# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2017 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:'GarciaEtAl2005SSlab',
:class:'GarciaEtAl2005SSlabVert'
"""
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 SA, PGA, PGV
[docs]class GarciaEtAl2005SSlab(GMPE):
"""
Implements GMPE developed by Garcia, D., Singh, S. K., Harraiz, M,
Ordaz, M., and Pacheco, J. F. and published in BSSA as:
"Inslab earthquakes of Central Mexico: Peak ground-motion parameters and
response spectra", vol. 95, No. 6, pp. 2272-2282."
The original formulation predict peak ground acceleration (PGA), in
cm/s*s, peak ground velocity PGV (cm/s) and 5% damped pseudo-acceleration
response spectra (PSA) in cm/s*s for the geometric average of the
maximum component of the two horizontal component of ground motion (see
last paragraph of Summary in pag. 2272
The GMPE predicted values for Mexican inslab events and NEHRP B site
condition
"""
#: Supported tectonic region type is subduction intraslab,
#: given that the equations have been derived using Mexican inslab
#: events
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration. See Table 2 in page 1865
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
SA,
PGA,
PGV,
])
#: Supported intensity measure component is the geometric average of
# the maximum of the two horizontal components
#: :attr:`openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
#: see Data processing in page 2274.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types are inter-event, intra-event
#: and total
#: See Tables 2 and 3, page 2275.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: No site parameters required
#: All data from 51 hard (NEHRP B) sites.
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude and focal depth
#: See equation (1) in pag 2274
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth'))
#: Required distance measure is Rrup (closest distance to fault surface for
#: the larger events, Mw > 6.5) or Rhypo (hypocentral distance for the
#: rest (both in kilometers) as explained in page 2274
REQUIRES_DISTANCES = set(('rrup', '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.
"""
# Extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
mag = rup.mag
hypo_depth = rup.hypo_depth
mean = self._compute_mean(C, g, mag, hypo_depth, dists, imt)
stddevs = self._get_stddevs(C, stddev_types, sites.vs30.shape[0])
return mean, stddevs
def _compute_mean(self, C, g, mag, hypo_depth, dists, imt):
"""
Compute mean according to equation on Table 2, page 2275.
"""
delta = 0.00750 * 10 ** (0.507 * mag)
# computing R for different values of mag
if mag < 6.5:
R = np.sqrt(dists.rhypo ** 2 + delta ** 2)
else:
R = np.sqrt(dists.rrup ** 2 + delta ** 2)
mean = (
# 1st term
C['c1'] + C['c2'] * mag +
# 2nd term
C['c3'] * R -
# 3rd term
C['c4'] * np.log10(R) +
# 4th term
C['c5'] * hypo_depth
)
# convert from base 10 to base e
if imt == PGV():
mean = np.log(10 ** mean)
else:
# convert from cm/s**2 to g
mean = np.log((10 ** mean) * 1e-2 / g)
return mean
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return standard deviations as defined in table 2, pag 2275.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
# the standard deviation values are converted from base 10 to base e
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 ** C['s_t']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10 ** C['s_r']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10 ** C['s_e']) + np.zeros(num_sites))
return stddevs
#: Equation coefficients for geometric average of the maximum of the two
#: horizontal components, as described in Table 2 on pp. 2275, but
#: generated from a Fortran implementation code provided by Daniel Garcia
#: (higher precision than in the paper).
#: The original IMT values are defined as frequencies values.
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 s_t s_r s_e
0.04 0.02645 0.58792 -0.00430 1.0 0.00700 0.31829 0.30777 0.08115
0.05 0.10949 0.58046 -0.00433 1.0 0.00753 0.33560 0.32329 0.09005
0.07 0.22907 0.56961 -0.00429 1.0 0.00826 0.33640 0.32126 0.09979
0.10 0.40746 0.54939 -0.00414 1.0 0.00774 0.33431 0.31785 0.10358
0.20 0.05215 0.58676 -0.00369 1.0 0.00689 0.27971 0.24464 0.13559
0.30 -0.26507 0.62932 -0.00331 1.0 0.00485 0.27649 0.22833 0.15592
0.40 -0.55235 0.64414 -0.00280 1.0 0.00483 0.27187 0.23607 0.13484
0.50 -0.81731 0.67453 -0.00243 1.0 0.00351 0.26432 0.24081 0.10898
0.75 -1.31580 0.70924 -0.00198 1.0 0.00371 0.27422 0.25957 0.08843
1.00 -1.75050 0.75555 -0.00168 1.0 0.00296 0.27728 0.26232 0.08985
1.50 -2.30120 0.80760 -0.00144 1.0 0.00167 0.28030 0.26085 0.10261
2.00 -2.75190 0.84564 -0.00123 1.0 0.00137 0.26353 0.24282 0.10240
3.00 -3.34700 0.89255 -0.00092 1.0 0.00085 0.26279 0.22360 0.13806
4.00 -3.87460 0.93748 -0.00079 1.0 0.00093 0.25328 0.22226 0.12147
5.00 -4.26750 0.96929 -0.00074 1.0 0.00104 0.24643 0.21638 0.11793
pga -0.23170 0.58726 -0.00394 1.0 0.00767 0.28520 0.26662 0.10123
pgv -2.35950 0.70759 -0.00235 1.0 0.00436 0.25745 0.23917 0.09529
""")
[docs]class GarciaEtAl2005SSlabVert(GarciaEtAl2005SSlab):
"""
Extend :class:`GarciaEtAl2005SSlab`
Implements GMPE developed by Garcia, D., Singh, S. K., Harraiz, M,
Ordaz, M., and Pacheco, J. F. and published in BSSA as:
"Inslab earthquakes of Central Mexico: Peak ground-motion parameters and r
esponse spectra", vol. 95, No. 6, pp. 2272-2282."
The original formulation predict peak ground acceleration (PGA), in
cm/s*s, peak ground velocity PGV (cm/s) and 5% damped pseudo-acceleration
response spectra (PSA) in cm/s*s for the vertical component of ground
motion (see last paragraph of Summary in pag. 2272
The GMPE predicted values for Mexican inslab events and NEHRP B site
"""
#: Equation coefficients for Vertical Component, as described in Table 3
#: on pp 2275.
#: The original imt values are defined as frequencies values
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 s_t s_r s_e
0.04 -0.300 0.620 -0.0041 1.00 0.0060 0.31 0.30 0.07
0.05 -0.200 0.620 -0.0043 1.00 0.0070 0.32 0.31 0.08
0.07 -0.060 0.600 -0.0041 1.00 0.0070 0.32 0.31 0.09
0.10 -0.040 0.590 -0.0039 1.00 0.0070 0.31 0.29 0.11
0.20 -0.070 0.590 -0.0033 1.00 0.0040 0.26 0.22 0.14
0.30 -0.200 0.600 -0.0029 1.00 0.0030 0.26 0.22 0.15
0.40 -0.700 0.640 -0.0022 1.00 0.0030 0.26 0.23 0.13
0.50 -0.900 0.660 -0.0018 1.00 0.0020 0.26 0.23 0.11
0.75 -1.300 0.690 -0.0014 1.00 0.0020 0.25 0.22 0.11
1.00 -1.800 0.750 -0.0010 1.00 0.0010 0.27 0.24 0.12
1.50 -2.400 0.800 -0.0008 1.00 0.0004 0.26 0.23 0.12
2.00 -2.800 0.830 -0.0006 1.00 -0.0005 0.27 0.24 0.14
3.00 -3.300 0.880 -0.0005 1.00 -0.0004 0.28 0.23 0.17
4.00 -4.000 0.950 -0.0004 1.00 -0.0003 0.27 0.23 0.15
5.00 -4.400 0.980 -0.0003 1.00 -0.0002 0.26 0.22 0.14
pga -0.400 0.600 -0.0036 1.00 0.0060 0.27 0.25 0.11
pgv -2.400 0.700 -0.0018 1.00 0.0020 0.24 0.21 0.11
""")