# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2021 GEM Foundation
#
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# under the terms of the GNU Affero General Public License as published
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"""
Module exports :class:`CampbellBozorgnia2003NSHMP2007`.
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class CampbellBozorgnia2003NSHMP2007(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 Responce Spectra", Bulletin of the Seismological Society of
America, Vol. 93, No. 1, pp. 314-331, 2003.
The class implement the equation as modified by the United States
Geological Survey - National Seismic Hazard Mapping Project (USGS-NSHMP)
for the 2007 Alaska model
(http://earthquake.usgs.gov/hazards/products/ak/2007/).
The class replicates the equation as coded in ``subroutine getCamp2000``
in ``hazFXv7.f`` available from
http://earthquake.usgs.gov/hazards/products/ak/2007/software/.
The equation compute mean value for the 'firm rock' conditon.
"""
#: 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 = set([
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.AVERAGE_HORIZONTAL
#: Supported standard deviation type is Total (see equations 11, 12 pp. 319
#: 320)
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: No sites parameters are required. Mean value is computed for
#: 'firm rock'.
DEFINED_FOR_REFERENCE_VELOCITY = 760.
REQUIRES_SITES_PARAMETERS = set()
#: 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 get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
C = self.COEFFS[imt]
mean = self._get_mean(
C, rup.mag, rup.rake, rup.dip, dists.rrup, dists.rjb
)
stddevs = self._get_stddevs(C, rup.mag, stddev_types, dists.rrup.size)
return mean, stddevs
def _get_mean(self, C, mag, rake, dip, rrup, rjb):
"""
Return mean value (eq. 1, page 319).
"""
f1 = self._compute_magnitude_scaling(C, mag)
f2 = self._compute_distance_scaling(C, mag, rrup)
f3 = self._compute_faulting_mechanism(C, rake, dip)
f4 = self._compute_far_source_soil_effect(C)
f5 = self._compute_hanging_wall_effect(C, rjb, rrup, dip, mag)
mean = (
C['c1'] + f1 + C['c4'] * np.log(np.sqrt(f2)) + f3 + f4 + f5
)
return mean
def _get_stddevs(self, C, mag, stddev_types, num_sites):
"""
Return standard deviation as defined in eq.11 page 319.
"""
std = C['c16'] + np.zeros(num_sites)
if mag < 7.4:
std -= 0.07 * mag
else:
std -= 0.518
# only the 'total' standard deviation is supported, therefore the
# std is always the same for all types
stddevs = [std for _ in stddev_types]
return stddevs
def _compute_magnitude_scaling(self, C, mag):
"""
Compute and return magnitude scaling term (eq.2, page 319)
"""
return C['c2'] * mag + C['c3'] * (8.5 - mag) ** 2
def _compute_distance_scaling(self, C, mag, rrup):
"""
Compute distance scaling term (eq.3, page 319).
The distance scaling assumes the near-source effect of local site
conditions due to 50% very firm soil and soft rock and 50% firm rock.
"""
g = C['c5'] + C['c6'] * 0.5 + C['c7'] * 0.5
return (
rrup ** 2 +
(np.exp(C['c8'] * mag + C['c9'] * (8.5 - mag) ** 2) * g) ** 2
)
def _compute_faulting_mechanism(self, C, rake, dip):
"""
Compute faulting mechanism term (see eq. 5, page 319).
Reverse faulting is defined as occurring on steep faults (dip > 45)
and rake in (22.5, 157.5).
Thrust faulting is defined as occurring on shallow dipping faults
(dip <=45) and rake in (22.5, 157.5)
"""
# flag for reverse faulting
frv = float((dip > 45) and (22.5 <= rake <= 157.5))
# flag for thrust faulting
fth = float((dip <= 45) and (22.5 <= rake <= 157.5))
return C['c10'] * frv + C['c11'] * fth
def _compute_far_source_soil_effect(self, C):
"""
Compute far-source effect of local site conditions (see eq. 6,
page 319) assuming 'firm rock' conditions.
"""
return C['c14']
def _compute_hanging_wall_effect(self, C, rjb, rrup, dip, mag):
"""
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.
"""
# eq. 8 (to be noticed that the USGS-NSHMP implementation defines
# the hanging-wall term for all rjb distances, while in the original
# manuscript, hw is computed only for rjb < 5). Again the 'firm rock'
# is considered
hw = np.zeros_like(rjb)
if dip <= 70.:
hw = (5. - rjb) / 5.
# eq. 9
f_m = 1 if mag > 6.5 else mag - 5.5
# # eq. 10
f_rrup = C['c15'] + np.zeros_like(rrup)
idx = rrup < 8
f_rrup[idx] *= rrup[idx] / 8
# eq. 7 (to be noticed that the f3 factor is not included
# while this is defined in the original manuscript)
f_hw = hw * f_m * f_rrup
return f_hw
#: Coefficient table (table 4, page 321. Coefficients for horizontal
#: component 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
0.10 -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 -0.299 0.370 0.958
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 -0.330 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 -0.453 0.370 0.984
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 -0.528 0.370 0.990
1.0 -3.867 0.812 -0.101 -0.964 0.019 0 0 0.842 -0.105 0.329 0.338 -0.073 -0.072 -0.607 0.281 1.021
2.0 -4.311 0.812 -0.180 -0.964 0.019 0 0 0.842 -0.187 0.060 0.064 -0.124 -0.116 -0.649 0.160 1.021
""")