# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2016 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:`DrouetBrazil2015`
:class:`DrouetBrazil2015_with_depth`
"""
from __future__ import division
import numpy as np
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
from scipy.constants import g
[docs]class DrouetBrazil2015(GMPE):
"""
Implements GMPE developed by S. Drouet unpublished for Brazil based on the
method described in Douet & Cotton (2015) BSSA doi: 10.1785/0120140240.
"""
#: Supported tectonic region type is stable continental crust 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, see table 6, page 1022 (PGA is assumed
#: to be equal to SA at 0.01 s)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
PGV,
SA
])
#: Supported intensity measure component is the geometric mean of
#two : horizontal components
#:attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation type is only total, see equation 35, page
#: 1021
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: No site parameters are needed
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameter is only magnitude, see equation 30 page
#: 1021.
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is closest distance to rupture, see equation
#: 30 page 1021.
REQUIRES_DISTANCES = set(('rjb', ))
[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.
"""
#assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
# for stddev_type in stddev_types)
C = self.COEFFS[imt]
mean = self._compute_mean(C, rup, dists.rjb)
if isinstance(imt, (SA, PGA)): # Convert from m/s**2 to g
mean -= np.log(g)
elif isinstance(imt, PGV): # Convert from m/s to cm/s
mean += np.log(100.0)
stddevs = self._get_stddevs(C, stddev_types, rup.mag,
dists.rjb.shape)
return mean, stddevs
def _compute_mean(self, C, rup, rjb):
"""
Compute mean value according to equation 30, page 1021.
"""
mean = (C['c1'] +
self._compute_magnitude_term(C, rup) +
self._compute_distance_term(C, rup, rjb))
return mean
def _get_stddevs(self, C, stddev_types, mag, num_sites):
"""
Return total standard deviation as for equation 35, page 1021.
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigma_t = np.sqrt(C['sigma'] ** 2. + C['tau'] ** 2.)
stddevs.append(sigma_t + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(C['sigma'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['tau'] + np.zeros(num_sites))
return stddevs
def _compute_magnitude_term(self, C, rup):
"""
This computes the term f1 equation 8 Drouet & Cotton (2015)
"""
return C['c2'] * (rup.mag - 8.0) + C['c3'] * (rup.mag - 8.0) ** 2
def _compute_distance_term(self, C, rup, rjb):
"""
This computes the term f2 equation 8 Drouet & Cotton (2015)
"""
return (C['c4'] + C['c5'] * rup.mag) * np.log(
np.sqrt(rjb ** 2. + C['c6'] ** 2.)) + C['c7'] * rjb
#: Coefficient tables are constructed from the electronic suplements of
#: the original paper.
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 sigma tau
pgv 0.457169 0.230048 -0.140795 -1.785544 0.162408 7.201555 -0.002832 0.526166 0.393025
pga 2.575109 -0.243140 -0.155164 -1.807995 0.156084 7.629410 -0.003996 0.625075 0.481226
0.010 2.586201 -0.242271 -0.154703 -1.808695 0.156141 7.623170 -0.004020 0.630187 0.481707
0.020 2.717172 -0.261739 -0.152580 -1.859646 0.160136 7.773640 -0.004048 0.688591 0.486003
0.030 2.930319 -0.236637 -0.147729 -1.831982 0.155727 7.918015 -0.004558 0.751663 0.490319
0.040 3.156209 -0.266436 -0.143032 -1.915769 0.162181 8.224381 -0.004350 0.779379 0.498289
0.050 3.268731 -0.189794 -0.140262 -1.753521 0.144779 7.767181 -0.004910 0.780218 0.497182
0.075 3.352582 -0.164010 -0.140254 -1.691894 0.140095 7.428414 -0.004756 0.706350 0.493511
0.100 3.455122 -0.203575 -0.148680 -1.708867 0.139700 7.707583 -0.004261 0.652456 0.490010
0.150 3.456514 -0.169395 -0.160434 -1.607720 0.131021 7.274064 -0.004025 0.587130 0.480912
0.200 3.480893 -0.155262 -0.168476 -1.646459 0.132556 7.424609 -0.002871 0.556933 0.462619
0.250 3.358985 -0.255601 -0.194574 -1.669187 0.134462 7.753731 -0.002732 0.533650 0.458696
0.300 3.115954 -0.237559 -0.215762 -1.451276 0.114182 7.212529 -0.003761 0.526336 0.452876
0.400 2.806835 -0.340296 -0.250121 -1.418762 0.114054 6.837724 -0.004081 0.519411 0.440790
0.500 2.837393 -0.355473 -0.271003 -1.453916 0.111753 7.298391 -0.003037 0.512892 0.427910
0.750 2.383076 -0.374649 -0.298428 -1.472297 0.117984 7.051676 -0.002899 0.507442 0.405868
1.000 2.070536 -0.263869 -0.303220 -1.410898 0.117144 6.815268 -0.003307 0.511352 0.384417
1.250 1.944386 -0.196142 -0.309115 -1.408815 0.116519 6.904435 -0.003017 0.511909 0.376152
1.500 1.973072 -0.160616 -0.313180 -1.493457 0.122469 7.427893 -0.002316 0.511871 0.370833
1.750 1.747518 -0.129961 -0.320672 -1.400692 0.116855 7.143261 -0.003402 0.508641 0.361738
2.000 1.667278 -0.083863 -0.319818 -1.405853 0.114769 7.128404 -0.003174 0.505025 0.353357
3.000 1.292331 0.312316 -0.263539 -1.464213 0.130085 6.416692 -0.002621 0.512370 0.344082
""")
[docs]class DrouetBrazil2015withDepth(DrouetBrazil2015):
"""
Implements GMPE developed by S. Drouet unpublished for Brazil based on the
method described in Douet & Cotton (2015) BSSA doi: 10.1785/0120140240.
Model with magnitude-dependent depth distribution and depth-dependent
stress distribution
"""
#: Required rupture parameter is only magnitude, see equation 30 page
#: 1021.
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth'))
def _compute_distance_term(self, C, rup, rjb):
"""
This computes the term f2 equation 8 Drouet & Cotton (2015)
"""
return (C['c4'] + C['c5'] * rup.mag) * np.log(
np.sqrt(rjb ** 2. + rup.hypo_depth ** 2.)) + C['c6'] * rjb
#: Coefficient tables are constructed from the electronic supplements of
#: the original paper.
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 sigma tau
pgv 1.296890 0.307642 -0.155927 -1.727495 0.128331 -0.002079 0.507600 0.474106
pga 3.393123 -0.139286 -0.169796 -1.695729 0.116686 -0.003491 0.609317 0.573384
0.010000 3.405471 -0.138584 -0.169352 -1.696947 0.116766 -0.003513 0.614578 0.574138
0.020000 3.512058 -0.152120 -0.167461 -1.725659 0.119114 -0.003688 0.674715 0.580870
0.030000 3.695045 -0.123957 -0.162204 -1.688566 0.114624 -0.004259 0.738161 0.585416
0.040000 3.856703 -0.140850 -0.157819 -1.721169 0.117496 -0.004400 0.768733 0.597967
0.050000 4.085005 -0.080044 -0.155124 -1.628430 0.103907 -0.004434 0.766573 0.593676
0.075000 4.242841 -0.056117 -0.154044 -1.601802 0.100823 -0.004025 0.691819 0.587975
0.100000 4.278594 -0.087360 -0.162257 -1.582776 0.098667 -0.003803 0.638952 0.582946
0.150000 4.358265 -0.063108 -0.173452 -1.530628 0.092988 -0.003244 0.572059 0.565676
0.200000 4.385790 -0.041305 -0.181717 -1.553364 0.092537 -0.002134 0.539692 0.543338
0.250000 4.162408 -0.135372 -0.207677 -1.531599 0.092853 -0.002369 0.520273 0.534858
0.300000 3.991746 -0.134064 -0.227479 -1.386035 0.078380 -0.002944 0.511192 0.519484
0.400000 3.746791 -0.248433 -0.261965 -1.396553 0.080903 -0.002965 0.502079 0.499394
0.500000 3.728968 -0.246365 -0.282618 -1.384885 0.074963 -0.002185 0.495203 0.483281
0.750000 3.298203 -0.278081 -0.310518 -1.431361 0.083594 -0.001906 0.488881 0.452970
1.000000 2.966504 -0.185734 -0.315139 -1.405592 0.087333 -0.002169 0.492014 0.426399
1.250000 2.810007 -0.117505 -0.320881 -1.394705 0.086834 -0.001981 0.493565 0.416078
1.500000 2.760153 -0.068911 -0.325231 -1.426076 0.089344 -0.001624 0.494063 0.410019
1.750000 2.538491 -0.052014 -0.332247 -1.367936 0.087458 -0.002541 0.491032 0.398572
2.000000 2.485648 -0.001655 -0.331560 -1.370772 0.084286 -0.002297 0.487175 0.392599
3.000000 2.205128 0.365128 -0.276508 -1.504904 0.104957 -0.001304 0.492143 0.384311
""")