# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2023 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,
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
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"""
Module exports :class:`SadighEtAl1997`.
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
#: IMT-independent coefficients for deep soil ctx (table 4).
COEFFS_SOIL_IMT_INDEPENDENT = {
'c1ss': -2.17,
'c1r': -1.92,
'c2': 1.0,
'c3': 1.7,
'c4lowmag': 2.1863,
'c5lowmag': 0.32,
'c4himag': 0.3825,
'c5himag': 0.5882
}
#: If site vs30 is more than 750 m/s -- treat the soil as rock.
#: See page 180.
ROCK_VS30 = 750
#: Magnitude value to separate coefficients table because of near field
#: saturation effect is 6.5. See page 184.
NEAR_FIELD_SATURATION_MAG = 6.5
[docs]def get_mean_deep_soil(mag, rrup, is_reverse, C):
"""
Calculate and return the mean intensity for deep soil ctx.
Implements an equation from table 4.
"""
c1 = np.where(is_reverse,
COEFFS_SOIL_IMT_INDEPENDENT['c1r'],
COEFFS_SOIL_IMT_INDEPENDENT['c1ss'])
c2 = COEFFS_SOIL_IMT_INDEPENDENT['c2']
c3 = COEFFS_SOIL_IMT_INDEPENDENT['c3']
c4 = np.where(mag <= NEAR_FIELD_SATURATION_MAG,
COEFFS_SOIL_IMT_INDEPENDENT['c4lowmag'],
COEFFS_SOIL_IMT_INDEPENDENT['c4himag'])
c5 = np.where(mag <= NEAR_FIELD_SATURATION_MAG,
COEFFS_SOIL_IMT_INDEPENDENT['c5lowmag'],
COEFFS_SOIL_IMT_INDEPENDENT['c5himag'])
c6 = np.where(is_reverse, C['c6r'], C['c6ss'])
# clip mag if greater than 8.5. This is to avoid
# ValueError: negative number cannot be raised to a fractional power
mag = np.clip(mag, None, 8.5)
return (c1 + c2 * mag + c6 + C['c7'] * ((8.5 - mag) ** 2.5)
- c3 * np.log(rrup + c4 * np.exp(c5 * mag)))
[docs]def get_mean_rock(mag, rrup, is_reverse, low_coeffs, hi_coeffs):
"""
Calculate and return the mean intensity for rock ctx.
Implements an equation from table 2.
"""
# clip mag if greater than 8.5. This is to avoid
# ValueError: negative number cannot be raised to a fractional power
mag = np.clip(mag, None, 8.5)
# determine the coefficients to use depending on the mag
C = np.where(mag <= NEAR_FIELD_SATURATION_MAG, low_coeffs, hi_coeffs)
# compute the mean
mean = (C['c1'] + C['c2'] * mag + C['c3'] * ((8.5 - mag) ** 2.5)
+ C['c4'] * np.log(rrup + np.exp(C['c5'] + C['c6'] * mag))
+ C['c7'] * np.log(rrup + 2))
# footnote in table 2 says that for reverse ruptures
# the mean amplitude value should be multiplied by 1.2
mean[is_reverse] += 0.1823215567939546 # == log(1.2)
return mean
[docs]def get_stddev_rock(mag, C):
"""
Calculate and return total standard deviation for rock ctx.
Implements formulae from table 3.
"""
return np.where(
mag > C['maxmag'], C['maxsigma'], C['sigma0'] + C['magfactor'] * mag)
[docs]def get_stddev_deep_soil(mag, C):
"""
Calculate and return total standard deviation for deep soil ctx.
Implements formulae from the last column of table 4.
"""
# footnote from table 4 says that stderr for magnitudes over 7
# is equal to one of magnitude 7.
return C['sigma0'] + C['magfactor'] * np.clip(mag, None, 7)
[docs]class SadighEtAl1997(GMPE):
"""
Implements GMPE developed by Sadigh, K., C. -Y. Chang, J. A. Egan,
F. Makdisi, and R. R. Youngs (1997) and published as "Attenuation
relationships for shallow crustal earthquakes based on California
strong motion data", Seismological Research Letters, 68(1), 180-189.
"""
#: Supported tectonic region type is active shallow crust,
#: since data consists of California earthquakes mainly.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration, see page 180.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is the geometric mean of
#: two : horizontal components
#: :attr:`~openquake.hazardlib.const.IMC.GEOMETRIC_MEAN`, : see
#: page 180.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation type is only total, see table 3.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
#: Required site parameter is only Vs30 (used to distinguish rock
#: and deep soil).
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is RRup (eq. 1).
REQUIRES_DISTANCES = {'rrup'}
[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.
"""
# GMPE differentiates strike-slip, reverse and normal ruptures,
# but combines normal and strike-slip into one category. See page 180.
reverse = (45 <= ctx.rake) & (ctx.rake <= 135)
is_rock = ctx.vs30 > ROCK_VS30
is_soil = ctx.vs30 <= ROCK_VS30
mag_r = ctx.mag[is_rock]
mag_s = ctx.mag[is_soil]
rrup_r = ctx.rrup[is_rock]
rrup_s = ctx.rrup[is_soil]
reverse_r = reverse[is_rock]
reverse_s = reverse[is_soil]
for m, imt in enumerate(imts):
mean[m, is_rock] = get_mean_rock(
mag_r, rrup_r, reverse_r,
self.COEFFS_ROCK_LOWMAG[imt],
self.COEFFS_ROCK_HIMAG[imt])
sig[m, is_rock] = get_stddev_rock(
mag_r, self.COEFFS_ROCK_STDDERR[imt])
mean[m, is_soil] = get_mean_deep_soil(
mag_s, rrup_s, reverse_s, self.COEFFS_SOIL[imt])
sig[m, is_soil] = get_stddev_deep_soil(
mag_s, self.COEFFS_SOIL[imt])
#: Coefficients tables for rock ctx (table 2), for magnitude
#: values of :attr:`NEAR_FIELD_SATURATION_MAG` and below. Damping
#: for spectral acceleration here and in other SA-tables is 5%,
#: see "introduction" section.
COEFFS_ROCK_LOWMAG = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7
PGA -0.624 1.0 0.000 -2.100 1.29649 0.250 0.0
0.07 0.110 1.0 0.006 -2.128 1.29649 0.250 -0.082
0.10 0.275 1.0 0.006 -2.148 1.29649 0.250 -0.041
0.20 0.153 1.0 -0.004 -2.080 1.29649 0.250 0.0
0.30 -0.057 1.0 -0.017 -2.028 1.29649 0.250 0.0
0.40 -0.298 1.0 -0.028 -1.990 1.29649 0.250 0.0
0.50 -0.588 1.0 -0.040 -1.945 1.29649 0.250 0.0
0.75 -1.208 1.0 -0.050 -1.865 1.29649 0.250 0.0
1.0 -1.705 1.0 -0.055 -1.800 1.29649 0.250 0.0
1.5 -2.407 1.0 -0.065 -1.725 1.29649 0.250 0.0
2.0 -2.945 1.0 -0.070 -1.670 1.29649 0.250 0.0
3.0 -3.700 1.0 -0.080 -1.610 1.29649 0.250 0.0
4.0 -4.230 1.0 -0.100 -1.570 1.29649 0.250 0.0
""")
#: Coefficients tables for rock ctx (table 2), for magnitude
#: values above :attr:`NEAR_FIELD_SATURATION_MAG`.
COEFFS_ROCK_HIMAG = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7
PGA -1.274 1.1 0.000 -2.100 -0.48451 0.524 0.0
0.07 -0.540 1.1 0.006 -2.128 -0.48451 0.524 -0.082
0.10 -0.375 1.1 0.006 -2.148 -0.48451 0.524 -0.041
0.20 -0.497 1.1 -0.004 -2.080 -0.48451 0.524 0.0
0.30 -0.707 1.1 -0.017 -2.028 -0.48451 0.524 0.0
0.40 -0.948 1.1 -0.028 -1.990 -0.48451 0.524 0.0
0.50 -1.238 1.1 -0.040 -1.945 -0.48451 0.524 0.0
0.75 -1.858 1.1 -0.050 -1.865 -0.48451 0.524 0.0
1.0 -2.355 1.1 -0.055 -1.800 -0.48451 0.524 0.0
1.5 -3.057 1.1 -0.065 -1.725 -0.48451 0.524 0.0
2.0 -3.595 1.1 -0.070 -1.670 -0.48451 0.524 0.0
3.0 -4.350 1.1 -0.080 -1.610 -0.48451 0.524 0.0
4.0 -4.880 1.1 -0.100 -1.570 -0.48451 0.524 0.0
""")
#: Coefficient tables for standard error on rock ctx (table 3).
COEFFS_ROCK_STDDERR = CoeffsTable(sa_damping=5, table="""\
IMT sigma0 magfactor maxsigma maxmag
PGA 1.39 -0.14 0.38 7.21
0.07 1.40 -0.14 0.39 7.21
0.10 1.41 -0.14 0.40 7.21
0.20 1.43 -0.14 0.42 7.21
0.30 1.45 -0.14 0.44 7.21
0.40 1.48 -0.14 0.47 7.21
0.50 1.50 -0.14 0.49 7.21
0.75 1.52 -0.14 0.51 7.21
1.0 1.53 -0.14 0.52 7.21
4.0 1.53 -0.14 0.52 7.21
""")
#: Coefficient tables for deep soil ctx (table 4).
COEFFS_SOIL = CoeffsTable(sa_damping=5, table="""\
IMT c6ss c6r c7 sigma0 magfactor maxmag
PGA 0.0000 0.0000 0.0 1.52 -0.16 7
0.075 0.4572 0.4572 0.005 1.54 -0.16 7
0.1 0.6395 0.6395 0.005 1.54 -0.16 7
0.2 0.9187 0.9187 -0.004 1.565 -0.16 7
0.3 0.9547 0.9547 -0.014 1.58 -0.16 7
0.4 0.9251 0.9005 -0.024 1.595 -0.16 7
0.5 0.8494 0.8285 -0.033 1.61 -0.16 7
0.75 0.7010 0.6802 -0.051 1.635 -0.16 7
1.0 0.5665 0.5075 -0.065 1.66 -0.16 7
1.5 0.3235 0.2215 -0.090 1.69 -0.16 7
2.0 0.1001 -0.0526 -0.108 1.70 -0.16 7
3.0 -0.2801 -0.4905 -0.139 1.71 -0.16 7
4.0 -0.6274 -0.8907 -0.160 1.71 -0.16 7
""")