# The Hazard Library
# Copyright (C) 2012-2014, 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:`SadighEtAl1997`.
"""
from __future__ import division
import numpy
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class SadighEtAl1997(GMPE):
"""
Implements GMPE developed by Sadigh, K., C. -Y. Chang, J. A. Egan,
F. Makdisi, and R. R. Youngs (1997) and published as "Attenuation
relationships for shallow crustal earthquakes based on California
strong motion data", Seismological Research Letters, 68(1), 180-189.
"""
#: Supported tectonic region type is active shallow crust,
#: since data consists of California earthquakes mainly.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration, see page 180.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is the geometric mean of
#two : horizontal components
#:attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, : see
#page 180.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation type is only total, see table 3.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: Required site parameter is only Vs30 (used to distinguish rock
#: and deep soil).
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag'))
#: Required distance measure is RRup (eq. 1).
REQUIRES_DISTANCES = set(('rrup', ))
#: If site vs30 is more than 750 m/s -- treat the soil as rock.
#: See page 180.
ROCK_VS30 = 750
#: Magnitude value to separate coefficients table because of near field
#: saturation effect is 6.5. See page 184.
NEAR_FIELD_SATURATION_MAG = 6.5
[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)
# GMPE differentiates strike-slip, reverse and normal ruptures,
# but combines normal and strike-slip into one category. See page 180.
is_reverse = (45 <= rup.rake <= 135)
stddevs = [numpy.zeros_like(sites.vs30) for _ in stddev_types]
means = numpy.zeros_like(sites.vs30)
[rocks_i] = (sites.vs30 > self.ROCK_VS30).nonzero()
if len(rocks_i):
rrup = dists.rrup.take(rocks_i)
mean_rock = self._get_mean_rock(rup.mag, rup.rake, rrup,
is_reverse, imt)
means.put(rocks_i, mean_rock)
for stddev_arr in stddevs:
stddev_rock = self._get_stddev_rock(rup.mag, imt)
stddev_arr.put(rocks_i, stddev_rock)
[soils_i] = (sites.vs30 <= self.ROCK_VS30).nonzero()
if len(soils_i):
rrup = dists.rrup.take(soils_i)
mean_soil = self._get_mean_deep_soil(rup.mag, rup.rake, rrup,
is_reverse, imt)
means.put(soils_i, mean_soil)
for stddev_arr in stddevs:
stddev_soil = self._get_stddev_deep_soil(rup.mag, imt)
stddev_arr.put(soils_i, stddev_soil)
return means, stddevs
def _get_mean_deep_soil(self, mag, rake, rrup, is_reverse, imt):
"""
Calculate and return the mean intensity for deep soil sites.
Implements an equation from table 4.
"""
if mag <= self.NEAR_FIELD_SATURATION_MAG:
c4 = self.COEFFS_SOIL_IMT_INDEPENDENT['c4lowmag']
c5 = self.COEFFS_SOIL_IMT_INDEPENDENT['c5lowmag']
else:
c4 = self.COEFFS_SOIL_IMT_INDEPENDENT['c4himag']
c5 = self.COEFFS_SOIL_IMT_INDEPENDENT['c5himag']
c2 = self.COEFFS_SOIL_IMT_INDEPENDENT['c2']
c3 = self.COEFFS_SOIL_IMT_INDEPENDENT['c3']
C = self.COEFFS_SOIL[imt]
if is_reverse:
c1 = self.COEFFS_SOIL_IMT_INDEPENDENT['c1r']
c6 = C['c6r']
else:
c1 = self.COEFFS_SOIL_IMT_INDEPENDENT['c1ss']
c6 = C['c6ss']
# clip mag if greater than 8.5. This is to avoid
# ValueError: negative number cannot be raised to a fractional power
mag = 8.5 if mag > 8.5 else mag
return (c1 + c2 * mag + c6 + C['c7'] * ((8.5 - mag) ** 2.5)
- c3 * numpy.log(rrup + c4 * numpy.exp(c5 * mag)))
def _get_mean_rock(self, mag, _rake, rrup, is_reverse, imt):
"""
Calculate and return the mean intensity for rock sites.
Implements an equation from table 2.
"""
if mag <= self.NEAR_FIELD_SATURATION_MAG:
C = self.COEFFS_ROCK_LOWMAG[imt]
else:
C = self.COEFFS_ROCK_HIMAG[imt]
# clip mag if greater than 8.5. This is to avoid
# ValueError: negative number cannot be raised to a fractional power
mag = 8.5 if mag > 8.5 else mag
mean = (
C['c1'] + C['c2'] * mag + C['c3'] * ((8.5 - mag) ** 2.5)
+ C['c4'] * numpy.log(rrup + numpy.exp(C['c5'] + C['c6'] * mag))
+ C['c7'] * numpy.log(rrup + 2)
)
if is_reverse:
# footnote in table 2 says that for reverse ruptures
# the mean amplitude value should be multiplied by 1.2
mean += 0.1823215567939546 # == log(1.2)
return mean
def _get_stddev_rock(self, mag, imt):
"""
Calculate and return total standard deviation for rock sites.
Implements formulae from table 3.
"""
C = self.COEFFS_ROCK_STDDERR[imt]
if mag > C['maxmag']:
return C['maxsigma']
else:
return C['sigma0'] + C['magfactor'] * mag
def _get_stddev_deep_soil(self, mag, imt):
"""
Calculate and return total standard deviation for deep soil sites.
Implements formulae from the last column of table 4.
"""
# footnote from table 4 says that stderr for magnitudes over 7
# is equal to one of magnitude 7.
if mag > 7:
mag = 7
C = self.COEFFS_SOIL[imt]
return C['sigma0'] + C['magfactor'] * mag
#: Coefficients tables for rock sites (table 2), for magnitude
#: values of :attr:`NEAR_FIELD_SATURATION_MAG` and below. Damping
#: for spectral acceleration here and in other SA-tables is 5%,
#: see "introduction" section.
COEFFS_ROCK_LOWMAG = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7
PGA -0.624 1.0 0.000 -2.100 1.29649 0.250 0.0
0.07 0.110 1.0 0.006 -2.128 1.29649 0.250 -0.082
0.10 0.275 1.0 0.006 -2.148 1.29649 0.250 -0.041
0.20 0.153 1.0 -0.004 -2.080 1.29649 0.250 0.0
0.30 -0.057 1.0 -0.017 -2.028 1.29649 0.250 0.0
0.40 -0.298 1.0 -0.028 -1.990 1.29649 0.250 0.0
0.50 -0.588 1.0 -0.040 -1.945 1.29649 0.250 0.0
0.75 -1.208 1.0 -0.050 -1.865 1.29649 0.250 0.0
1.0 -1.705 1.0 -0.055 -1.800 1.29649 0.250 0.0
1.5 -2.407 1.0 -0.065 -1.725 1.29649 0.250 0.0
2.0 -2.945 1.0 -0.070 -1.670 1.29649 0.250 0.0
3.0 -3.700 1.0 -0.080 -1.610 1.29649 0.250 0.0
4.0 -4.230 1.0 -0.100 -1.570 1.29649 0.250 0.0
""")
#: Coefficients tables for rock sites (table 2), for magnitude
#: values above :attr:`NEAR_FIELD_SATURATION_MAG`.
COEFFS_ROCK_HIMAG = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7
PGA -1.274 1.1 0.000 -2.100 -0.48451 0.524 0.0
0.07 -0.540 1.1 0.006 -2.128 -0.48451 0.524 -0.082
0.10 -0.375 1.1 0.006 -2.148 -0.48451 0.524 -0.041
0.20 -0.497 1.1 -0.004 -2.080 -0.48451 0.524 0.0
0.30 -0.707 1.1 -0.017 -2.028 -0.48451 0.524 0.0
0.40 -0.948 1.1 -0.028 -1.990 -0.48451 0.524 0.0
0.50 -1.238 1.1 -0.040 -1.945 -0.48451 0.524 0.0
0.75 -1.858 1.1 -0.050 -1.865 -0.48451 0.524 0.0
1.0 -2.355 1.1 -0.055 -1.800 -0.48451 0.524 0.0
1.5 -3.057 1.1 -0.065 -1.725 -0.48451 0.524 0.0
2.0 -3.595 1.1 -0.070 -1.670 -0.48451 0.524 0.0
3.0 -4.350 1.1 -0.080 -1.610 -0.48451 0.524 0.0
4.0 -4.880 1.1 -0.100 -1.570 -0.48451 0.524 0.0
""")
#: Coefficient tables for standard error on rock sites (table 3).
COEFFS_ROCK_STDDERR = CoeffsTable(sa_damping=5, table="""\
IMT sigma0 magfactor maxsigma maxmag
PGA 1.39 -0.14 0.38 7.21
0.07 1.40 -0.14 0.39 7.21
0.10 1.41 -0.14 0.40 7.21
0.20 1.43 -0.14 0.42 7.21
0.30 1.45 -0.14 0.44 7.21
0.40 1.48 -0.14 0.47 7.21
0.50 1.50 -0.14 0.49 7.21
0.75 1.52 -0.14 0.51 7.21
1.0 1.53 -0.14 0.52 7.21
4.0 1.53 -0.14 0.52 7.21
""")
#: Coefficient tables for deep soil sites (table 4).
COEFFS_SOIL = CoeffsTable(sa_damping=5, table="""\
IMT c6ss c6r c7 sigma0 magfactor maxmag
PGA 0.0000 0.0000 0.0 1.52 -0.16 7
0.075 0.4572 0.4572 0.005 1.54 -0.16 7
0.1 0.6395 0.6395 0.005 1.54 -0.16 7
0.2 0.9187 0.9187 -0.004 1.565 -0.16 7
0.3 0.9547 0.9547 -0.014 1.58 -0.16 7
0.4 0.9251 0.9005 -0.024 1.595 -0.16 7
0.5 0.8494 0.8285 -0.033 1.61 -0.16 7
0.75 0.7010 0.6802 -0.051 1.635 -0.16 7
1.0 0.5665 0.5075 -0.065 1.66 -0.16 7
1.5 0.3235 0.2215 -0.090 1.69 -0.16 7
2.0 0.1001 -0.0526 -0.108 1.70 -0.16 7
3.0 -0.2801 -0.4905 -0.139 1.71 -0.16 7
4.0 -0.6274 -0.8907 -0.160 1.71 -0.16 7
""")
#: IMT-independent coefficients for deep soil sites (table 4).
COEFFS_SOIL_IMT_INDEPENDENT = {
'c1ss': -2.17,
'c1r': -1.92,
'c2': 1.0,
'c3': 1.7,
'c4lowmag': 2.1863,
'c5lowmag': 0.32,
'c4himag': 0.3825,
'c5himag': 0.5882
}