# The Hazard Library
# Copyright (C) 2013-2014, 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:'PezeshkEtAl2011'.
"""
from __future__ import division
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
""")