# -*- 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:`LanzanoEtAl2016`.
"""
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
from openquake.baselib.general import CallableDict
_compute_distance = CallableDict()
@_compute_distance.add('rjb')
def _compute_distance_rjb(dist_type, ctx, C):
"""
Compute the third term of the equation 1:
FD(Mw,R) = [c1j + c2j(M-Mr)] * log10(R/Rh) con j=1,...4 (eq 4)
c coeffs are in matrix C
"""
Mr = 5.0
Rh = 70
LATref = -0.33 * ctx.lon + 48.3
diff = ctx.lat - LATref
R = np.sqrt(ctx.rjb**2 + C['h']**2)
dist_term = (diff >= 0) * (C['c11'] + C['c21'] * (ctx.mag - Mr)) *\
(R <= Rh) * np.log10(R/Rh) +\
(diff >= 0) * (C['c12'] + C['c22'] * (ctx.mag - Mr)) *\
(R > Rh) * np.log10(R/Rh) +\
(diff < 0) * (C['c13'] + C['c23'] * (ctx.mag - Mr)) *\
(R <= Rh) * np.log10(R/Rh) +\
(diff < 0) * (C['c14'] + C['c24'] * (ctx.mag - Mr)) *\
(R > Rh) * np.log10(R/Rh)
return dist_term
@_compute_distance.add('rhypo')
def _compute_distance_rhypo(dist_type, ctx, C):
"""
Compute the third term of the equation 1:
FD(Mw,R) = [c1j + c2j(M-Mr)] * log10(R/Rh) con j=1,...4 (eq 4)
c coeffs are in matrix C
"""
Mr = 5.0
Rh = 70
LATref = -0.33 * ctx.lon + 48.3
diff = ctx.lat - LATref
R = ctx.rhypo
dist_term = (diff >= 0) * (C['c11'] + C['c21'] * (ctx.mag - Mr)) *\
(R <= Rh) * np.log10(R/Rh) +\
(diff >= 0) * (C['c12'] + C['c22'] * (ctx.mag - Mr)) *\
(R > Rh) * np.log10(R/Rh) +\
(diff < 0) * (C['c13'] + C['c23'] * (ctx.mag - Mr)) *\
(R <= Rh) * np.log10(R/Rh) +\
(diff < 0) * (C['c14'] + C['c24'] * (ctx.mag - Mr)) *\
(R > Rh) * np.log10(R/Rh)
return dist_term
def _compute_magnitude(ctx, C):
"""
Compute the second term of the equation 1:
Fm(M) = b1(M-Mr) + b2(M-Mr)^2 Eq (5)
"""
Mr = 5
return C['a'] + C['b1'] * (ctx.mag - Mr) + C['b2'] * (ctx.mag - Mr)**2
def _get_basin_effect_term(ctx, C):
"""
Get basin correction for ctx in the Po Plain.
if ctx.bas == 0 the correction is not necessary,
otherwise if ctx.bas == 1 the site is in the Po Plain
and the correction is applied.
"""
delta = np.zeros(len(ctx.vs30))
delta[ctx.bas == 1] = 1.0
return C['dbas'] * delta
def _get_mechanism(ctx, C):
"""
Compute the part of the second term of the equation 1 (FM(SoF)):
Get fault type dummy variables
"""
UN, NF, TF = utils.get_fault_type_dummy_variables(ctx)
return C['fNF'] * NF + C['fTF'] * TF + C['fUN'] * UN
def _get_site_amplification(ctx, C):
"""
Compute the fourth term of the equation 1 described on paragraph :
The functional form Fs in Eq. (1) represents the site amplification and
it is given by FS = sj Cj , for j = 1,...,3, where sj are the
coefficients to be determined through the regression analysis,
while Cj are dummy variables used to denote the five different EC8
site classes
"""
ssa, ssb, ssc = _get_site_type_dummy_variables(ctx)
return (C['sA'] * ssa) + (C['sB'] * ssb) + (C['sC'] * ssc)
def _get_site_type_dummy_variables(ctx):
"""
Get site type dummy variables, five different EC8 site classes
The recording ctx are classified into 3 classes,
based on the shear wave velocity intervals in the uppermost 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 < 360 m/s
"""
ssa = np.zeros(len(ctx.vs30))
ssb = np.zeros(len(ctx.vs30))
ssc = np.zeros(len(ctx.vs30))
# Class C; 180 m/s <= 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)
ssb[idx] = 1.0
# Class A; Vs30 > 800 m/s.
idx = (ctx.vs30 >= 800.0)
ssa[idx] = 1.0
return ssa, ssb, ssc
[docs]class LanzanoEtAl2016_RJB(GMPE):
"""
Implements GMPE developed by G.Lanzano, M. D'Amico, C.Felicetta, R.Puglia,
L.Luzi, F.Pacor, D.Bindi and published as
"Ground-Motion Prediction Equations
for Region-Specific Probabilistic Seismic-Hazard Analysis",
Bull Seismol. Soc. Am., DOI 10.1785/0120150096
SA are given up to 4 s.
The regressions are developed considering the geometrical mean of the
as-recorded horizontal components
"""
#: 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 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
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameter
REQUIRES_SITES_PARAMETERS = {'vs30', 'lon', 'lat', 'bas'}
#: 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.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
dist_type = 'rjb' if "RJB" in self.__class__.__name__ else 'rhypo'
imean = (_compute_magnitude(ctx, C) +
_compute_distance(dist_type, ctx, C) +
_get_site_amplification(ctx, C) +
_get_basin_effect_term(ctx, C) +
_get_mechanism(ctx, 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] = np.log(10.0 ** C['SigmaTot'])
tau[m] = np.log(10.0 ** C['tau'])
phi[m] = np.log(10.0 ** C['phi'])
#: Coefficients from SA PGA and PGV from Table S2
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT a b1 b2 c11 c21 c12 c22 c13 c23 c14 c24 h fNF fTF fUN sA sB sC dbas tau phi SigmaTot
0.040 0.122 0.565 -0.015 -1.967 0.305 -0.968 0.026 -1.872 0.567 -2.280 0.443 6.507 0.058 0.199 0.000 0.000 0.028 0.189 -0.094 0.108 0.324 0.342
0.070 0.258 0.555 -0.017 -2.131 0.299 -0.885 0.087 -1.986 0.593 -2.501 0.486 7.296 0.042 0.182 0.000 0.000 -0.002 0.161 -0.099 0.113 0.340 0.359
0.100 0.334 0.537 -0.011 -2.125 0.268 -0.742 0.123 -1.996 0.486 -2.573 0.451 7.463 0.032 0.193 0.000 0.000 0.018 0.180 -0.102 0.118 0.354 0.373
0.150 0.431 0.561 -0.008 -1.979 0.235 -0.804 0.070 -1.890 0.452 -2.443 0.348 7.073 0.024 0.183 0.000 0.000 0.033 0.180 -0.081 0.118 0.353 0.372
0.200 0.436 0.579 -0.014 -1.847 0.201 -0.810 0.066 -1.820 0.348 -2.321 0.364 6.698 0.022 0.191 0.000 0.000 0.058 0.209 -0.070 0.114 0.342 0.360
0.250 0.436 0.610 -0.020 -1.790 0.196 -0.905 0.022 -1.683 0.357 -2.205 0.311 6.933 0.035 0.183 0.000 0.000 0.065 0.201 -0.029 0.110 0.331 0.349
0.300 0.394 0.629 -0.015 -1.759 0.180 -0.963 0.009 -1.639 0.305 -2.065 0.343 7.016 0.038 0.177 0.000 0.000 0.075 0.219 -0.016 0.108 0.323 0.340
0.350 0.335 0.644 -0.008 -1.724 0.165 -1.009 0.015 -1.631 0.243 -1.979 0.328 7.304 0.044 0.178 0.000 0.000 0.081 0.241 0.012 0.105 0.316 0.333
0.400 0.284 0.662 -0.010 -1.662 0.155 -1.080 0.004 -1.641 0.182 -1.863 0.282 7.272 0.031 0.176 0.000 0.000 0.088 0.257 0.046 0.103 0.309 0.326
0.450 0.240 0.683 -0.010 -1.646 0.146 -1.045 -0.017 -1.648 0.169 -1.737 0.266 7.500 0.025 0.169 0.000 0.000 0.078 0.255 0.073 0.102 0.305 0.322
0.500 0.182 0.699 -0.009 -1.601 0.140 -1.027 -0.027 -1.638 0.166 -1.663 0.270 7.493 0.030 0.168 0.000 0.000 0.086 0.270 0.094 0.101 0.303 0.319
0.600 0.084 0.727 -0.017 -1.549 0.107 -0.963 0.000 -1.584 0.170 -1.492 0.244 7.135 0.024 0.150 0.000 0.000 0.097 0.280 0.125 0.101 0.303 0.319
0.700 0.010 0.751 -0.025 -1.509 0.091 -0.956 -0.001 -1.561 0.134 -1.373 0.209 7.044 0.006 0.131 0.000 0.000 0.108 0.292 0.123 0.100 0.301 0.317
0.800 -0.051 0.771 -0.034 -1.460 0.100 -0.989 0.028 -1.520 0.149 -1.307 0.225 6.943 -0.004 0.122 0.000 0.000 0.104 0.292 0.123 0.101 0.302 0.318
0.900 -0.114 0.799 -0.036 -1.417 0.114 -0.985 0.016 -1.463 0.180 -1.212 0.259 6.760 -0.004 0.108 0.000 0.000 0.100 0.293 0.131 0.100 0.300 0.316
1.000 -0.158 0.827 -0.043 -1.373 0.130 -1.009 0.000 -1.411 0.206 -1.189 0.207 6.500 -0.003 0.098 0.000 0.000 0.091 0.289 0.136 0.100 0.300 0.316
1.200 -0.260 0.879 -0.041 -1.316 0.166 -1.038 -0.020 -1.313 0.267 -1.173 0.121 6.026 0.004 0.091 0.000 0.000 0.087 0.289 0.131 0.100 0.299 0.315
1.400 -0.323 0.909 -0.052 -1.264 0.157 -1.139 0.053 -1.208 0.260 -1.262 0.116 5.366 -0.004 0.075 0.000 0.000 0.082 0.293 0.119 0.099 0.298 0.314
1.600 -0.409 0.946 -0.045 -1.238 0.150 -1.214 0.046 -1.128 0.323 -1.278 0.072 5.033 0.000 0.070 0.000 0.000 0.085 0.303 0.115 0.099 0.297 0.313
1.800 -0.486 0.977 -0.039 -1.218 0.141 -1.239 0.066 -1.103 0.313 -1.315 0.014 4.737 -0.001 0.067 0.000 0.000 0.080 0.303 0.119 0.100 0.299 0.315
2.000 -0.554 0.997 -0.037 -1.189 0.138 -1.263 0.069 -1.100 0.282 -1.345 0.057 4.241 -0.010 0.056 0.000 0.000 0.081 0.308 0.117 0.099 0.298 0.314
2.500 -0.742 1.034 -0.027 -1.164 0.151 -1.326 0.045 -1.072 0.299 -1.385 0.060 4.126 0.040 0.054 0.000 0.000 0.085 0.327 0.115 0.100 0.301 0.317
3.000 -0.881 1.057 -0.019 -1.152 0.165 -1.378 0.018 -1.020 0.339 -1.449 0.084 4.170 0.072 0.045 0.000 0.000 0.089 0.325 0.114 0.101 0.304 0.320
4.000 -1.084 1.134 0.019 -1.101 0.244 -1.488 -0.153 -0.971 0.414 -1.619 -0.119 4.454 0.073 0.019 0.000 0.000 0.096 0.322 0.131 0.113 0.298 0.318
pga 0.071 0.603 -0.019 -1.895 0.286 -0.926 0.035 -1.838 0.511 -2.256 0.455 6.701 0.035 0.181 0.000 0.000 0.050 0.203 -0.060 0.106 0.318 0.336
pgv -1.142 0.767 -0.005 -1.623 0.230 -1.037 -0.054 -1.596 0.379 -1.741 0.348 5.904 0.022 0.144 0.000 0.000 0.085 0.260 0.037 0.096 0.288 0.304
""")
[docs]class LanzanoEtAl2016_Rhypo(LanzanoEtAl2016_RJB):
"""
Implements GMPE developed by G.Lanzano, M. D'Amico, C.Felicetta, R.Puglia,
L.Luzi, F.Pacor, D.Bindi and published as "Ground-Motion Prediction Equations
for Region-Specific Probabilistic Seismic-Hazard Analysis",
Bull Seismol. Soc. Am., DOI 10.1785/0120150096
SA are given up to 4 s.
The regressions are developed considering the geometrical mean of the
as-recorded horizontal components
"""
#: Required distance measure is R Hypocentral Distance.
REQUIRES_DISTANCES = {'rhypo'}
#: Coefficients from SA PGA and PGV from esupp Table S3
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT a b1 b2 c11 c21 c12 c22 c13 c23 c14 c24 fNF fTF fUN sA sB sC dbas tau phi SigmaTot
0.040 0.096 0.586 0.036 -2.119 0.151 -0.970 -0.009 -2.191 0.438 -2.263 0.428 0.029 0.207 0.000 0.000 0.040 0.199 -0.084 0.111 0.333 0.351
0.070 0.236 0.569 0.030 -2.242 0.137 -0.918 0.055 -2.270 0.437 -2.509 0.497 0.018 0.196 0.000 0.000 0.010 0.173 -0.094 0.116 0.348 0.367
0.100 0.318 0.553 0.035 -2.221 0.110 -0.785 0.083 -2.281 0.305 -2.586 0.463 0.005 0.205 0.000 0.000 0.027 0.190 -0.097 0.120 0.361 0.380
0.150 0.411 0.578 0.038 -2.106 0.086 -0.830 0.027 -2.181 0.300 -2.436 0.361 -0.001 0.195 0.000 0.000 0.043 0.189 -0.079 0.120 0.359 0.379
0.200 0.416 0.594 0.030 -1.992 0.056 -0.833 0.028 -2.110 0.193 -2.312 0.380 0.000 0.203 0.000 0.000 0.067 0.219 -0.071 0.116 0.349 0.368
0.250 0.421 0.628 0.022 -1.909 0.065 -0.938 -0.019 -1.918 0.238 -2.212 0.313 0.016 0.193 0.000 0.000 0.073 0.209 -0.028 0.113 0.338 0.356
0.300 0.380 0.648 0.027 -1.868 0.054 -0.997 -0.034 -1.860 0.192 -2.079 0.335 0.020 0.187 0.000 0.000 0.082 0.227 -0.014 0.110 0.330 0.347
0.350 0.325 0.664 0.032 -1.809 0.043 -1.051 -0.031 -1.831 0.142 -2.003 0.313 0.026 0.188 0.000 0.000 0.088 0.249 0.016 0.108 0.323 0.340
0.400 0.274 0.682 0.030 -1.745 0.039 -1.119 -0.042 -1.845 0.077 -1.887 0.263 0.012 0.185 0.000 0.000 0.094 0.265 0.049 0.105 0.315 0.332
0.450 0.232 0.702 0.028 -1.713 0.031 -1.089 -0.064 -1.843 0.063 -1.764 0.247 0.006 0.178 0.000 0.000 0.084 0.263 0.077 0.104 0.311 0.328
0.500 0.173 0.718 0.028 -1.668 0.027 -1.068 -0.073 -1.835 0.062 -1.689 0.249 0.010 0.177 0.000 0.000 0.092 0.278 0.099 0.103 0.309 0.325
0.600 0.073 0.746 0.019 -1.639 -0.009 -0.998 -0.052 -1.797 0.073 -1.513 0.215 0.004 0.159 0.000 0.000 0.103 0.287 0.128 0.103 0.308 0.325
0.700 -0.001 0.771 0.012 -1.602 -0.022 -0.990 -0.060 -1.777 0.045 -1.395 0.169 -0.013 0.140 0.000 0.000 0.113 0.300 0.126 0.102 0.305 0.322
0.800 -0.062 0.792 0.001 -1.554 -0.006 -1.022 -0.037 -1.736 0.073 -1.329 0.178 -0.024 0.131 0.000 0.000 0.110 0.299 0.126 0.102 0.306 0.323
0.900 -0.126 0.818 -0.003 -1.521 0.008 -1.010 -0.041 -1.679 0.112 -1.228 0.217 -0.023 0.116 0.000 0.000 0.105 0.300 0.133 0.101 0.304 0.321
1.000 -0.176 0.844 -0.009 -1.490 0.025 -1.028 -0.051 -1.622 0.140 -1.197 0.175 -0.017 0.109 0.000 0.000 0.097 0.297 0.136 0.101 0.304 0.320
1.200 -0.278 0.896 -0.008 -1.444 0.073 -1.053 -0.071 -1.526 0.214 -1.175 0.092 -0.008 0.102 0.000 0.000 0.092 0.296 0.131 0.101 0.303 0.320
1.400 -0.345 0.928 -0.016 -1.417 0.067 -1.141 0.001 -1.437 0.212 -1.255 0.082 -0.014 0.086 0.000 0.000 0.087 0.300 0.118 0.101 0.302 0.319
1.600 -0.432 0.966 -0.008 -1.402 0.062 -1.211 -0.007 -1.357 0.290 -1.268 0.033 -0.011 0.082 0.000 0.000 0.090 0.309 0.114 0.101 0.302 0.318
1.800 -0.510 0.999 0.000 -1.393 0.055 -1.235 0.005 -1.339 0.283 -1.300 -0.025 -0.011 0.078 0.000 0.000 0.085 0.309 0.117 0.101 0.304 0.320
2.000 -0.581 1.020 0.003 -1.380 0.053 -1.255 0.000 -1.350 0.250 -1.324 0.010 -0.017 0.069 0.000 0.000 0.085 0.313 0.116 0.101 0.303 0.319
2.500 -0.766 1.063 0.015 -1.340 0.079 -1.324 -0.043 -1.315 0.286 -1.365 -0.002 0.032 0.063 0.000 0.000 0.087 0.332 0.118 0.102 0.305 0.322
3.000 -0.903 1.086 0.023 -1.322 0.096 -1.377 -0.070 -1.242 0.340 -1.430 0.025 0.065 0.053 0.000 0.000 0.091 0.329 0.117 0.102 0.307 0.324
4.000 -1.105 1.161 0.062 -1.243 0.188 -1.475 -0.209 -1.169 0.418 -1.596 -0.153 0.065 0.027 0.000 0.000 0.098 0.324 0.136 0.101 0.302 0.318
pga 0.053 0.619 0.023 -2.036 0.150 -0.949 -0.006 -2.129 0.383 -2.257 0.455 0.011 0.192 0.000 0.000 0.059 0.212 -0.059 0.109 0.327 0.344
pgv -1.160 0.788 0.033 -1.792 0.124 -1.050 -0.116 -1.868 0.318 -1.740 0.314 0.003 0.155 0.000 0.000 0.092 0.268 0.034 0.099 0.296 0.312
""")
