# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2018 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:'PezeshkEtAl2011',
:class:'PezeshkEtAl2011NEHRPBC'.
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class PezeshkEtAl2011(GMPE):
"""
Implements GMPE developed by Shahram Pezeshk, Arash Zandieh
and Behrooz Tavakoli. Published as "Hybrid Empirical Ground-Motion
Prediction Equations for Eastern North America Using NGA Models and
Updated Seismological Parameters", 2011, Bulletin of the Seismological
Society of America, vol. 101, no. 4, 1859 - 1870.
"""
#: Supported tectonic region type is 'stable continental region'
#: equation has been derived from data from Eastern North America (ENA)
# 'Instroduction', page 1859.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration. See Table 2 in page 1865
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Geometric mean determined from the fiftieth percentile values of the
#: geometric means computed for all nonredundant rotation angles and all
#: periods less than the maximum useable period, independent of
#: sensor orientation. See page 1864.
#: :attr:'~openquake.hazardlib.const.IMC.GMRotI50'.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GMRotI50
#: Supported standard deviation types is total.
#: See equation 6 and 7, page 1866.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: No site parameters are needed. The GMPE was developed for hard-rock site
# with Vs30 >= 2000 m/s (NEHRP site class A) only. Page 1864.
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude (eq. 4, page 1866).
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is RRup, explained in page 1864 (eq. 2 page
#: 1861, eq. 5 page 1866).
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.
"""
# Extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
imean = (self._compute_magnitude(rup, C) +
self._compute_attenuation(rup, dists, imt, C) +
self._compute_distance(rup, dists, imt, C))
mean = np.log(10.0 ** (imean))
istddevs = self._get_stddevs(C, stddev_types, rup, imt,
num_sites=len(dists.rrup))
stddevs = np.log(10.0 ** np.array(istddevs))
return mean, stddevs
def _get_stddevs(self, C, stddev_types, rup, imt, num_sites):
"""
Return standard deviations as defined in eq. 6 and 7, pag. 1866,
based on table 2, p. 1865.
"""
stddevs = []
for stddev_type in stddev_types:
sigma_mean = self._compute_standard_dev(rup, imt, C)
sigma_tot = np.sqrt((sigma_mean ** 2) + (C['SigmaReg'] ** 2))
stddevs.append(sigma_tot + np.zeros(num_sites))
return stddevs
def _compute_magnitude(self, rup, C):
"""
Compute the first term of the equation described on p. 1866:
"c1 + (c2 * M) + (c3 * M**2) "
"""
return C['c1'] + (C['c2'] * rup.mag) + (C['c3'] * (rup.mag ** 2))
def _compute_attenuation(self, rup, dists, imt, C):
"""
Compute the second term of the equation described on p. 1866:
" [(c4 + c5 * M) * min{ log10(R), log10(70.) }] +
[(c4 + c5 * M) * max{ min{ log10(R/70.), log10(140./70.) }, 0.}] +
[(c8 + c9 * M) * max{ log10(R/140.), 0}] "
"""
vec = np.ones(len(dists.rrup))
a1 = (np.log10(np.sqrt(dists.rrup ** 2.0 + C['c11'] ** 2.0)),
np.log10(70. * vec))
a = np.column_stack([a1[0], a1[1]])
b3 = (np.log10(np.sqrt(dists.rrup ** 2.0 + C['c11'] ** 2.0) /
(70. * vec)),
np.log10((140. / 70.) * vec))
b2 = np.column_stack([b3[0], b3[1]])
b1 = ([np.min(b2, axis=1), 0. * vec])
b = np.column_stack([b1[0], b1[1]])
c1 = (np.log10(np.sqrt(dists.rrup ** 2.0 + C['c11'] ** 2.0) /
(140.) * vec), 0. * vec)
c = np.column_stack([c1[0], c1[1]])
return (((C['c4'] + C['c5'] * rup.mag) * np.min(a, axis=1)) +
((C['c6'] + C['c7'] * rup.mag) * np.max(b, axis=1)) +
((C['c8'] + C['c9'] * rup.mag) * np.max(c, axis=1)))
def _compute_distance(self, rup, dists, imt, C):
"""
Compute the third term of the equation described on p. 1866:
" c10 * R "
"""
return (C['c10'] * np.sqrt(dists.rrup ** 2.0 + C['c11'] ** 2.0))
def _compute_standard_dev(self, rup, imt, C):
"""
Compute the the standard deviation in terms of magnitude
described on p. 1866, eq. 6
"""
sigma_mean = 0.
if rup.mag <= 7.0:
sigma_mean = (C['c12'] * rup.mag) + C['c13']
elif rup.mag > 7.0:
sigma_mean = (-0.00695 * rup.mag) + C['c14']
return sigma_mean
#: Equation coefficients, described in Table 2 on pp. 1865
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 SigmaReg
pga 1.58278500 0.22980485 -0.038467279 -3.8325245 0.35351790 0.332086450 -0.091649259 -2.55169890 0.183070910 -0.000422375 6.6520975 -0.021050254 0.37776584 0.27905505 0.020605025
0.010 2.04335530 0.19869692 -0.038373068 -4.0520987 0.36880267 0.199480560 -0.089184795 -2.59482830 0.184720410 -0.000396518 7.0644860 -0.019743027 0.36878898 0.27922877 0.021612537
0.020 2.30502180 0.18772175 -0.036967652 -4.0442826 0.36162763 -0.122224550 -0.091565623 -2.99982330 0.194066370 -0.000170722 7.3313536 -0.019743461 0.36914553 0.27958228 0.022866162
0.030 1.98482400 0.22034946 -0.036162832 -3.8031855 0.33840184 0.078141783 -0.112603350 -3.31249830 0.201652180 -5.32179E-05 7.1182747 -0.020937771 0.38173747 0.28381405 0.022372523
0.040 1.68540590 0.24043926 -0.035776383 -3.6128750 0.32469480 0.295613210 -0.118021140 -3.33203870 0.197668130 -0.000111254 6.8113199 -0.021802452 0.39139487 0.28741869 0.023605119
0.050 1.45173560 0.24141515 -0.034675707 -3.4682843 0.31767228 0.522379110 -0.129556390 -3.21086740 0.195626560 -0.000266881 6.3705068 -0.022441733 0.39897679 0.29052564 0.025051344
0.075 1.06977950 0.29887294 -0.038974596 -3.3769847 0.31798753 0.742235930 -0.121484440 -2.68887410 0.172335850 -0.000665924 6.0817334 -0.023123141 0.41078656 0.29756555 0.025095256
0.100 0.93139390 0.30877617 -0.038436152 -3.2926201 0.30631958 0.706381220 -0.095214253 -2.20903630 0.147206520 -0.000925354 6.1620694 -0.022592868 0.41023283 0.30072374 0.022233811
0.150 0.39643437 0.43169606 -0.045775593 -3.2111790 0.29369212 0.608391200 -0.067269233 -1.61208100 0.107162070 -0.001076688 6.2666878 -0.021848921 0.40660604 0.30230457 0.015582655
0.200 -0.48833625 0.62775027 -0.056541133 -3.0304035 0.26733511 0.542189400 -0.053474958 -1.35161460 0.087841291 -0.001045251 6.1904808 -0.020458744 0.39785283 0.30328260 0.014475725
0.250 -1.00980480 0.74012641 -0.063085510 -2.9959199 0.26228068 0.442112110 -0.036248505 -1.23093190 0.077330183 -0.000964827 6.0635084 -0.019334356 0.39083594 0.30413643 0.014820287
0.300 -1.68000460 0.88602986 -0.071623704 -2.8893864 0.24814951 0.486938120 -0.043237709 -1.14899390 0.070555429 -0.000904897 5.9890843 -0.018365879 0.38669103 0.30677086 0.014961957
0.400 -2.31061360 1.02152740 -0.079650976 -2.9265220 0.25151054 0.471589720 -0.040392223 -1.09230140 0.065542242 -0.000785255 6.0262775 -0.016832386 0.37737845 0.30819274 0.017221468
0.500 -3.13650760 1.20145830 -0.090369654 -2.8822916 0.24557786 0.333343350 -0.021047931 -1.00224290 0.055192621 -0.000706937 5.9116595 -0.015559903 0.37216518 0.31188685 0.016787106
0.750 -4.54936770 1.50802900 -0.108711700 -2.8613890 0.24235022 0.402313090 -0.030918512 -0.97503715 0.055361787 -0.000568498 5.9835259 -0.013391470 0.36543753 0.32033822 0.020791085
1.000 -5.41133340 1.69017010 -0.119600830 -2.8998486 0.24646305 0.376637070 -0.029283940 -0.94703476 0.052492510 -0.000456318 6.1234329 -0.011795872 0.35880759 0.32487746 0.022183642
1.500 -6.48064580 1.86695490 -0.128177110 -2.9338076 0.25251393 0.263262110 -0.014416940 -0.90065097 0.049739355 -0.000353991 5.9874702 -0.010403524 0.35692188 0.33273819 0.018625013
2.000 -6.93399290 1.90680910 -0.128724930 -3.0128154 0.26392116 0.317152250 -0.021502488 -0.87493043 0.047742343 -0.000302477 6.1355097 -0.009442865 0.35611062 0.33865155 0.020962228
3.000 -7.42641010 1.88127470 -0.120486060 -2.9742397 0.25760353 0.258510050 -0.015195139 -0.88213320 0.053758057 -0.000264063 6.0597555 -0.008508698 0.35402644 0.34310654 0.02428989
4.000 -7.80636730 1.89546280 -0.118292150 -3.0049879 0.25879498 0.306906560 -0.025450016 -0.88079876 0.057030983 -0.000242251 6.2536484 -0.007859427 0.35270488 0.34632987 0.029899076
5.000 -8.27036650 1.93795990 -0.117965260 -2.9501142 0.25032167 0.329567930 -0.030227728 -1.01253690 0.073323916 -0.000200169 6.3422591 -0.006899636 0.35767668 0.35802021 0.031592909
7.500 -8.33763300 1.80623080 -0.104248570 -2.9838785 0.25418641 0.287880220 -0.022521612 -1.18165170 0.095976523 -0.000162413 6.5180975 -0.007239689 0.37304593 0.37100909 0.029567069
10.00 -9.10461860 1.89872240 -0.107604830 -2.8611231 0.23953867 0.286847230 -0.022896491 -1.37862210 0.122158550 -0.000126810 6.5383616 -0.007485065 0.38476363 0.38100915 0.024448978
""")
[docs]class PezeshkEtAl2011NEHRPBC(PezeshkEtAl2011):
"""
Adaptation of Pezeshk et al. (2011) to amplify the ground motions from
the original hard rock (Vs30 2880 m/s) sites to the NEHRP B/C site class
using the factors of Atkinson & Boore (2006) (Table 4)
"""
[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.
"""
C_AMP = self.SITE_COEFFS[imt]
# Get method from superclass
mean, stddevs = super().get_mean_and_stddevs(
sites, rup, dists, imt, stddev_types)
return mean + np.log(C_AMP["F"]), stddevs
SITE_COEFFS = CoeffsTable(sa_damping=5, table="""
IMT F
pga 2.5000
0.0100 2.5000
0.0122 2.4970
0.0299 2.4740
0.0471 2.4520
0.0797 2.4110
0.1577 2.3130
0.2484 2.2020
0.3505 2.0790
0.5192 1.8840
0.7225 1.6720
1.2715 1.3940
2.2381 1.2370
4.1632 1.1450
9.8619 1.0730
10.000 1.0000
""")