Source code for openquake.hazardlib.gsim.atkinson_2015
# The Hazard Library
# Copyright (C) 2015 GEM Foundation
#
# This program 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.
#
# This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports :class:'Atkinson2015'
"""
from __future__ import division
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 = set(('mag', ))
#: Required distance measure is hypocentral distance
REQUIRES_DISTANCES = set(('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 isinstance(imt, (PGA, SA)):
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 -4.198 1.818 -0.1009 -1.721 0.28 0.18 0.33
pga -2.427 1.877 -0.1214 -1.806 0.29 0.24 0.37
0.0303 -2.313 1.840 -0.1119 -1.708 0.29 0.26 0.39
0.0500 -2.337 1.902 -0.1252 -1.838 0.29 0.29 0.41
0.1000 -2.839 1.905 -0.1134 -1.658 0.30 0.25 0.39
0.2000 -3.918 2.112 -0.1266 -1.591 0.31 0.20 0.37
0.3000 -2.076 1.889 -0.1257 -1.886 0.31 0.18 0.36
0.5000 -4.128 1.792 -0.0791 -1.526 0.30 0.19 0.35
1.0000 -2.009 1.890 -0.1248 -1.828 0.27 0.21 0.34
2.0000 -4.503 1.532 -0.0430 -1.404 0.25 0.22 0.33
3.0303 -3.869 1.110 0.0039 -1.447 0.25 0.21 0.33
5.0000 -4.374 1.134 0.0038 -1.426 0.26 0.17 0.31
""")