Source code for openquake.hazardlib.gsim.atkinson_2015
# -*- 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
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# 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:'Atkinson2015'
"""
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, PGV, SA
[docs]class Atkinson2015(GMPE):
"""
Implements the Induced Seismicity GMPE of Atkinson (2015)
Atkinson, G. A. (2015) Ground-Motion Prediction Equation for Small-to-
Moderate Events at Short Hypocentral Distances, with Application to
Induced-Seismicity Hazards. Bulletin of the Seismological Society of
America. 105(2).
"""
#: The GMPE is derived from induced earthquakes
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.INDUCED
#: Supported intensity measure types are peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
PGV,
SA
])
#: Supported intensity measure component is the larger of two components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: Supported standard deviation types is total.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: No required site parameters, the GMPE is derived for B/C site
#: amplification factors
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is hypocentral distance
REQUIRES_DISTANCES = {'rhypo'}
#: GMPE not tested against independent implementation so raise
#: not verified warning
non_verified = True
[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.rhypo, rup.mag))
# Convert mean from cm/s and cm/s/s
if imt.name in "SA PGA":
mean = np.log((10.0 ** (imean - 2.0)) / g)
else:
mean = np.log(10.0 ** imean)
stddevs = self._get_stddevs(C, len(dists.rhypo), stddev_types)
return mean, stddevs
def _get_magnitude_term(self, C, mag):
"""
Returns the magnitude scaling term
"""
return C["c0"] + (C["c1"] * mag) + (C["c2"] * (mag ** 2.0))
def _get_distance_term(self, C, rhypo, mag):
"""
Returns the distance scaling term
"""
h_eff = self._get_effective_distance(mag)
r_val = np.sqrt(rhypo ** 2.0 + h_eff ** 2.0)
return C["c3"] * np.log10(r_val)
def _get_effective_distance(self, mag):
"""
Returns the effective distance term in equation 3. This may be
overwritten in sub-classes
"""
h_eff = 10.0 ** (-1.72 + 0.43 * mag)
if h_eff > 1.0:
return h_eff
else:
return 1.0
def _get_stddevs(self, C, num_sites, stddev_types):
"""
Return standard deviations, 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))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0 ** C["tau"]) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0 ** C["phi"]) + np.zeros(num_sites))
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c0 c1 c2 c3 phi tau sigma
pgv -4.151 1.762 -0.09509 -1.669 0.27 0.19 0.33
pga -2.376 1.818 -0.1153 -1.752 0.28 0.24 0.37
0.0303 -2.283 1.842 -0.1189 -1.785 0.28 0.27 0.39
0.0500 -2.018 1.826 -0.1192 -1.831 0.28 0.30 0.41
0.1000 -1.954 1.830 -0.1185 -1.774 0.29 0.25 0.39
0.2000 -2.266 1.785 -0.1061 -1.657 0.30 0.21 0.37
0.3000 -2.794 1.852 -0.1078 -1.608 0.30 0.19 0.36
0.5000 -3.873 2.060 -0.1212 -1.544 0.29 0.20 0.35
1.0000 -4.081 1.742 -0.07381 -1.481 0.26 0.22 0.34
2.0000 -4.462 1.485 -0.03815 -1.361 0.24 0.23 0.33
3.0303 -3.827 1.060 0.009086 -1.398 0.24 0.22 0.32
5.0000 -4.321 1.080 0.009376 -1.378 0.25 0.18 0.31
""")