# -*- 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:`ZafaraniEtAl2018`
class:`ZafaraniEtAl2018VHratio`
"""
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, SA
def _compute_distance(C, ctx):
"""
Compute the second term of the equation 1 which is presented in eq.3 and c2 is zero:
``c1 * log(sqrt(Rjb ** 2 + h ** 2)/Rref)``
"""
rref = 1.0
rval = np.sqrt(ctx.rjb ** 2 + C['h'] ** 2)
return C['c1'] * np.log10(rval / rref)
def _compute_magnitude(C, ctx):
"""
Compute the third term of the equation 1:
e1 + b1 * (M-Mh) + b2 * (M-Mh)**2 for M<=Mh
e1 + b3 * (M-Mh) otherwise
"""
return np.where(
ctx.mag <= C['mh'],
C["e1"] + C['b1'] * (ctx.mag - C['mh']) + C['b2'] * (ctx.mag - C['mh']) ** 2,
C["e1"] + C['b3'] * (ctx.mag - C['mh']))
def _get_mechanism(C, ctx):
"""
Compute the fifth term of the equation 1 described on paragraph :
Get fault type dummy variables, see Table 1
"""
SS, U, TF = utils.get_fault_type_dummy_variables(ctx)
fU = 0
return C['fTF'] * TF + C['fSS'] * SS + fU * U
def _get_site_amplification(C, ctx):
"""
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,...,5, 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, ssd = _get_site_type_dummy_variables(ctx)
sA = 0
return (sA * ssa + C['sB'] * ssb + C['sC'] * ssc +
C['sD'] * ssd)
def _get_site_type_dummy_variables(ctx):
"""
Get site type dummy variables, five different EC8 site classes
The recording ctx are classified into 5 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 = 180 - 360 m/s
class D: Vs30 < 180 m/s
"""
ssa = np.zeros(len(ctx.vs30))
ssb = np.zeros(len(ctx.vs30))
ssc = np.zeros(len(ctx.vs30))
ssd = np.zeros(len(ctx.vs30))
# Class D; Vs30 < 180 m/s.
idx = (ctx.vs30 >= 1E-10) & (ctx.vs30 < 180.0)
ssd[idx] = 1.0
# SClass C; 180 m/s <= Vs30 <= 360 m/s.
idx = (ctx.vs30 >= 180.0) & (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, ssd
[docs]class ZafaraniEtAl2018(GMPE):
"""
Implements GMPE developed by H.Zafarani, L.Luzi, G.Lanzano,
M.R.Soghrat and published as "Empirical equations for the
prediction of PGA and pseudo spectral accelerations using
Iranian strong-motion data",
J Seismol, DOI 10.1007/s10950-017-9704-y.
SA are given from 0.04 s to 4 s.
The regressions are developed considering the geometrical mean of the
horizontal components
"""
#: Supported tectonic region type is 'active shallow crust' because the
#: equations have been derived from data from Iran database, as
#: explained in the 'Introduction'.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are PGA and SA
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, 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 only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is Rjb (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]
imean = (_compute_magnitude(C, ctx) +
_compute_distance(C, ctx) +
_get_site_amplification(C, ctx) +
_get_mechanism(C, ctx))
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
# Return stddevs in terms of natural log scaling
sig[m] = np.log(10.0 ** C['SigmaTot'])
tau[m] = np.log(10.0 ** C['SigmaB'])
phi[m] = np.log(10.0 ** C['SigmaW'])
#: Coefficients for PGA and SA from Table 1
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT mh e1 b1 b2 b3 c1 h fSS fTF sB sC sD SigmaB SigmaW SigmaTot
pga 5.0 2.880 0.554 0.103 0.244 -0.960 7.283 -0.030 -0.039 0.027 0.010 -0.017 0.094 0.283 0.298
0.04 5.0 3.065 0.491 0.043 0.237 -1.027 6.835 -0.023 -0.045 0.010 -0.003 -0.039 0.098 0.294 0.310
0.07 5.3 3.473 0.241 -0.153 0.204 -1.137 8.311 -0.014 -0.046 -0.006 -0.037 -0.055 0.113 0.298 0.319
0.10 5.4 3.673 0.283 -0.116 0.180 -1.159 9.376 -0.024 -0.056 0.007 -0.052 -0.049 0.115 0.305 0.326
0.15 5.6 3.623 0.249 -0.097 0.183 -1.090 10.228 -0.020 -0.028 0.061 -0.001 -0.029 0.105 0.315 0.332
0.20 5.8 3.401 0.193 -0.124 0.207 -0.963 8.795 0.001 0.000 0.071 0.022 0.000 0.103 0.309 0.326
0.25 5.9 3.429 0.227 -0.112 0.232 -0.986 11.315 0.006 0.013 0.080 0.073 0.031 0.102 0.306 0.323
0.30 6.0 3.383 0.245 -0.118 0.227 -0.959 11.012 -0.008 0.010 0.073 0.104 0.048 0.103 0.308 0.325
0.35 6.0 3.325 0.305 -0.104 0.241 -0.947 11.250 -0.012 0.008 0.073 0.113 0.065 0.103 0.310 0.326
0.40 6.1 3.148 0.277 -0.128 0.254 -0.861 7.953 -0.016 0.010 0.076 0.114 0.077 0.104 0.313 0.330
0.45 6.1 3.089 0.286 -0.140 0.262 -0.848 7.498 -0.022 0.011 0.074 0.112 0.097 0.104 0.312 0.329
0.50 6.2 3.085 0.287 -0.139 0.263 -0.847 7.525 -0.013 0.020 0.060 0.095 0.100 0.104 0.313 0.330
0.60 6.3 3.029 0.311 -0.139 0.277 -0.836 6.723 -0.002 0.021 0.056 0.086 0.115 0.106 0.318 0.335
0.70 6.4 2.926 0.280 -0.157 0.302 -0.803 4.967 0.017 0.031 0.047 0.076 0.133 0.107 0.321 0.338
0.80 6.4 2.873 0.317 -0.159 0.330 -0.798 4.966 0.017 0.032 0.047 0.065 0.144 0.108 0.323 0.341
0.90 6.5 2.838 0.303 -0.164 0.373 -0.787 4.973 0.016 0.035 0.043 0.059 0.142 0.108 0.324 0.341
1.00 6.5 2.791 0.341 -0.161 0.372 -0.782 4.975 0.022 0.041 0.034 0.056 0.146 0.108 0.325 0.342
1.20 6.6 2.738 0.397 -0.145 0.388 -0.776 4.976 0.040 0.048 0.038 0.056 0.139 0.108 0.324 0.341
1.40 6.7 2.691 0.442 -0.128 0.377 -0.769 4.980 0.062 0.059 0.039 0.054 0.135 0.109 0.327 0.345
1.60 6.7 2.640 0.511 -0.110 0.410 -0.777 4.981 0.077 0.065 0.040 0.058 0.116 0.110 0.329 0.347
1.80 6.8 2.642 0.558 -0.091 0.395 -0.778 4.994 0.078 0.068 0.047 0.062 0.114 0.109 0.327 0.344
2.00 6.8 2.600 0.631 -0.072 0.397 -0.772 5.001 0.077 0.066 0.051 0.065 0.098 0.107 0.322 0.339
2.50 6.9 2.665 0.789 -0.026 0.135 -0.795 6.960 0.086 0.054 0.053 0.056 0.078 0.104 0.311 0.328
3.00 7.0 2.697 0.851 -0.008 -0.062 -0.809 8.447 0.099 0.048 0.047 0.041 0.043 0.101 0.303 0.319
4.00 7.2 2.626 0.877 0.001 -0.455 -0.775 8.296 0.107 0.023 0.048 0.025 0.032 0.134 0.290 0.319
""")
[docs]class ZafaraniEtAl2018VHratio(ZafaraniEtAl2018):
"""
Calculates the V/H ratio.
"""
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.VERTICAL_TO_HORIZONTAL_RATIO
[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(C, ctx) +
_compute_distance(C, ctx) +
_get_site_amplification(C, ctx) +
_get_mechanism(C, ctx))
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['SigmaB'])
phi[m] = np.log(10.0 ** C['SigmaW'])
#: Coefficients for V/H from Table 2
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT mh e1 b1 b2 b3 c1 h fSS fTF sB sC sD SigmaB SigmaW SigmaTot
PGA 5.0 -0.058 0.054 0.098 0.021 -0.140 6.107 0.005 0.006 0.009 0.033 -0.019 0.056 0.169 0.179
0.04 5.0 0.215 0.022 0.037 0.021 -0.257 6.679 0.021 0.000 0.018 0.016 -0.017 0.059 0.177 0.186
0.07 5.3 0.153 0.116 0.071 0.032 -0.195 7.182 -0.014 -0.023 0.056 0.03 0.013 0.062 0.185 0.195
0.10 5.4 -0.133 -0.023 -0.018 0.041 -0.093 5.187 0.022 0.020 0.075 0.097 -0.007 0.064 0.192 0.203
0.15 5.6 -0.194 0.016 -0.001 0.061 -0.073 7.047 0.000 0.007 0.001 0.087 0.012 0.070 0.209 0.221
0.20 5.8 -0.196 0.048 0.014 0.041 -0.072 5.152 0.008 0.012 -0.051 0.046 -0.021 0.067 0.200 0.210
0.25 5.9 -0.176 0.075 0.032 0.038 -0.067 5.136 -0.022 -0.017 -0.070 -0.018 -0.034 0.067 0.201 0.212
0.30 6.0 -0.118 0.058 0.009 0.040 -0.082 5.130 -0.033 -0.031 -0.082 -0.093 -0.050 0.067 0.201 0.212
0.35 6.0 -0.113 0.058 0.012 0.043 -0.080 5.136 -0.027 -0.025 -0.092 -0.122 -0.049 0.068 0.204 0.215
0.40 6.1 -0.096 0.070 0.019 0.018 -0.082 5.142 -0.021 -0.019 -0.093 -0.139 -0.046 0.068 0.204 0.216
0.45 6.1 -0.090 0.058 0.010 0.027 -0.082 6.776 -0.029 -0.015 -0.090 -0.151 -0.068 0.069 0.207 0.218
0.50 6.2 -0.083 0.048 0.000 0.017 -0.079 5.152 -0.028 -0.021 -0.083 -0.143 -0.078 0.069 0.208 0.219
0.60 6.3 -0.168 -0.017 -0.024 0.015 -0.046 6.935 -0.006 -0.006 -0.073 -0.131 -0.081 0.071 0.213 0.225
0.70 6.4 -0.181 -0.016 -0.021 0.025 -0.030 7.434 -0.008 -0.005 -0.078 -0.126 -0.117 0.074 0.221 0.233
0.80 6.4 -0.174 -0.014 -0.021 0.005 -0.024 7.562 -0.011 -0.003 -0.078 -0.125 -0.140 0.075 0.224 0.236
0.90 6.5 -0.159 0.016 -0.006 -0.027 -0.019 7.186 -0.026 -0.009 -0.073 -0.111 -0.141 0.075 0.225 0.237
1.00 6.5 -0.157 0.020 -0.001 -0.022 -0.022 7.448 -0.016 0.001 -0.073 -0.112 -0.150 0.075 0.225 0.237
1.20 6.6 -0.158 0.002 -0.004 -0.020 -0.029 7.518 -0.001 0.034 -0.083 -0.102 -0.138 0.074 0.223 0.235
1.40 6.7 -0.112 -0.001 -0.009 0.001 -0.044 12.481 -0.012 0.034 -0.085 -0.101 -0.126 0.073 0.220 0.232
1.60 6.7 -0.120 -0.004 -0.011 0.016 -0.041 13.310 -0.007 0.044 -0.073 -0.087 -0.114 0.073 0.220 0.232
1.80 6.8 -0.113 -0.005 -0.011 -0.027 -0.037 12.995 -0.011 0.038 -0.067 -0.089 -0.125 0.073 0.220 0.232
2.00 6.8 -0.117 0.006 -0.005 -0.052 -0.035 13.411 -0.002 0.040 -0.063 -0.090 -0.098 0.073 0.220 0.232
2.50 6.9 -0.184 0.011 0.000 -0.004 0.011 12.964 0.008 0.050 -0.065 -0.089 -0.081 0.070 0.209 0.220
3.00 7.0 -0.188 0.023 0.005 -0.052 0.020 11.714 0.007 0.055 -0.057 -0.084 -0.047 0.069 0.207 0.218
4.00 7.2 -0.212 0.014 0.005 -0.232 0.036 12.426 0.000 0.047 -0.064 -0.082 -0.028 0.074 0.223 0.235
""")
