -0.659793326 0.127546199 0.010135258 44.77159699 6.7
8.000 0.878221711 0.047664714 -0.530125235 0.110275005 -0.004572099 40.26392403 6.7
9.000 0.521928688 0.041132751 -0.318520893 0.08476785 -0.02866004 30.74731071 6.7
10.000 0.489350096 0.035146663 -0.296663906 0.0675214 -0.035733553 26.74188349 6.7
""")
