# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2021 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:`GhofraniAtkinson2014`,
:class:`GhofraniAtkinson2014Cascadia`,
:class:`GhofraniAtkinson2014Lower`,
:class:`GhofraniAtkinson2014Upper`,
:class:`GhofraniAtkinson2014CascadiaLower`,
:class:`GhofraniAtkinson2014CascadiaUpper`
"""
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g
from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
def _get_distance_term(C, rrup, backarc):
"""
Returns the distance scaling term, which varies depending on whether
the site is in the forearc or the backarc
"""
# Geometric attenuation function
distance_scale = -np.log10(np.sqrt(rrup ** 2 + 3600.0))
# Anelastic attenuation in the backarc
distance_scale[backarc] += (C["c2"] * rrup[backarc])
# Anelastic Attenuation in the forearc
idx = np.logical_not(backarc)
distance_scale[idx] += (C["c1"] * rrup[idx])
return distance_scale
def _get_magnitude_term(C, mag):
"""
Returns the linear magnitude scaling term
"""
return C["a"] + C["b"] * mag
_get_scaling_term = CallableDict()
@_get_scaling_term.add("base")
def _get_scaling_term_1(kind, C, rrup):
"""
Returns a scaling term, which is over-ridden in subclasses
"""
return 0.0
@_get_scaling_term.add("cascadia")
def _get_scaling_term_2(kind, C, rrup):
"""
Applies the log of the Cascadia multiplicative factor (as defined in
Table 2)
"""
return C["af"]
@_get_scaling_term.add("upper")
def _get_scaling_term_3(kind, C, rrup):
"""
Applies the positive correction factor given on Page 567
"""
a_f = 0.15 + 0.0007 * rrup
a_f[a_f > 0.35] = 0.35
return a_f
@_get_scaling_term.add("lower")
def _get_scaling_term_4(kind, C, rrup):
"""
Applies the negative correction factor given on Page 567
"""
a_f = 0.15 + 0.0007 * rrup
a_f[a_f > 0.35] = 0.35
return -a_f
@_get_scaling_term.add("cascadia_upper")
def _get_scaling_term_5(kind, C, rrup):
"""
Applies the Cascadia correction factor from Table 2 and the positive
correction factor given on Page 567
"""
a_f = 0.15 + 0.0007 * rrup
a_f[a_f > 0.35] = 0.35
return C["af"] + a_f
@_get_scaling_term.add("cascadia_lower")
def _get_scaling_term_6(kind, C, rrup):
"""
Applies the Cascadia correction factor from Table 2 and the negative
correction factor given on Page 567
"""
a_f = 0.15 + 0.0007 * rrup
a_f[a_f > 0.35] = 0.35
return C["af"] - a_f
def _get_site_term(C, vs30):
"""
Returns the linear site scaling term
"""
return C["c3"] * np.log10(vs30 / 760.0)
[docs]class GhofraniAtkinson2014(GMPE):
"""
Implements the Subduction Interface GMPE of Ghofrani & Atkinson (2014)
for large magnitude earthquakes, based on the Tohoku records.
Ghofrani, H. and Atkinson, G. M. (2014) Ground Motion Prediction Equations
for Interface Earthquakes of M7 to M9 based on Empirical Data from Japan.
Bulletin of Earthquake Engineering, 12, 549 - 571
"""
kind = "base"
#: The GMPE is derived for subduction interface earthquakes in Japan
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
#: Supported intensity measure types are peak ground acceleration,
#: peak ground velocity and spectral acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is assumed to be geometric mean
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types is total.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT, const.StdDev.TOTAL}
#: The GMPE provides a Vs30-dependent site scaling term and a forearc/
#: backarc attenuation term
REQUIRES_SITES_PARAMETERS = {'vs30', 'backarc'}
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is rupture distance
REQUIRES_DISTANCES = {'rrup'}
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imean = (_get_magnitude_term(C, ctx.mag) +
_get_distance_term(C, ctx.rrup, ctx.backarc) +
_get_site_term(C, ctx.vs30) +
_get_scaling_term(self.kind, C, ctx.rrup))
# Convert mean from cm/s and cm/s/s and from common logarithm to
# natural logarithm
if imt.string.startswith(('PGA', 'SA')):
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
else:
mean[m] = np.log((10.0 ** (imean)))
sig[m] = np.log(10.0 ** np.sqrt(C["tau"] ** 2. + C["sigma"] ** 2.))
tau[m] = np.log(10.0 ** C["tau"])
phi[m] = np.log(10.0 ** C["sigma"])
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c0 a b c1 c2 c3 sig_init af sigma tau sig_tot
pgv 3.3900 0.8540 0.2795 -0.00070 -0.00099 -0.331 0.195 0.000 0.195 0.138 0.238
pga 4.6460 2.8193 0.1908 -0.00219 -0.00298 -0.219 0.284 -0.301 0.284 0.196 0.345
0.07 4.8880 3.1807 0.1759 -0.00236 -0.00329 -0.046 0.313 -0.357 0.313 0.215 0.380
0.09 5.0220 3.3592 0.1700 -0.00244 -0.00346 0.027 0.326 -0.357 0.326 0.220 0.393
0.11 5.0820 3.4483 0.1669 -0.00245 -0.00356 0.010 0.329 -0.319 0.329 0.218 0.394
0.14 5.0720 3.5005 0.1604 -0.00240 -0.00357 -0.082 0.324 -0.272 0.324 0.212 0.387
0.18 5.0510 3.4463 0.1650 -0.00235 -0.00358 -0.180 0.312 -0.237 0.312 0.206 0.374
0.22 5.0150 3.3178 0.1763 -0.00235 -0.00355 -0.289 0.310 -0.183 0.310 0.202 0.370
0.27 4.9580 3.2008 0.1839 -0.00233 -0.00346 -0.386 0.312 -0.114 0.312 0.199 0.370
0.34 4.9070 3.0371 0.1970 -0.00231 -0.00333 -0.438 0.307 -0.046 0.307 0.191 0.361
0.42 4.8200 2.7958 0.2154 -0.00224 -0.00315 -0.520 0.295 0.002 0.295 0.171 0.341
0.53 4.7060 2.5332 0.2331 -0.00213 -0.00290 -0.606 0.276 0.007 0.276 0.155 0.316
0.65 4.5870 2.3234 0.2435 -0.00200 -0.00262 -0.672 0.257 0.011 0.257 0.147 0.296
0.81 4.4640 2.1321 0.2522 -0.00183 -0.00234 -0.705 0.249 0.014 0.249 0.131 0.281
1.01 4.3360 1.9852 0.2561 -0.00158 -0.00205 -0.690 0.249 0.021 0.249 0.115 0.274
1.25 4.2140 1.8442 0.2599 -0.00133 -0.00177 -0.646 0.261 0.089 0.261 0.110 0.283
1.56 4.1050 1.6301 0.2730 -0.00112 -0.00152 -0.578 0.274 0.139 0.274 0.113 0.296
1.92 3.9900 1.4124 0.2851 -0.00086 -0.00125 -0.518 0.285 0.174 0.285 0.121 0.310
2.44 3.8290 1.1154 0.3015 -0.00059 -0.00097 -0.513 0.275 0.129 0.275 0.132 0.305
3.03 3.6570 0.7965 0.3197 -0.00039 -0.00075 -0.554 0.264 0.079 0.264 0.137 0.298
3.70 3.5020 0.5093 0.3361 -0.00023 -0.00057 -0.574 0.252 0.044 0.252 0.138 0.287
4.55 3.3510 0.2578 0.3497 -0.00005 -0.00040 -0.561 0.237 0.013 0.237 0.147 0.279
5.88 3.2320 -0.1469 0.3835 0.00000 -0.00027 -0.491 0.218 0.000 0.218 0.151 0.265
7.14 3.1220 -0.5012 0.4119 0.00000 -0.00019 -0.462 0.201 0.000 0.201 0.148 0.250
9.09 2.9850 -1.0932 0.4641 0.00000 -0.00019 -0.413 0.175 0.000 0.175 0.155 0.233
""")
[docs]class GhofraniAtkinson2014Cascadia(GhofraniAtkinson2014):
"""
Implements the Subduction Interface GMPE of Ghofrani & Atkinson (2014)
adapted for application to Cascadia
"""
kind = "cascadia"
[docs]class GhofraniAtkinson2014Upper(GhofraniAtkinson2014):
"""
Implements the Subduction Interface GMPE of Ghofrani & Atkinson (2014)
with the "upper" epistemic uncertainty model
"""
kind = "upper"
[docs]class GhofraniAtkinson2014Lower(GhofraniAtkinson2014):
"""
Implements the Subduction Interface GMPE of Ghofrani & Atkinson (2014)
with the "lower" epistemic uncertainty model
"""
kind = "lower"
[docs]class GhofraniAtkinson2014CascadiaUpper(GhofraniAtkinson2014):
"""
Implements the Subduction Interface GMPE of Ghofrani & Atkinson (2014)
with the "upper" epistemic uncertainty model and the Cascadia correction
term.
"""
kind = "cascadia_upper"
[docs]class GhofraniAtkinson2014CascadiaLower(GhofraniAtkinson2014):
"""
Implements the Subduction Interface GMPE of Ghofrani & Atkinson (2014)
with the "lower" epistemic uncertainty model and the Cascadia correction
term.
"""
kind = "cascadia_lower"