# Source code for openquake.hazardlib.gsim.atkinson_boore_1995

```
# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2020 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:`AtkinsonBoore1995GSCBest`,
:class:`AtkinsonBoore1995GSCLowerLimit`,
:class:`AtkinsonBoore1995GSCUpperLimit`
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class AtkinsonBoore1995GSCBest(GMPE):
"""
Implement equation used by the Geological Survey of Canada (GSC) for
the 2010 Eastern Canada National Seismic Hazard Model. The equation fits
the table values defined by Gail M. Atkinson and David M. Boore in
"Ground-Motion Relations for Eastern North America", Bullettin of the
Seismological Society of America, Vol. 85, No. 1, pp. 17-30, February 1995.
Table of coefficients were provided by GSC and are associated to the 'Best'
case (that is mean value unaffected).
The class assumes magnitude to be in Mblg scale. The Atkinson 1993
conversion equation is used to obtain Mw values.
"""
#: Supported tectonic region type is stable continental, 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
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is random horizontal
#: :attr:`~openquake.hazardlib.const.IMC.RANDOM_HORIZONTAL`,
#: see page 22 in Atkinson and Boore's manuscript
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RANDOM_HORIZONTAL
#: Supported standard deviation type is total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: site params are not required
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameter is magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is hypocentral distance
#: see page 18 in Atkinson and Boore's manuscript
REQUIRES_DISTANCES = {'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]
# clip rhypo at 10 (this is the minimum distance used in
# deriving the equation), see page 22, this avoids singularity
# in mean value equation
rhypo = dists.rhypo.copy()
rhypo[rhypo < 10] = 10
# convert magnitude from Mblg to Mw
mag = rup.mag * 0.98 - 0.39 if rup.mag <= 5.5 else \
2.715 - 0.277 * rup.mag + 0.127 * rup.mag * rup.mag
# functional form as explained in 'Youngs_fit_to_AB95lookup.doc'
f1 = np.minimum(np.log(rhypo), np.log(70.))
f2 = np.maximum(np.log(rhypo / 130.), 0)
mean = (
C['c1'] + C['c2'] * mag + C['c3'] * mag ** 2 +
(C['c4'] + C['c5'] * mag) * f1 +
(C['c6'] + C['c7'] * mag) * f2 +
C['c8'] * rhypo
)
stddevs = self._get_stddevs(stddev_types, dists.rhypo.shape[0])
return mean, stddevs
def _get_stddevs(self, stddev_types, num_sites):
"""
Return total standard deviation.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
stddevs = [np.zeros(num_sites) + 0.69 for _ in stddev_types]
return stddevs
#: coefficient table provided by GSC
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8
pga -1.329 1.272 -0.08240 -2.556 0.17220 -1.9600 0.17460 -0.0045350
0.1 -2.907 1.522 -0.08528 -2.052 0.12484 -1.4224 0.07965 -0.0043090
0.2 -5.487 1.932 -0.10290 -1.818 0.09797 -1.0760 0.06075 -0.0033250
0.3 -7.567 2.284 -0.11930 -1.734 0.08814 -0.9551 0.04392 -0.0025700
0.5 -9.476 2.503 -0.12310 -1.631 0.07610 -1.0490 0.06224 -0.0019590
1.0 -11.134 2.470 -0.10569 -1.520 0.06165 -0.9106 0.05248 -0.001497
2.0 -13.210 2.945 -0.15670 -1.864 0.11620 -0.7653 0.02729 -0.0009921
""")
[docs]class AtkinsonBoore1995GSCLowerLimit(AtkinsonBoore1995GSCBest):
"""
Implement equation used by the Geological Survey of Canada (GSC) for
the 2010 Eastern Canada National Seismic Hazard Model. The equation fits
the table values defined by Gail M. Atkinson and David M. Boore in
"Ground-Motion Relations for Eastern North America", Bullettin of the
Seismological Society of America, Vol. 85, No. 1, pp. 17-30, February 1995.
Table of coefficients were provided by GSC and are associated to the 'Lower
Limit' case (that is mean value decreased).
"""
#: coefficient table provided by GSC
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8
pga -2.204 1.272 -0.08240 -2.556 0.17220 -1.9600 0.17460 -0.0045350
0.1 -3.782 1.522 -0.08528 -2.052 0.12484 -1.4224 0.07965 -0.0043090
0.2 -6.224 1.932 -0.10290 -1.818 0.09797 -1.0760 0.06075 -0.0033250
0.3 -8.212 2.284 -0.11930 -1.734 0.08814 -0.9551 0.04392 -0.0025700
0.5 -10.029 2.503 -0.12310 -1.631 0.07610 -1.0490 0.06224 -0.0019590
1.0 -11.548 2.470 -0.10569 -1.520 0.06165 -0.9106 0.05248 -0.001497
""")
[docs]class AtkinsonBoore1995GSCUpperLimit(AtkinsonBoore1995GSCBest):
"""
Implement equation used by the Geological Survey of Canada (GSC) for
the 2010 Eastern Canada National Seismic Hazard Model. The equation fits
the table values defined by Gail M. Atkinson and David M. Boore in
"Ground-Motion Relations for Eastern North America", Bullettin of the
Seismological Society of America, Vol. 85, No. 1, pp. 17-30, February 1995.
Table of coefficients were provided by GSC and are associated to the 'Upper
Limit' case (that is mean value increased).
"""
#: coefficient table provided by GSC
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8
pga -1.030 1.272 -0.08240 -2.556 0.17220 -1.9600 0.17460 -0.0045350
0.1 -2.608 1.522 -0.08528 -2.052 0.12484 -1.4224 0.07965 -0.0043090
0.2 -4.911 1.932 -0.10290 -1.818 0.09797 -1.0760 0.06075 -0.0033250
0.3 -6.784 2.284 -0.11930 -1.734 0.08814 -0.9551 0.04392 -0.0025700
0.5 -8.509 2.503 -0.12310 -1.631 0.07610 -1.0490 0.06224 -0.0019590
1.0 -9.891 2.470 -0.10569 -1.520 0.06165 -0.9106 0.05248 -0.001497
""")
```