# -*- 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:`CampbellBozorgnia2003`
class:`CampbellBozorgnia2003Vertical`.
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
from openquake.hazardlib.gsim.campbell_bozorgnia_2003 import (
_compute_magnitude_scaling, _compute_faulting_mechanism
)
def _get_mean(C, mag, rake, dip, rrup, rjb, vs30):
"""
Return mean value (eq. 1, page 319).
"""
f1 = _compute_magnitude_scaling(C, mag)
f2 = _compute_distance_scaling(C, mag, rrup, vs30)
f3 = _compute_faulting_mechanism(C, rake, dip)
f4 = _compute_far_source_soil_effect(C, vs30)
f5 = _compute_hanging_wall_effect(C, rjb, rrup, dip, mag, rake, vs30)
return C['c1'] + f1 + C['c4'] * np.log(np.sqrt(f2)) + f3 + f4 + f5
def _compute_distance_scaling(C, mag, rrup, vs30):
"""
Compute distance scaling term (eq.3, page 319).
"""
svfs , ssr, sfr = _get_site_type_dummy_variables(vs30)
g = C['c5'] + C['c6'] * (svfs + ssr) + C['c7'] * sfr
return rrup ** 2 + (np.exp(
C['c8'] * mag + C['c9'] * (8.5 - mag) ** 2) * g) ** 2
def _get_site_type_dummy_variables(vs30):
"""
Get site type dummy variables, four site types are considered
based on the shear wave velocity intervals in the uppermost 30 m, Vs30:
firm soil: 298 < Vs30 <= 368 m/s
very firm soil: 368 < Vs30 <= 421 m/s
soft rock: 421 < Vs30 <= 830 m/s
firm rock: Vs30 > 830 m/s
"""
svfs = np.zeros(len(vs30))
ssr = np.zeros(len(vs30))
sfr = np.zeros(len(vs30))
# very firm soil
idx = (vs30 >= 368) & (vs30 <= 421)
svfs[idx] = 1.0
# soft rock
idx = (vs30 > 421) & (vs30 <= 830)
ssr[idx] = 1.0
# firm rock
idx = (vs30 > 830)
sfr[idx] = 1.0
return svfs, ssr ,sfr
def _compute_far_source_soil_effect(C, vs30):
"""
Compute far-source effect of local site conditions (see eq. 6,
page 319).
"""
svfs , ssr, sfr = _get_site_type_dummy_variables(vs30)
return C['c12']*svfs + C['c13']*ssr + C['c14']*sfr
def _compute_hanging_wall_effect(C, rjb, rrup, dip, mag, rake, vs30):
"""
Compute hanging-wall effect (see eq. 7, 8, 9 and 10 page 319).
Considers correct version of equation 8 as given in the erratum and not
in the original paper.
"""
# flag for reverse faulting
frv = (dip > 45) & (22.5 <= rake) & (rake <= 157.5)
# flag for thrust faulting
fth = (dip <= 45) & (22.5 <= rake) & (rake <= 157.5)
svfs , ssr, sfr = _get_site_type_dummy_variables(vs30)
# eq. 8
hw = np.zeros_like(rjb)
idx1 = rjb < 5
svfs = ((svfs*((5 - rjb) / 5))*idx1 + 0.0)*(dip <= 70)
ssr = ((ssr*((5 - rjb) / 5))*idx1 + 0.0)*(dip <= 70)
sfr = ((sfr*((5 - rjb) / 5))*idx1 + 0.0)*(dip <= 70)
hw = svfs+ssr+sfr
# eq. 9
f_m = np.where(mag>6.5, 1, np.where(mag<5.5, 0, mag-5.5))
# eq. 10
f_rrup = C['c15'] + np.zeros_like(rrup)
idx = rrup < 8
f_rrup[idx] *= rrup[idx] / 8
# eq. 7
f_hw = (hw * f_m * f_rrup * (frv + fth))
return f_hw
[docs]class CampbellBozorgnia2003(GMPE):
"""
Implements GMPE developed by Kenneth W. Campbell and Yousef Bozorgnia and
published as "Updated Near-Source Ground-Motion (Attenuation) Relations for
the Horizontal and Vertical Components of Peak Ground Acceleration and
Acceleration Response Spectra", Bulletin of the Seismological Society of
America, Vol. 93, No. 1, pp. 314-331, 2003.
"""
#: Supported tectonic region type is 'active shallow crust' (see Abstract)
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are PGA and SA (see Abstract)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is the geometric mean of two
#: horizontal components (see paragraph 'Strong-Motion Database', page 316)
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation type is Total (see equations 11, 12 pp. 319
#: 320)
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
#: Required site parameter is only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude, rake and dip (eq. 1 and
#: following, page 319).
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'dip'}
#: Required distance measure are RRup and Rjb (eq. 1 and following,
#: page 319).
REQUIRES_DISTANCES = {'rrup', '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]
mean[m] = _get_mean(
C, ctx.mag, ctx.rake, ctx.dip, ctx.rrup, ctx.rjb, ctx.vs30)
sig[m] = C['c16'] - np.where(ctx.mag < 7.4, 0.07 * ctx.mag, 0.518)
#: Coefficient table (table 4, page 321. Coefficients for horizontal
#: component SA and for corrected PGA)
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 c16
PGA -4.033 0.812 0.036 -1.061 0.041 -0.005 -0.018 0.766 0.034 0.343 0.351 -0.123 -0.138 -0.289 0.370 0.920
0.05 -3.740 0.812 0.036 -1.121 0.058 -0.004 -0.028 0.724 0.032 0.302 0.362 -0.140 -0.158 -0.205 0.370 0.940
0.08 -3.076 0.812 0.050 -1.252 0.121 -0.005 -0.051 0.648 0.040 0.243 0.333 -0.150 -0.196 -0.208 0.370 0.952
0.10 -2.661 0.812 0.060 -1.308 0.166 -0.009 -0.068 0.621 0.046 0.224 0.313 -0.146 -0.253 -0.258 0.370 0.958
0.15 -2.270 0.812 0.041 -1.324 0.212 -0.033 -0.081 0.613 0.031 0.318 0.344 -0.176 -0.267 -0.284 0.370 0.974
0.20 -2.771 0.812 0.030 -1.153 0.098 -0.014 -0.038 0.704 0.026 0.296 0.342 -0.148 -0.183 -0.359 0.370 0.981
0.30 -2.999 0.812 0.007 -1.080 0.059 -0.007 -0.022 0.752 0.007 0.359 0.385 -0.162 -0.157 -0.585 0.370 0.984
0.40 -3.511 0.812 -0.015 -0.964 0.024 -0.002 -0.005 0.842 -0.016 0.379 0.438 -0.078 -0.129 -0.557 0.370 0.987
0.50 -3.556 0.812 -0.035 -0.964 0.023 -0.002 -0.004 0.842 -0.036 0.406 0.479 -0.122 -0.130 -0.701 0.370 0.990
0.75 -3.709 0.812 -0.071 -0.964 0.021 -0.002 -0.002 0.842 -0.074 0.347 0.419 -0.108 -0.124 -0.796 0.331 1.021
1.00 -3.867 0.812 -0.101 -0.964 0.019 0.000 0.000 0.842 -0.105 0.329 0.338 -0.073 -0.072 -0.858 0.281 1.021
1.50 -4.093 0.812 -0.150 -0.964 0.019 0.000 0.000 0.842 -0.155 0.217 0.188 -0.079 -0.056 -0.954 0.210 1.021
2.00 -4.311 0.812 -0.180 -0.964 0.019 0.000 0.000 0.842 -0.187 0.060 0.064 -0.124 -0.116 -0.916 0.160 1.021
3.00 -4.817 0.812 -0.193 -0.964 0.019 0.000 0.000 0.842 -0.200 -0.079 0.021 -0.154 -0.117 -0.873 0.089 1.021
4.00 -5.211 0.812 -0.202 -0.964 0.019 0.000 0.000 0.842 -0.209 -0.061 0.057 -0.054 -0.261 -0.889 0.039 1.021
""")
[docs]class CampbellBozorgnia2003Vertical(CampbellBozorgnia2003):
#: Supported intensity measure component is vertical
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.VERTICAL
#: Coefficient table (table 4, page 321. Coefficients for vertical
#: component SA and for corrected PGA)
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 c16
PGA -3.108 0.756 0.000 -1.287 0.142 0.046 -0.040 0.587 0.000 0.253 0.173 -0.135 -0.138 -0.256 0.630 0.975
0.05 -1.918 0.756 0.000 -1.517 0.309 0.069 -0.023 0.498 0.000 0.058 0.100 -0.195 -0.274 -0.219 0.630 1.031
0.08 -1.504 0.756 0.000 -1.551 0.343 0.083 0.000 0.487 0.000 0.135 0.182 -0.224 -0.303 -0.263 0.630 1.031
0.10 -1.672 0.756 0.000 -1.473 0.282 0.062 0.001 0.513 0.000 0.168 0.210 -0.198 -0.275 -0.252 0.630 1.031
0.15 -2.323 0.756 0.000 -1.280 0.171 0.045 0.008 0.591 0.000 0.223 0.238 -0.170 -0.175 -0.270 0.630 1.031
0.20 -2.998 0.756 0.000 -1.131 0.089 0.028 0.004 0.668 0.000 0.234 0.256 -0.098 -0.041 -0.311 0.571 1.031
0.30 -3.721 0.756 0.007 -1.028 0.050 0.010 0.004 0.736 0.007 0.249 0.328 -0.026 0.082 -0.265 0.488 1.031
0.40 -4.536 0.756 -0.015 -0.812 0.012 0.000 0.000 0.931 -0.018 0.299 0.317 -0.017 0.022 -0.257 0.428 1.031
0.50 -4.651 0.756 -0.035 -0.812 0.012 0.000 0.000 0.931 -0.043 0.243 0.354 -0.020 0.092 -0.293 0.383 1.031
0.75 -4.903 0.756 -0.071 -0.812 0.012 0.000 0.000 0.931 -0.087 0.295 0.418 0.078 0.091 -0.349 0.299 1.031
1.00 -4.950 0.756 -0.101 -0.812 0.012 0.000 0.000 0.931 -0.124 0.266 0.315 0.043 0.101 -0.481 0.240 1.031
1.50 -5.073 0.756 -0.150 -0.812 0.012 0.000 0.000 0.931 -0.184 0.171 0.211 -0.038 -0.018 -0.518 0.240 1.031
2.00 -5.292 0.756 -0.180 -0.812 0.012 0.000 0.000 0.931 -0.222 0.114 0.115 0.033 -0.022 -0.503 0.240 1.031
3.00 -5.748 0.756 -0.193 -0.812 0.012 0.000 0.000 0.931 -0.238 0.179 0.159 -0.010 -0.047 -0.539 0.240 1.031
4.00 -6.042 0.756 -0.202 -0.812 0.012 0.000 0.000 0.931 -0.248 0.237 0.134 -0.059 -0.267 -0.606 0.240 1.031
""")
