# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2020 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:`Campbell2003`, :class:`Campbell2003SHARE`,
:class:`Campbell2003MblgAB1987NSHMP2008`,
:class:`Campbell2003MblgJ1996NSHMP2008`,
:class:`Campbell2003MwNSHMP2008`
"""
import numpy as np
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib.gsim.utils import (
mblg_to_mw_atkinson_boore_87,
mblg_to_mw_johnston_96,
clip_mean)
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class Campbell2003(GMPE):
"""
Implements GMPE developed by K.W Campbell and published as "Prediction of
Strong Ground Motion Using the Hybrid Empirical Method and Its Use in the
Development of Ground Motion (Attenuation) Relations in Eastern North
America" (Bulletting of the Seismological Society of America, Volume 93,
Number 3, pages 1012-1033, 2003). The class implements also the corrections
given in the erratum (2004).
"""
#: Supported tectonic region type is stable continental crust given that
#: the equations have been derived for Eastern North America.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration, see table 6, page 1022 (PGA is assumed
#: to be equal to SA at 0.01 s)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is the geometric mean of
#: two horizontal components
#: :attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation type is only total, see equation 35, page
#: 1021
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: No site parameters are needed
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameter is only magnitude, see equation 30 page
#: 1021.
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is closest distance to rupture, see equation
#: 30 page 1021.
REQUIRES_DISTANCES = {'rrup'}
[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._compute_mean(C, rup.mag, dists.rrup)
stddevs = self._get_stddevs(C, stddev_types, rup.mag,
dists.rrup.shape[0])
return mean, stddevs
def _compute_mean(self, C, mag, rrup):
"""
Compute mean value according to equation 30, page 1021.
"""
mean = (C['c1'] +
self._compute_term1(C, mag) +
self._compute_term2(C, mag, rrup) +
self._compute_term3(C, rrup))
return mean
def _get_stddevs(self, C, stddev_types, mag, num_sites):
"""
Return total standard deviation as for equation 35, page 1021.
"""
stddevs = []
for _ in stddev_types:
if mag < 7.16:
sigma = C['c11'] + C['c12'] * mag
elif mag >= 7.16:
sigma = C['c13']
stddevs.append(np.zeros(num_sites) + sigma)
return stddevs
def _compute_term1(self, C, mag):
"""
This computes the term f1 in equation 31, page 1021
"""
return (C['c2'] * mag) + C['c3'] * (8.5 - mag) ** 2
def _compute_term2(self, C, mag, rrup):
"""
This computes the term f2 in equation 32, page 1021
"""
c78_factor = (C['c7'] * np.exp(C['c8'] * mag)) ** 2
R = np.sqrt(rrup ** 2 + c78_factor)
return C['c4'] * np.log(R) + (C['c5'] + C['c6'] * mag) * rrup
def _compute_term3(self, C, rrup):
"""
This computes the term f3 in equation 34, page 1021 but corrected
according to the erratum.
"""
f3 = np.zeros_like(rrup)
idx_between_70_130 = (rrup > 70) & (rrup <= 130)
idx_greater_130 = rrup > 130
f3[idx_between_70_130] = (
C['c9'] * (np.log(rrup[idx_between_70_130]) - np.log(70))
)
f3[idx_greater_130] = (
C['c9'] * (np.log(rrup[idx_greater_130]) - np.log(70)) +
C['c10'] * (np.log(rrup[idx_greater_130]) - np.log(130))
)
return f3
#: Coefficient tables are constructed from the electronic suplements of
#: the original paper.
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13
pga 0.0305 0.633 -0.0427 -1.591 -0.00428 0.000483 0.683 0.416 1.140 -0.873 1.030 -0.0860 0.414
0.020 1.3535 0.630 -0.0404 -1.787 -0.00388 0.000497 1.020 0.363 0.851 -0.715 1.030 -0.0860 0.414
0.030 1.1860 0.622 -0.0362 -1.691 -0.00367 0.000501 0.922 0.376 0.759 -0.922 1.030 -0.0860 0.414
0.050 0.3736 0.616 -0.0353 -1.469 -0.00378 0.000500 0.630 0.423 0.771 -1.239 1.042 -0.0838 0.443
0.075 -0.0395 0.615 -0.0353 -1.383 -0.00421 0.000486 0.491 0.463 0.955 -1.349 1.052 -0.0838 0.453
0.100 -0.1475 0.613 -0.0353 -1.369 -0.00454 0.000460 0.484 0.467 1.096 -1.284 1.059 -0.0838 0.460
0.150 -0.1901 0.616 -0.0478 -1.368 -0.00473 0.000393 0.461 0.478 1.239 -1.079 1.068 -0.0838 0.469
0.200 -0.4328 0.617 -0.0586 -1.320 -0.00460 0.000337 0.399 0.493 1.250 -0.928 1.077 -0.0838 0.478
0.300 -0.6906 0.609 -0.0786 -1.280 -0.00414 0.000263 0.349 0.502 1.241 -0.753 1.081 -0.0838 0.482
0.500 -0.5907 0.534 -0.1379 -1.216 -0.00341 0.000194 0.318 0.503 1.166 -0.606 1.098 -0.0824 0.508
0.750 -0.5429 0.480 -0.1806 -1.184 -0.00288 0.000160 0.304 0.504 1.110 -0.526 1.105 -0.0806 0.528
1.000 -0.6104 0.451 -0.2090 -1.158 -0.00255 0.000141 0.299 0.503 1.067 -0.482 1.110 -0.0793 0.543
1.500 -0.9666 0.441 -0.2405 -1.135 -0.00213 0.000119 0.304 0.500 1.029 -0.438 1.099 -0.0771 0.547
2.000 -1.4306 0.459 -0.2552 -1.124 -0.00187 0.000103 0.310 0.499 1.015 -0.417 1.093 -0.0758 0.551
3.000 -2.2331 0.492 -0.2646 -1.121 -0.00154 0.000084 0.310 0.499 1.014 -0.393 1.090 -0.0737 0.562
4.000 -2.7975 0.507 -0.2738 -1.119 -0.00135 0.000074 0.294 0.506 1.018 -0.386 1.092 -0.0722 0.575
""")
[docs]class Campbell2003SHARE(Campbell2003):
"""
Extends
:class:`~openquake.hazardlib.gsim.campbell_2003.Campbell2003` and
introduces adjustments for style of faulting and default rock soil
conditions as needed by the SHARE (http://www.share-eu.org/)
project.
"""
#: Required rupture parameters are magnitude and rake
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'}
#: Shear-wave velocity for reference soil conditions in [m s-1]
DEFINED_FOR_REFERENCE_VELOCITY = 800.
[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.
"""
# extract faulting style and rock adjustment coefficients for the
# given imt
C_ADJ = self.COEFFS_FS_ROCK[imt]
mean, stddevs = super().get_mean_and_stddevs(
sites, rup, dists, imt, stddev_types)
# apply faulting style and rock adjustment factor for mean and std
mean = np.log(np.exp(mean) *
_compute_faulting_style_term(C_ADJ['Frss'],
self.CONSTS_FS['pR'],
self.CONSTS_FS['Fnss'],
self.CONSTS_FS['pN'],
rup.rake) * C_ADJ['AFrock'])
stddevs = np.array(stddevs)
return mean, stddevs
#: Coefficients for faulting style and rock adjustment
COEFFS_FS_ROCK = CoeffsTable(sa_damping=5, table="""\
IMT Frss AFrock
pga 1.220000 0.735106
0.020000 1.192000 0.474275
0.030000 1.178000 0.423049
0.050000 1.150000 0.550323
0.075000 1.115000 0.730061
0.100000 1.080000 0.888509
0.150000 1.150000 1.094622
0.200000 1.190000 1.197291
0.300000 1.230000 1.288309
0.500000 1.230000 1.311421
0.750000 1.199444 1.298212
1.000000 1.196667 1.265762
1.500000 1.191111 1.197583
2.000000 1.140000 1.215779
3.000000 1.140000 1.215779
4.000000 1.140000 1.215779
""")
#: Constants for faulting style adjustment
CONSTS_FS = {'Fnss': 0.95, 'pN': 0.01, 'pR': 0.81}
def _compute_faulting_style_term(Frss, pR, Fnss, pN, rake):
"""
Compute SHARE faulting style adjustment term.
"""
if rake > 30.0 and rake <= 150.0:
return np.power(Frss, 1 - pR) * np.power(Fnss, -pN)
elif rake > -120.0 and rake <= -60.0:
return np.power(Frss, - pR) * np.power(Fnss, 1 - pN)
else:
return np.power(Frss, - pR) * np.power(Fnss, - pN)
[docs]class Campbell2003MblgAB1987NSHMP2008(Campbell2003):
"""
Implement GMPE developed by Ken Campbell and described in
"Development of semi-empirical attenuation relationships for the CEUS",
U.S. Geological Survey, Award 01HQGR0011, final report.
Document available at:
http://earthquake.usgs.gov/research/external/reports/01HQGR0011.pdf
This GMPE is used by the National Seismic Hazard Mapping Project (NSHMP)
for the 2008 central and eastern US hazard model.
This class replicates the algorithm as implemented in
``subroutine getCampCEUS`` in the ``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 (given that MFDs
for central and eastern US are given in this scale). Mblg is converted to
Mw using Atkinson and Boore 1987 conversion equation
Coefficients are given for the B/C (firm rock) conditions.
"""
#: Shear-wave velocity for reference soil conditions in [m s-1]
DEFINED_FOR_REFERENCE_VELOCITY = 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)
C = self.COEFFS[imt]
mag = self._convert_magnitude(rup.mag)
mean = self._compute_mean(C, mag, dists.rrup)
mean = clip_mean(imt, mean)
stddevs = self._get_stddevs(C, stddev_types, mag, dists.rrup.size)
return mean, stddevs
def _convert_magnitude(self, mag):
"""
Convert magnitude from Mblg to Mw using Atkinson and Boore 1987
equation.
"""
return mblg_to_mw_atkinson_boore_87(mag)
def _compute_mean(self, C, mag, rrup):
"""
Compute mean value (Equation 30 in USGS report)
"""
mean = np.zeros_like(rrup)
mean += C['c1'] + C['c2'] * mag + C['c3'] * (8.5 - mag) ** 2
idx = rrup > 70.
mean[idx] += C['c7'] * (np.log(rrup[idx]) - np.log(70.))
idx = rrup > 130.
mean[idx] += C['c8'] * (np.log(rrup[idx]) - np.log(130.))
R = np.sqrt(
rrup ** 2 + (C['c5'] * np.exp(C['c6'] * mag)) ** 2
)
mean += C['c4'] * np.log(R) + (C['c9'] + C['c10'] * mag) * rrup
return mean
#: Coefficient tables extracted from ``subroutine getCampCEUS`` in
#: ``hazgridXnga2.f``
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13
pga 0.4492 0.633 -0.0427 -1.591 0.683 0.416 1.140 -0.873 -0.00428 0.000483 1.030 -0.0860 0.414
0.1 0.4064 0.613 -0.0353 -1.369 0.484 0.467 1.096 -1.284 -0.00454 0.00046 1.059 -0.0838 0.460
0.2 0.1325 0.617 -0.0586 -1.32 0.399 0.493 1.25 -0.928 -0.0046 0.000337 1.077 -0.0838 0.478
0.3 -0.1483 0.609 -0.0786 -1.28 0.349 0.502 1.241 -0.753 -0.00414 0.000263 1.081 -0.0838 0.482
0.5 -0.1333 0.534 -0.1379 -1.216 0.318 0.503 1.116 -0.606 -0.00341 0.000194 1.098 -0.0824 0.508
1.0 -0.3177 0.451 -0.2090 -1.158 0.299 0.503 1.067 -0.482 -0.00255 0.000141 1.110 -0.0793 0.543
2.0 -1.2483 0.459 -0.2552 -1.124 0.310 0.499 1.015 -0.417 -0.00187 0.000103 1.093 -0.0758 0.551
""")
[docs]class Campbell2003MblgJ1996NSHMP2008(Campbell2003MblgAB1987NSHMP2008):
"""
Extend :class:`Campbell2003MblgAB1987NSHMP2008` but uses Johnston 1996
equation for converting Mblg to Mw
"""
def _convert_magnitude(self, mag):
"""
Convert magnitude from Mblg to Mw using Johnston 1996 equation.
"""
return mblg_to_mw_johnston_96(mag)
[docs]class Campbell2003MwNSHMP2008(Campbell2003MblgAB1987NSHMP2008):
"""
Extend :class:`Campbell2003MblgAB1987NSHMP2008` but assumes magnitude
to be in Mw scale, so no converion is applied.
"""
def _convert_magnitude(self, mag):
"""
Return magnitude value unchanged
"""
return mag