# -*- 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:`TavakoliPezeshk2005`,
:class:`TavakoliPezeshk2005MblgAB1987NSHMP2008`,
:class:`TavakoliPezeshk2005MblgJ1996NSHMP2008`,
:class:`TavakoliPezeshk2005MwNSHMP2008`
"""
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.utils import (
mblg_to_mw_atkinson_boore_87,
mblg_to_mw_johnston_96,
clip_mean)
def _compute_anelastic_attenuation_term(C, rrup, mag):
"""
Compute magnitude-distance scaling term as defined in equation 21,
page 2291 (Tavakoli and Pezeshk, 2005)
"""
r = (rrup**2. + (C['c5'] * np.exp(C['c6'] * mag +
C['c7'] * (8.5 - mag)**2.5))**2.)**.5
f3 = ((C['c4'] + C['c13'] * mag) * np.log(r) +
(C['c8'] + C['c12'] * mag) * r)
return f3
def _compute_geometrical_spreading_term(C, rrup):
"""
Compute magnitude scaling term as defined in equation 19, page 2291
(Tavakoli and Pezeshk, 2005)
"""
f2 = np.ones_like(rrup)
idx1 = np.nonzero(rrup <= 70.)
idx2 = np.nonzero((rrup > 70.) & (rrup <= 130.))
idx3 = np.nonzero(rrup > 130.)
f2[idx1] = (C['c9'] * np.log(rrup[idx1] + 4.5))
f2[idx2] = (C['c10'] * np.log(rrup[idx2]/70.) +
C['c9'] * np.log(rrup[idx2] + 4.5))
f2[idx3] = (C['c11'] * np.log(rrup[idx3]/130.) +
C['c10'] * np.log(rrup[idx3]/70.) +
C['c9'] * np.log(rrup[idx3] + 4.5))
return f2
def _compute_magnitude_scaling_term(C, mag):
"""
Compute magnitude scaling term as defined in equation 19, page 2291
(Tavakoli and Pezeshk, 2005)
"""
if (mag > 8.5).any():
raise ValueError('Magnitude %s > 8.5' % mag)
return C['c1'] + C['c2'] * mag + C['c3'] * (8.5 - mag) ** 2.5
[docs]class TavakoliPezeshk2005(GMPE):
"""
Implements the GMPE developed by B. Tavakoli and S. Pezeshk in 2005
and published as "Empirical-Stochastic Ground-Motion Prediction for
Eastern North America" (2005, Bull. Seism. Soc. Am., Volume 95, No. 6,
pages 2283-2296).
"""
#: Supported tectonic region type is stable continental crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are peak ground acceleration
#: and spectral acceleration, see abstract
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure horizontal.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL
#: Supported standard deviation type is total, see equation 23, pag 2291.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
#: This GMPE doesn't require site parameters since it has been developed
#: for hard rock ctx (see page 2290)
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters is magnitude
#: See equation 18 page page 2291
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is Rrup.
#: See equation 18 page page 2291
REQUIRES_DISTANCES = {'rrup'}
kind = 'base'
[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]
if self.kind == 'Mblg':
mag = mblg_to_mw_johnston_96(ctx.mag)
elif self.kind == 'Mblg2008':
mag = mblg_to_mw_atkinson_boore_87(ctx.mag)
else:
mag = ctx.mag
# computing the magnitude term. Equation 19, page 2291
f1 = _compute_magnitude_scaling_term(C, mag)
# computing the geometrical spreading term. Equation 20, page 2291
f2 = _compute_geometrical_spreading_term(C, ctx.rrup)
# computing the anelastic attenuation term. Equation 21, page 2291
f3 = _compute_anelastic_attenuation_term(C, ctx.rrup, mag)
# computing the mean ln(IMT) using equation 18 at page 2290
mean[m] = f1 + f2 + f3
if self.kind != 'base': # in subclasses
mean[m] = clip_mean(imt, mean[m])
# computing the total standard deviation
sig[m] = np.where(mag < 7.2, C['c14'] + C['c15'] * mag, C['c16'])
#: Coefficient table is constructed from an excel spreadsheet available
#: on Pezeshk's website http://www.ce.memphis.edu/pezeshk
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 c16
pga 1.139E+00 6.228E-01 -4.834E-02 -1.807E+00 -6.516E-01 4.465E-01 -2.933E-05 -4.045E-03 9.456E-03 1.410E+00 -9.611E-01 4.315E-04 1.332E-04 1.205E+00 -1.109E-01 4.091E-01
0.05 1.823E+00 5.333E-01 -4.748E-02 -1.631E+00 -5.672E-01 4.538E-01 7.771E-03 -4.907E-03 -3.139E-03 9.797E-01 -9.386E-01 5.121E-04 9.301E-04 1.216E+00 -1.080E-01 4.413E-01
0.08 6.826E-01 7.428E-01 -2.928E-02 -1.715E+00 -7.562E-01 4.601E-01 -9.677E-04 -4.941E-03 -5.500E-03 1.135E+00 -9.156E-01 4.822E-04 7.331E-04 1.224E+00 -1.081E-01 4.494E-01
0.10 8.692E-01 6.070E-01 -4.736E-02 -1.522E+00 -7.044E-01 4.491E-01 -6.188E-03 -4.702E-03 -4.239E-03 1.039E+00 -9.129E-01 4.108E-04 3.584E-04 1.232E+00 -1.081E-01 4.562E-01
0.15 2.383E+00 5.009E-01 -6.422E-02 -1.732E+00 -9.763E-01 4.137E-01 6.598E-03 -4.805E-03 3.928E-03 1.506E+00 -8.650E-01 3.642E-04 6.841E-04 1.240E+00 -1.082E-01 4.643E-01
0.20 -5.476E-01 8.570E-01 -2.622E-02 -1.684E+00 -8.607E-01 4.332E-01 2.786E-03 -3.655E-03 -2.025E-03 1.643E+00 -9.252E-01 1.615E-04 6.434E-04 1.240E+00 -1.082E-01 4.691E-01
0.30 -5.130E-01 6.673E-01 -4.431E-02 -1.421E+00 -4.695E-01 4.681E-01 1.076E-02 -5.407E-03 6.436E-03 1.519E+00 -9.153E-01 4.324E-04 2.870E-04 1.260E+00 -1.088E-01 4.788E-01
0.50 2.403E-01 6.106E-01 -7.889E-02 -1.548E+00 -8.438E-01 4.145E-01 7.889E-03 -3.648E-03 -2.654E-04 1.592E+00 -8.586E-01 2.770E-04 1.457E-04 1.275E+00 -1.073E-01 5.051E-01
0.75 -6.789E-01 6.659E-01 -8.304E-02 -1.481E+00 -7.340E-01 4.347E-01 9.531E-03 -3.374E-03 -1.189E-03 1.546E+00 -7.839E-01 2.454E-04 5.470E-04 1.276E+00 -1.050E-01 5.222E-01
1.00 -1.550E+00 7.644E-01 -8.585E-02 -1.491E+00 -9.409E-01 4.238E-01 -5.836E-03 -2.088E-03 3.298E-03 1.519E+00 -7.568E-01 1.166E-04 7.589E-04 1.275E+00 -1.029E-01 5.368E-01
1.50 -2.296E+00 7.941E-01 -8.842E-02 -1.453E+00 -8.860E-01 4.122E-01 8.299E-03 -3.272E-03 2.506E-03 1.706E+00 -7.688E-01 2.329E-04 1.656E-04 1.268E+00 -9.990E-02 5.509E-01
2.00 -2.704E+00 8.053E-01 -9.294E-02 -1.444E+00 -9.235E-01 4.077E-01 2.062E-02 -2.143E-03 2.301E-03 1.426E+00 -7.551E-01 2.138E-04 3.908E-04 1.264E+00 -9.780E-02 5.617E-01
3.00 -2.421E+00 8.008E-01 -1.077E-01 -1.648E+00 -8.976E-01 4.368E-01 1.675E-02 -2.033E-03 3.576E-03 1.934E+00 -8.183E-01 1.158E-04 3.983E-04 1.257E+00 -9.520E-02 5.729E-01
4.00 -3.685E+00 8.166E-01 -1.177E-01 -1.463E+00 -8.448E-01 4.249E-01 1.135E-02 -1.719E-03 -3.345E-03 1.689E+00 -7.374E-01 1.100E-04 3.592E-04 1.254E+00 -9.260E-02 5.893E-01
""")
[docs]class TavakoliPezeshk2005MblgAB1987NSHMP2008(TavakoliPezeshk2005):
"""
Extend :class:`TavakoliPezeshk2005` and implements equation as defined
by the National Seismic Hazard Mapping Project (NSHMP) for the 2008
US model.
The class replicates the equation as coded in suroutine ``getTP05`` in
``hazgridXnga2.f`` Fortran code available at:
http://earthquake.usgs.gov/hazards/products/conterminous/2008/software/
The class assumes rupture magnitude to be in Mblg scale. Therefore Mblg
is converted to Mw using the Atkinson & Boore 1987 conversion equation.
Coefficients are given for the B/C site conditions.
"""
kind = 'Mblg2008'
#: Shear-wave velocity for reference soil conditions in [m s-1]
DEFINED_FOR_REFERENCE_VELOCITY = 760.
#: Coefficient table is constructed using the values included in
#: hazgridXnga2.f
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 c16
pga 1.56E+00 6.23E-01 -4.83E-02 -1.81E+00 -6.52E-01 4.46E-01 -2.93E-05 -4.05E-03 9.46E-03 1.41E+00 -9.61E-01 4.32E-04 1.33E-04 1.21E+00 -1.11E-01 4.09E-01
5.00E-02 2.24E+00 5.33E-01 -4.75E-02 -1.63E+00 -5.67E-01 4.54E-01 7.77E-03 -4.91E-03 -3.14E-03 9.80E-01 -9.39E-01 5.12E-04 9.30E-04 1.22E+00 -1.08E-01 4.41E-01
8.00E-02 1.10E+00 7.43E-01 -2.93E-02 -1.71E+00 -7.56E-01 4.60E-01 -9.68E-04 -4.94E-03 -5.50E-03 1.13E+00 -9.16E-01 4.82E-04 7.33E-04 1.22E+00 -1.08E-01 4.49E-01
1.00E-01 1.4229 6.07E-01 -4.74E-02 -1.52E+00 -7.04E-01 4.49E-01 -6.19E-03 -4.70E-03 -4.24E-03 1.04E+00 -9.13E-01 4.11E-04 3.58E-04 1.23E+00 -1.08E-01 4.56E-01
1.50E-01 2.87E+00 5.01E-01 -6.42E-02 -1.73E+00 -9.76E-01 4.14E-01 6.60E-03 -4.80E-03 3.93E-03 1.51E+00 -8.65E-01 3.64E-04 6.84E-04 1.24E+00 -1.08E-01 4.64E-01
2.00E-01 1.70E-02 8.57E-01 -2.62E-02 -1.68E+00 -8.61E-01 4.33E-01 2.79E-03 -3.65E-03 -2.02E-03 1.64E+00 -9.25E-01 1.61E-04 6.43E-04 1.24E+00 -1.08E-01 4.69E-01
3.00E-01 0.491 6.67E-01 -4.43E-02 -1.42E+00 -4.70E-01 4.68E-01 1.08E-02 -5.41E-03 6.44E-03 1.52E+00 -9.15E-01 4.32E-04 2.87E-04 1.26E+00 -1.09E-01 4.79E-01
5.00E-01 6.97E-01 6.11E-01 -7.89E-02 -1.55E+00 -8.44E-01 4.14E-01 7.89E-03 -3.65E-03 -2.65E-04 1.59E+00 -8.59E-01 2.77E-04 1.46E-04 1.28E+00 -1.07E-01 5.05E-01
7.50E-01 -3.23E-01 6.66E-01 -8.30E-02 -1.48E+00 -7.34E-01 4.35E-01 9.53E-03 -3.37E-03 -1.19E-03 1.55E+00 -7.84E-01 2.45E-04 5.47E-04 1.28E+00 -1.05E-01 5.22E-01
1.00E+00 -1.26E+00 7.64E-01 -8.59E-02 -1.49E+00 -9.41E-01 4.24E-01 -5.84E-03 -2.09E-03 3.30E-03 1.52E+00 -7.57E-01 1.17E-04 7.59E-04 1.28E+00 -1.03E-01 5.37E-01
1.50E+00 -1.94E+00 7.94E-01 -8.84E-02 -1.45E+00 -8.86E-01 4.12E-01 8.30E-03 -3.27E-03 2.51E-03 1.71E+00 -7.69E-01 2.33E-04 1.66E-04 1.27E+00 -9.99E-02 5.51E-01
2.00E+00 -2.5177 8.05E-01 -9.29E-02 -1.44E+00 -9.23E-01 4.08E-01 2.06E-02 -2.14E-03 2.30E-03 1.43E+00 -7.55E-01 2.14E-04 3.91E-04 1.26E+00 -9.78E-02 5.62E-01
3.00E+00 -2.28 8.01E-01 -1.08E-01 -1.65E+00 -8.98E-01 4.37E-01 1.67E-02 -2.03E-03 3.58E-03 1.93E+00 -8.18E-01 1.16E-04 3.98E-04 1.26E+00 -9.52E-02 5.73E-01
4.00E+00 -2.28 8.17E-01 -1.18E-01 -1.46E+00 -8.45E-01 4.25E-01 1.13E-02 -1.72E-03 -3.34E-03 1.69E+00 -7.37E-01 1.10E-04 3.59E-04 1.25E+00 -9.26E-02 5.89E-01
""")
[docs]class TavakoliPezeshk2005MblgJ1996NSHMP2008(
TavakoliPezeshk2005MblgAB1987NSHMP2008):
"""
Extend :class:`TavakoliPezeshk2005MblgAB1987NSHMP2008` but uses Johnston
1996 equation to convert Mblg to Mw
"""
kind = 'Mblg'
[docs]class TavakoliPezeshk2005MwNSHMP2008(TavakoliPezeshk2005MblgAB1987NSHMP2008):
"""
Extend :class:`TavakoliPezeshk2005MblgAB1987NSHMP2008` but assumes
magnitude to be in Mw scale, and therefore no conversion is applied
"""
kind = '2008'