Source code for openquake.hazardlib.gsim.atkinson_macias_2009
# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2021 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.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# GNU Affero General Public License for more details.
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# 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:'AtkinsonMacias2009'
"""
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class AtkinsonMacias2009(GMPE):
"""
Implements the Subduction Interface GMPE of Atkinson & Macias (2009) for
large interface earthquakes in the Cascadia subduction zone.
Atkinson, G. M. and Macias, M. (2009) "Predicted Ground Motions for
Great Interface Earthquakes in the Cascadia Subduction Zone", Bulletin
of the Seismological Society of America, 99(3), 1552 - 1578
"""
#: The GMPE is derived for subduction interface earthquakes in Cascadia
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
#: Supported intensity measure types are peak ground acceleration and
#: Spectral Acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is assumed to be equivalent
#: to the random horizontal component
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RANDOM_HORIZONTAL
#: Supported standard deviation types is total.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
])
#: No required site parameters, the GMPE is derived for B/C site
#: conditions
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is rupture distance
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.
"""
C = self.COEFFS[imt]
imean = (self._get_magnitude_term(C, rup.mag) +
self._get_distance_term(C, dists.rrup, rup.mag))
# Convert mean from cm/s and cm/s/s and from common logarithm to
# natural logarithm
mean = np.log((10.0 ** (imean - 2.0)) / g)
stddevs = self._get_stddevs(C, len(dists.rrup), stddev_types)
return mean, stddevs
def _get_magnitude_term(self, C, mag):
"""
Returns the magnitude scaling term provided in Equation (5)
"""
dmag = mag - 8.0
return C["c0"] + C["c3"] * dmag + C["c4"] * (dmag ** 2.)
def _get_distance_term(self, C, rrup, mag):
"""
Returns the distance scaling given in Equation (4), page 1569,
with distance adjusted by the magnitude-dependent depth scaling
factor given in Equation (6)
"""
r_adj = np.sqrt(rrup ** 2.0 + (mag ** 2.0 - 3.1 * mag - 14.55) ** 2.)
return C["c1"] * np.log10(r_adj) + C["c2"] * r_adj
def _get_stddevs(self, C, num_sites, stddev_types):
"""
Returns the total standard deviation, converting from log10 to log
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(
np.log(10.0 ** C["sigma"]) + np.zeros(num_sites))
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c0 c1 c2 c3 c4 sigma
pga 5.0060 -1.5573 -0.000340 0.1774 0.0827 0.24
0.050000 5.8430 -1.9391 0.000000 0.1813 0.0199 0.26
0.063091 5.8230 -1.8889 -0.000220 0.1845 0.0160 0.26
0.079365 5.6760 -1.7633 -0.000710 0.1784 0.0245 0.27
0.100000 5.4900 -1.6257 -0.001150 0.1736 0.0261 0.27
0.125000 5.2090 -1.4404 -0.001630 0.1788 0.0151 0.27
0.158730 4.9300 -1.2671 -0.002040 0.1645 0.0301 0.27
0.200000 4.7460 -1.1691 -0.002120 0.1593 0.0432 0.27
0.250000 4.4720 -1.0133 -0.002340 0.1713 0.0255 0.27
0.316456 4.3030 -0.9322 -0.002310 0.1713 0.0270 0.27
0.400000 4.1670 -0.8854 -0.002110 0.1802 0.0258 0.27
0.500000 3.9990 -0.8211 -0.001950 0.1870 0.0271 0.27
0.632911 3.8590 -0.7746 -0.001790 0.2010 0.0153 0.28
0.793651 3.7330 -0.7473 -0.001590 0.2035 0.0292 0.28
1.000000 3.6210 -0.7376 -0.001280 0.2116 0.0328 0.29
1.265823 3.4530 -0.6885 -0.001190 0.2417 0.0125 0.29
1.587302 3.3930 -0.7101 -0.000890 0.2483 0.0103 0.29
2.000000 3.2410 -0.6741 -0.000810 0.2696 -0.0064 0.30
2.500000 3.1040 -0.6585 -0.000630 0.2990 -0.0074 0.30
3.125000 2.9780 -0.6431 -0.000570 0.3258 -0.0103 0.30
4.000000 2.8140 -0.6108 -0.000460 0.3490 -0.0299 0.30
5.000000 2.6710 -0.5942 -0.000400 0.3822 -0.0417 0.32
6.250000 2.5690 -0.6048 -0.000240 0.4324 -0.0641 0.34
7.692308 2.4890 -0.6412 -0.000030 0.4760 -0.0629 0.35
10.00000 2.3380 -0.6311 0.000000 0.5357 -0.0737 0.38
""")