# 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:'AllenEtAl2012',
'AllenEtAl2012Rhypo'
"""
from __future__ import division
import numpy as np
from openquake.hazardlib.gsim.base import IPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import MMI
[docs]class AllenEtAl2012(IPE):
"""
Implements the Intensity Prediction Equation of Allen, Wald and Worden
(2012) for Modified Mercalli Intensity in Active Crustal Regions
Allen, T. I., Wald, D. J. and Worden, C. B. (2012) Intensity attenuation
in active crustal regions, J. Seismology, 16: 409 - 433
This class implements the version using rupture distance, neglecting
site amplification
"""
#: The GMPE is derived from induced earthquakes
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are peak ground acceleration
#: and peak ground velocity
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
MMI,
])
#: Supported intensity measure component is not considered for IPEs, so
#: we assume equivalent to 'average horizontal'
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types is total.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: No required site parameters (in the present version)
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude (ML is used)
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is rupture distance
REQUIRES_DISTANCES = set(('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]
mean = (self._compute_magnitude_term(C, rup.mag) +
self._compute_distance_term(C, dists.rrup, rup.mag))
stddevs = self._get_stddevs(C, dists.rrup, stddev_types)
return mean, stddevs
def _compute_magnitude_term(self, C, mag):
"""
Returns the magnitude scaling term
"""
return C["c0"] + (C["c1"] * mag)
def _compute_distance_term(self, C, rrup, mag):
"""
Returns the distance scaling term
"""
exponent_term = (1.0 + C["c3"] * np.exp(mag - 5.)) ** 2.
return C["c2"] * np.log(np.sqrt(rrup ** 2. + exponent_term))
def _get_stddevs(self, C, distance, stddev_types):
"""
Returns the total standard deviation, which is a function of distance
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigma = C["s1"] + (C["s2"] / (1.0 +
((distance / C["s3"]) ** 2.)))
stddevs.append(sigma + np.zeros_like(distance))
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c0 c1 c2 c3 s1 s2 s3
mmi 3.950 0.913 -1.107 0.813 0.72 0.23 44.7
""")
[docs]class AllenEtAl2012Rhypo(AllenEtAl2012):
"""
Version of the Allen, Wald and Worden (2012) IPE for hypocentral distance
"""
#: Required distance measure is hypocentral distance
REQUIRES_DISTANCES = set(('rhypo',))
[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]
mean = (self._compute_magnitude_term(C, rup.mag) +
self._compute_distance_term(C, dists.rhypo, rup.mag))
stddevs = self._get_stddevs(C, dists.rhypo, stddev_types)
return mean, stddevs
def _compute_distance_term(self, C, rhypo, mag):
"""
Returns the distance scaling term
"""
r_m = C["m1"] + C["m2"] * np.exp(mag - 5.)
f_r = C["c2"] * np.log(np.sqrt(rhypo ** 2. + r_m ** 2.))
# For distances greater than 50 km an anelastic term is added
idx = rhypo > 50.0
f_r[idx] += C["c4"] * np.log(rhypo[idx] / 50.)
return f_r
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c0 c1 c2 c3 c4 m1 m2 s1 s2 s3
mmi 2.085 1.428 -1.402 0.0 0.078 -0.209 2.042 0.82 0.37 22.9
""")