# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2021 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.
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"""
Module exports :class:`YoungsEtAl1997SInter`, :class:`YoungsEtAl1997SSlab`,
:class:`YoungsEtAl1997GSCSSlabBest`, :class:`YoungsEtAl1997GSCSSlabUpperLimit`,
:class:`YoungsEtAl1997GSCSSlabLowerLimit`,
:class:`YoungsEtAl1997SInterNSHMP2008`.
"""
import numpy as np
import copy
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class YoungsEtAl1997SInter(GMPE):
"""
Implements GMPE developed by R.R Youngs, S-J, Chiou, W.J. Silva, J.R.
Humphrey and published as "Strong Ground Motion Attenuation Relationships
for Subduction Zone Earthquakes" (Seismological Research Letters Volume 68,
No. 1, pages 58-73, 1997).
This class implements the equations for 'Subduction Interface' (that's why
the class name ends with 'SInter').
Mean value for SA at 4 s on rock (not originally supported) is obtained
from mean value at 3 s divided by a factor equal to 0.399
(scaling factor computed in the context of the SHARE project obtained as
average ratio between median values at 4 and 3 seconds as predicted by
SHARE subduction GMPEs).
"""
#: Supported tectonic region type is subduction interface
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration, see table 2, page 67.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is the average horizontal
#: component
#: attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, see
#: paragraph: 'Analysis of peak horizontal accelerations', p. 59.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types is total, table 2, page 67.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
DEFINED_FOR_REFERENCE_VELOCITY = 760
#: Required site parameters is Vs30, used to distinguish between rock
#: and soil sites, see paragraph 'Strong Motion Data Base', page 59.
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and focal depth, see
#: equations 1 and 2, pages 59 and 66, respectively.
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'}
#: Required distance measure is Rrup, see equations 1 and 2, page 59 and
#: 66, respectively.
REQUIRES_DISTANCES = {'rrup'}
#: Vs30 value representing typical rock conditions in California.
ROCK_VS30 = 760
[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)
mean = np.zeros_like(sites.vs30)
stddevs = [np.zeros_like(sites.vs30) for _ in stddev_types]
idx_rock = sites.vs30 >= self.ROCK_VS30
idx_soil = sites.vs30 < self.ROCK_VS30
if idx_rock.any():
C = self.COEFFS_ROCK[imt]
self._compute_mean(C, self.CONSTS['A1_rock'],
self.CONSTS['A2_rock'], self.CONSTS['A3_rock'],
self.CONSTS['A4_rock'], self.CONSTS['A5_rock'],
self.CONSTS['A6_rock'], rup.mag, rup.hypo_depth,
dists.rrup, mean, idx_rock)
self._compute_std(C, rup.mag, stddevs, idx_rock)
if imt == SA(period=4.0, damping=5.0):
mean = mean / 0.399
if idx_soil.any():
C = self.COEFFS_SOIL[imt]
self._compute_mean(C, self.CONSTS['A1_soil'],
self.CONSTS['A2_soil'], self.CONSTS['A3_soil'],
self.CONSTS['A4_soil'], self.CONSTS['A5_soil'],
self.CONSTS['A6_soil'], rup.mag, rup.hypo_depth,
dists.rrup, mean, idx_soil)
self._compute_std(C, rup.mag, stddevs, idx_soil)
return mean, stddevs
def _compute_mean(self, C, A1, A2, A3, A4, A5, A6, mag, hypo_depth,
rrup, mean, idx):
"""
Compute mean for subduction interface events, as explained in table 2,
page 67.
"""
mean[idx] = (A1 + A2 * mag + C['C1'] + C['C2'] * (A3 - mag) ** 3 +
C['C3'] * np.log(rrup[idx] + A4 * np.exp(A5 * mag)) +
A6 * hypo_depth)
def _compute_std(self, C, mag, stddevs, idx):
"""
Compute total standard deviation, as explained in table 2, page 67.
"""
if mag > 8.0:
mag = 8.0
for stddev in stddevs:
stddev[idx] += C['C4'] + C['C5'] * mag
#: Coefficient table containing soil coefficients,
#: taken from table 2, p. 67
COEFFS_SOIL = CoeffsTable(sa_damping=5, table="""\
IMT C1 C2 C3 C4 C5
pga 0.000 0.0000 -2.329 1.45 -0.1
0.075 2.400 -0.0019 -2.697 1.45 -0.1
0.100 2.516 -0.0019 -2.697 1.45 -0.1
0.200 1.549 -0.0020 -2.464 1.45 -0.1
0.300 0.793 -0.0020 -2.327 1.45 -0.1
0.400 0.144 -0.0035 -2.230 1.45 -0.1
0.500 -0.438 -0.0048 -2.140 1.45 -0.1
0.750 -1.704 -0.0066 -1.952 1.45 -0.1
1.000 -2.870 -0.0114 -1.785 1.45 -0.1
1.500 -5.101 -0.0164 -1.470 1.50 -0.1
2.000 -6.433 -0.0221 -1.290 1.55 -0.1
3.000 -6.672 -0.0235 -1.347 1.65 -0.1
4.000 -7.618 -0.0235 -1.272 1.65 -0.1
""")
#: Coefficient table containing rock coefficients,
#: taken from table 2, p. 67
COEFFS_ROCK = CoeffsTable(sa_damping=5, table="""\
IMT C1 C2 C3 C4 C5
pga 0.000 0.0000 -2.552 1.45 -0.1
0.075 1.275 0.0000 -2.707 1.45 -0.1
0.100 1.188 -0.0011 -2.655 1.45 -0.1
0.200 0.722 -0.0027 -2.528 1.45 -0.1
0.300 0.246 -0.0036 -2.454 1.45 -0.1
0.400 -0.115 -0.0043 -2.401 1.45 -0.1
0.500 -0.400 -0.0048 -2.360 1.45 -0.1
0.750 -1.149 -0.0057 -2.286 1.45 -0.1
1.000 -1.736 -0.0064 -2.234 1.45 -0.1
1.500 -2.634 -0.0073 -2.160 1.50 -0.1
2.000 -3.328 -0.0080 -2.107 1.55 -0.1
3.000 -4.511 -0.0089 -2.033 1.65 -0.1
4.000 -4.511 -0.0089 -2.033 1.65 -0.1
""")
#: constants for mean value calculation, see table 2, page 67.
CONSTS = {'A1_rock': 0.2418,
'A2_rock': 1.414,
'A3_rock': 10,
'A4_rock': 1.7818,
'A5_rock': 0.554,
'A6_rock': 0.00607,
'A7_rock': 0.3846,
'A1_soil': -0.6687,
'A2_soil': 1.438,
'A3_soil': 10,
'A4_soil': 1.097,
'A5_soil': 0.617,
'A6_soil': 0.00648,
'A7_soil': 0.3643}
[docs]class YoungsEtAl1997SInterNSHMP2008(YoungsEtAl1997SInter):
"""
Extends :class:`YoungsEtAl1997SInter` and fix rupture hypocenter depth
at 20 km as defined by the National Seismic Hazard Mapping Project (NSHMP)
for the 2008 US model.
The class implement the equation as coded in ``subroutine getGeom`` in
``hazSUBXnga.f`` Fortran code available at:
http://earthquake.usgs.gov/hazards/products/conterminous/2008/software/
"""
[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.
Call superclass method by passing new rupture context object with
hypocentral depth set to 20 km
"""
# create new context to avoid changing the original one
new_rup = copy.copy(rup)
new_rup.hypo_depth = 20.
mean, stddevs = super().get_mean_and_stddevs(
sites, new_rup, dists, imt, stddev_types)
return mean, stddevs
[docs]class YoungsEtAl1997SSlab(YoungsEtAl1997SInter):
"""
Implements GMPE developed by R.R Youngs, S-J, Chiou, W.J. Silva, J.R.
Humphrey and published as "Strong Ground Motion Attenuation Relationships
for Subduction Zone Earthquakes" (Seismological Research Letters Volume 68,
No. 1, pages 58-73, 1997).
This class implements the equations for 'Subduction IntraSlab' (that's why
the class name ends with 'SSlab').
Mean value for SA at 4 s on rock (not originally supported) is obtained
from mean value at 3 s divided by a factor equal to 0.399
(scaling factor computed in the context of the SHARE project obtained as
average ratio between median values at 4 and 3 seconds as predicted by
SHARE subduction GMPEs).
"""
#: Supported tectonic region type is subduction intraslab
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB
[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.
"""
mean, stddevs = super().get_mean_and_stddevs(
sites, rup, dists, imt, stddev_types)
idx_rock = sites.vs30 >= self.ROCK_VS30
idx_soil = sites.vs30 < self.ROCK_VS30
if imt == SA(period=4.0, damping=5.0):
mean[idx_rock] += 0.3846 / 0.399
else:
mean[idx_rock] += 0.3846
mean[idx_soil] += 0.3643
return mean, stddevs
[docs]class YoungsEtAl1997GSCSSlabBest(YoungsEtAl1997SSlab):
"""
Implement modification to :class:`YoungsEtAl1997SSlab` as defined by GSC
(Geological Survey of Canada) for the 2010 Western Canada Model.
Includes adjustement for firm ground. The model is associated to the 'Best'
case, that is mean value unaffected.
"""
[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.
"""
mean, stddevs = super().get_mean_and_stddevs(
sites, rup, dists, imt, stddev_types)
# this is the firm ground adjustment
mean += np.log(1.162)
return mean, stddevs
[docs]class YoungsEtAl1997GSCSSlabUpperLimit(YoungsEtAl1997GSCSSlabBest):
"""
Implement modification to :class:`YoungsEtAl1997SSlab` as defined by GSC
(Geological Survey of Canada) for the 2010 Western Canada Model.
Includes adjustement for firm ground. The model is associated to the 'Upper
Limit' case, that is mean value plus 0.7 natural logarithm.
"""
[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.
"""
mean, stddevs = super().get_mean_and_stddevs(
sites, rup, dists, imt, stddev_types)
mean += 0.7
return mean, stddevs
[docs]class YoungsEtAl1997GSCSSlabLowerLimit(YoungsEtAl1997GSCSSlabBest):
"""
Implement modification to :class:`YoungsEtAl1997SSlab` as defined by GSC
(Geological Survey of Canada) for the 2010 Western Canada Model.
Includes adjustement for firm ground. The model is associated to the 'Lower
Limit' case, that is mean value minus 0.7 natural logarithm.
"""
[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.
"""
mean, stddevs = super().get_mean_and_stddevs(
sites, rup, dists, imt, stddev_types)
mean -= 0.7
return mean, stddevs