# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2021, 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/>.
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib.gsim.atkinson_boore_2006 import (
AtkinsonBoore2006, _get_pga_on_rock, _get_site_amplification_linear,
_get_site_amplification_non_linear, _compute_magnitude_scaling,
_compute_distance_scaling, set_sig)
from openquake.hazardlib import const, contexts
from openquake.hazardlib.imt import PGA, PGV, SA
[docs]def hawaii_adjust(mean, ctx, imt):
# Defining frequency
if imt == PGA():
freq = 50.0
elif imt == PGV():
freq = 2.0
else:
freq = 1./imt.period
# Equation 3 of Atkinson (2010)
x1 = np.min([-0.18+0.17*np.log10(freq), 0])
# Equation 4 a-b-c of Atkinson (2010)
if ctx.hypo_depth < 20.0:
x0 = np.max([0.217 - 0.321 * np.log10(freq), 0])
elif ctx.hypo_depth > 35.0:
x0 = np.min([0.263 + 0.0924 * np.log10(freq), 0.35])
else:
x0 = 0.2
# Limiting calculation distance to 1km
# (as suggested by C. Bruce Worden)
rjb = [d if d > 1 else 1 for d in ctx.rjb]
# Equation 2 and 5 of Atkinson (2010)
mean += (x0 + x1*np.log10(rjb)) / np.log10(np.e)
[docs]class BooreAtkinson2008(GMPE):
"""
Implements GMPE developed by David M. Boore and Gail M. Atkinson
and published as "Ground-Motion Prediction Equations for the
Average Horizontal Component of PGA, PGV, and 5%-Damped PSA
at Spectral Periods between 0.01 and 10.0 s" (2008, Earthquake Spectra,
Volume 24, No. 1, pages 99-138).
"""
#: Supported tectonic region type is active shallow crust, see
#: paragraph 'Introduction', page 99.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: peak ground velocity and peak ground acceleration, see table 3
#: pag. 110
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.GMRotI50`, see paragraph
#: 'Response Variables', page 100 and table 8, pag 121.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GMRotI50
#: Supported standard deviation types are inter-event, intra-event
#: and total, see equation 2, pag 106.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameters is Vs30.
#: See paragraph 'Predictor Variables', pag 103
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude, and rake.
#: See paragraph 'Predictor Variables', pag 103
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'}
#: Required distance measure is Rjb.
#: See paragraph 'Predictor Variables', pag 103
REQUIRES_DISTANCES = {'rjb'}
#: Shear-wave velocity for reference soil conditions in [m s-1]
DEFINED_FOR_REFERENCE_VELOCITY = 760.
kind = 'base'
sgn = 0
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
# horrible hack to fix the distance parameters; needed for the can15
# subclasses; extra distances are add in can15.eastern
# this also affects generic_gmpe_avgsa_test.py
vars(ctx).update(contexts.get_dists(ctx))
# compute PGA on rock conditions - needed to compute non-linear
# site amplification term
pga4nl = _get_pga_on_rock(self.COEFFS[PGA()], ctx)
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
C_SR = self.COEFFS_SOIL_RESPONSE[imt]
# equation 1, pag 106, without sigma term, that is only the first 3
# terms. The third term (site amplification) is computed as given
# in equation (6), that is the sum of a linear term - equation (7)
# - and a non-linear one - equations (8a) to (8c).
# Mref, Rref values are given in the caption to table 6, pag 119.
if imt == PGA():
# avoid recomputing PGA on rock, just add site terms
mean[m] = np.log(pga4nl) + \
_get_site_amplification_linear(ctx.vs30, C_SR) + \
_get_site_amplification_non_linear(ctx.vs30, pga4nl, C_SR)
else:
mean[m] = _compute_magnitude_scaling(ctx, C) + \
_compute_distance_scaling(ctx, C) + \
_get_site_amplification_linear(ctx.vs30, C_SR) + \
_get_site_amplification_non_linear(ctx.vs30, pga4nl, C_SR)
if self.kind in ('2011', 'prime'):
# correction factor (see Atkinson and Boore, 2011; equation 5
# at page 1126 and nga08_gm_tmr.for line 508
corr_fact = 10.0**(np.max([0, 3.888 - 0.674 * ctx.mag]) -
(np.max([0, 2.933 - 0.510 * ctx.mag]) *
np.log10(ctx.rjb + 10.)))
mean[m] = np.log(np.exp(mean[m]) * corr_fact)
if self.kind == 'hawaii':
hawaii_adjust(mean[m], ctx, imt)
elif self.kind == 'prime':
# Implements the Boore & Atkinson (2011) adjustment to the
# Atkinson (2008) GMPE
A08 = self.COEFFS_A08[imt]
f_ena = 10.0 ** (A08["c"] + A08["d"] * ctx.rjb)
mean[m] = np.log(np.exp(mean[m]) * f_ena)
set_sig(self.kind, C, sig[m], tau[m], phi[m])
#: Coefficient table is constructed from values in tables 6, 7 and 8
#: (pages 119, 120, 121). Spectral acceleration is defined for damping
#: of 5%, see 'Response Variables' page 100.
#: c1, c2, c3, h are the period-dependent distance scaling coefficients.
#: e1, e2, e3, e4, e5, e6, e7, Mh are the period-dependent magnitude-
# scaling coefficients.
#: sigma, tau, std are the intra-event uncertainty, inter-event
#: uncertainty, and total standard deviation, respectively.
#: Note that only the inter-event and total standard deviation for
#: 'specified' fault type are considered (because rake angle is always
#: specified)
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 h e1 e2 e3 e4 e5 e6 e7 Mh sigma tau std
pgv -0.87370 0.10060 -0.00334 2.54 5.00121 5.04727 4.63188 5.08210 0.18322 -0.12736 0.00000 8.50 0.500 0.256 0.560
pga -0.66050 0.11970 -0.01151 1.35 -0.53804 -0.50350 -0.75472 -0.50970 0.28805 -0.10164 0.00000 6.75 0.502 0.260 0.564
0.010 -0.66220 0.12000 -0.01151 1.35 -0.52883 -0.49429 -0.74551 -0.49966 0.28897 -0.10019 0.00000 6.75 0.502 0.262 0.566
0.020 -0.66600 0.12280 -0.01151 1.35 -0.52192 -0.48508 -0.73906 -0.48895 0.25144 -0.11006 0.00000 6.75 0.502 0.262 0.566
0.030 -0.69010 0.12830 -0.01151 1.35 -0.45285 -0.41831 -0.66722 -0.42229 0.17976 -0.12858 0.00000 6.75 0.507 0.274 0.576
0.050 -0.71700 0.13170 -0.01151 1.35 -0.28476 -0.25022 -0.48462 -0.26092 0.06369 -0.15752 0.00000 6.75 0.516 0.286 0.589
0.075 -0.72050 0.12370 -0.01151 1.55 0.00767 0.04912 -0.20578 0.02706 0.01170 -0.17051 0.00000 6.75 0.513 0.320 0.606
0.10 -0.70810 0.11170 -0.01151 1.68 0.20109 0.23102 0.03058 0.22193 0.04697 -0.15948 0.00000 6.75 0.520 0.318 0.608
0.15 -0.69610 0.09884 -0.01113 1.86 0.46128 0.48661 0.30185 0.49328 0.17990 -0.14539 0.00000 6.75 0.518 0.290 0.594
0.20 -0.58300 0.04273 -0.00952 1.98 0.57180 0.59253 0.40860 0.61472 0.52729 -0.12964 0.00102 6.75 0.523 0.288 0.596
0.25 -0.57260 0.02977 -0.00837 2.07 0.51884 0.53496 0.33880 0.57747 0.60880 -0.13843 0.08607 6.75 0.527 0.267 0.592
0.30 -0.55430 0.01955 -0.00750 2.14 0.43825 0.44516 0.25356 0.51990 0.64472 -0.15694 0.10601 6.75 0.546 0.269 0.608
0.40 -0.64430 0.04394 -0.00626 2.24 0.39220 0.40602 0.21398 0.46080 0.78610 -0.07843 0.02262 6.75 0.541 0.267 0.603
0.50 -0.69140 0.06080 -0.00540 2.32 0.18957 0.19878 0.00967 0.26337 0.76837 -0.09054 0.00000 6.75 0.555 0.265 0.615
0.75 -0.74080 0.07518 -0.00409 2.46 -0.21338 -0.19496 -0.49176 -0.10813 0.75179 -0.14053 0.10302 6.75 0.571 0.299 0.645
1.0 -0.81830 0.10270 -0.00334 2.54 -0.46896 -0.43443 -0.78465 -0.39330 0.67880 -0.18257 0.05393 6.75 0.573 0.302 0.647
1.5 -0.83030 0.09793 -0.00255 2.66 -0.86271 -0.79593 -1.20902 -0.88085 0.70689 -0.25950 0.19082 6.75 0.566 0.373 0.679
2.0 -0.82850 0.09432 -0.00217 2.73 -1.22652 -1.15514 -1.57697 -1.27669 0.77989 -0.29657 0.29888 6.75 0.580 0.389 0.700
3.0 -0.78440 0.07282 -0.00191 2.83 -1.82979 -1.74690 -2.22584 -1.91814 0.77966 -0.45384 0.67466 6.75 0.566 0.401 0.695
4.0 -0.68540 0.03758 -0.00191 2.89 -2.24656 -2.15906 -2.58228 -2.38168 1.24961 -0.35874 0.79508 6.75 0.583 0.385 0.698
5.0 -0.50960 -0.02391 -0.00191 2.93 -1.28408 -1.21270 -1.50904 -1.41093 0.14271 -0.39006 0.00000 8.50 0.601 0.437 0.744
7.5 -0.37240 -0.06568 -0.00191 3.00 -1.43145 -1.31632 -1.81022 -1.59217 0.52407 -0.37578 0.00000 8.50 0.626 0.477 0.787
10.0 -0.09824 -0.13800 -0.00191 3.04 -2.15446 -2.16137 -2.53323 -2.14635 0.40387 -0.48492 0.00000 8.50 0.645 0.477 0.801
""")
COEFFS_SOIL_RESPONSE = AtkinsonBoore2006.COEFFS_SOIL_RESPONSE
COEFFS_A08 = CoeffsTable(sa_damping=5, table="""\
IMT c d
pgv 0.450 0.00211
pga 0.419 0.00039
0.005 0.417 0.00192
0.050 0.417 0.00192
0.100 0.245 0.00273
0.200 0.042 0.00232
0.300 -0.078 0.00190
0.500 -0.180 0.00180
1.000 -0.248 0.00153
2.000 -0.214 0.00117
3.030 -0.084 0.00091
5.000 0.000 0.00000
10.00 0.000 0.00000
""")
[docs]class Atkinson2010Hawaii(BooreAtkinson2008):
"""
Modification of the original base class adjusted for application
to the Hawaii region as described in:
Atkinson, G. M. (2010) 'Ground-Motion Prediction Equations for Hawaii
from a Referenced Empirical Approach", Bulletin of the Seismological
Society of America, Vol. 100, No. 2, pp. 751–761
"""
kind = 'hawaii'
#: Supported tectonic region type is active volcanic, see
#: paragraph 'Introduction', page 99.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC
#: Supported intensity measure component is geometric mean, see paragraph
#: 'Response Variables', page 100 and table 8, pag 121.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.VECTORIAL
#: Supported standard deviation types is total
#: see equation 2, pag 106.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
# Adding hypocentral depth as required rupture parameter
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'hypo_depth'}