# Source code for openquake.hazardlib.gsim.fukushima_tanaka_1990

```
# -*- 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:'FukushimaTanaka1990' and :class:
'FukushimaTanakaSite1990'
"""
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 PGA
[docs]class FukushimaTanaka1990(GMPE):
"""
Implements the PGA GMPE of Fukushima and Tanaka (1990)
Fukushima, Y. and Tanaka, T. (1990) A New Attenuation Relation for Peak
Horizontal Acceleration of Strong Earthquake Ground Motion in Japan.
Bulletin of the Seismological Society of America, 80(4), 757 - 783
"""
#: The GMPE is derived from shallow earthquakes in California and Japan
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
])
#: Supported intensity measure component is the average horizontal
#: component
#: :attr:`openquake.hazardlib.const.IMC.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
])
#: Required site parameters. The GMPE was developed for an ''average''
#: site conditions. The authors specify that for rock sites the
#: values should be lowered by 40 % and for soil site they should be
#: raised by 40 %. For greatest consistencty the site condition is
#: neglected currently but a site-dependent GMPE may be implemented
#: inside a subclass.
REQUIRES_SITES_PARAMETERS = set(())
#: Required rupture parameters are magnitude
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.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
C = self.COEFFS[imt]
imean = (self._compute_magnitude_scaling(C, rup.mag) +
self._compute_distance_scaling(C, dists.rrup, rup.mag))
# Original GMPE returns log10 acceleration in cm/s/s
# Converts to natural logarithm of g
mean = np.log((10.0 ** (imean - 2.0)) / g)
istddevs = self._compute_stddevs(
C, dists.rrup.shape, stddev_types
)
# Convert from common logarithm to natural logarithm
stddevs = np.log(10 ** np.array(istddevs))
return mean, stddevs
def _compute_magnitude_scaling(self, C, mag):
"""
Returns the magnitude scaling term
"""
return C["c1"] * mag + C["c5"]
def _compute_distance_scaling(self, C, rrup, mag):
"""
Returns the distance scaling term
"""
rscale1 = rrup + C["c2"] * (10.0 ** (C["c3"] * mag))
return -np.log10(rscale1) - (C["c4"] * rrup)
def _compute_stddevs(self, C, num_sites, stddev_types):
"""
Return total standard deviation.
"""
std_total = C['sigma']
stddevs = []
for _ in stddev_types:
stddevs.append(np.zeros(num_sites) + std_total)
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c1 c2 c3 c4 c5 sigma
pga 0.41 0.032 0.41 0.0034 1.30 0.21
""")
[docs]class FukushimaTanakaSite1990(FukushimaTanaka1990):
"""
Implements the Fukushima and Tanaka (1990) model correcting for
site class. The authors specify that the ground motions should
be raised by 40 % on soft soil sites and reduced by 40 % on rock sites.
The specific site classification is not known, so it is assumed that
in this context "average" site conditions refer to NEHRP C, rock conditions
to NEHRP A and B, and soft soil conditions to NEHRP D and E
"""
#: Input sites as vs30 although only three classes considered
REQUIRES_SITES_PARAMETERS = set(("vs30",))
[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]
imean = (self._compute_magnitude_scaling(C, rup.mag) +
self._compute_distance_scaling(C, dists.rrup, rup.mag))
# Original GMPE returns log10 acceleration in cm/s/s
# Converts to natural logarithm of g
mean = np.log((10.0 ** (imean - 2.0)) / g)
mean = self._compute_site_scaling(sites.vs30, mean)
istddevs = self._compute_stddevs(
C, dists.rrup.shape, stddev_types
)
# Convert from common logarithm to natural logarithm
stddevs = np.log(10 ** np.array(istddevs))
return mean, stddevs
def _compute_site_scaling(self, vs30, mean):
"""
Scales the ground motions by increasing 40 % on NEHRP class D/E sites,
and decreasing by 40 % on NEHRP class A/B sites
"""
site_factor = np.ones(len(vs30), dtype=float)
idx = vs30 <= 360.
site_factor[idx] = 1.4
idx = vs30 > 760.0
site_factor[idx] = 0.6
return np.log(np.exp(mean) * site_factor)
```