# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2017 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:`MontalvaEtAl2016SInter`
:class:`MontalvaEtAl2016SSlab`
"""
from __future__ import division
import numpy as np
from openquake.hazardlib.gsim.base import CoeffsTable
from openquake.hazardlib.imt import PGA
from openquake.hazardlib.gsim.abrahamson_2015 import (AbrahamsonEtAl2015SInter,
AbrahamsonEtAl2015SSlab)
[docs]class MontalvaEtAl2016SInter(AbrahamsonEtAl2015SInter):
"""
Adaptation of the Abrahamson et al. (2015) BC Hydro subduction interface
GMPE, calibrated to Chilean strong motion data.
GMPE and related coefficients published by:
Montalva, G., Bastias, N., Rodriguez-Marek, A. (2016), 'Ground Motion
Prediction Equation for the Chilean Subduction Zone'. Submitted to
Seismological Research Letters
"""
[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.
"""
# extract dictionaries of coefficients specific to required
# intensity measure type and for PGA
C = self.COEFFS[imt]
C_PGA = self.COEFFS[PGA()]
dc1_pga = C_PGA["DC1"]
# compute median pga on rock (vs30=1000), needed for site response
# term calculation
pga1000 = np.exp(
self._compute_pga_rock(C_PGA, dc1_pga, sites, rup, dists))
mean = (self._compute_magnitude_term(C, C["DC1"], rup.mag) +
self._compute_distance_term(C, rup.mag, dists) +
self._compute_focal_depth_term(C, rup) +
self._compute_forearc_backarc_term(C, sites, dists) +
self._compute_site_response_term(C, sites, pga1000))
stddevs = self._get_stddevs(C, stddev_types, len(sites.vs30))
return mean, stddevs
def _compute_magnitude_term(self, C, dc1, mag):
"""
Computes the magnitude scaling term given by equation (2)
"""
base = C['theta1'] + (C['theta4'] * dc1)
dmag = self.CONSTS["C1"] + dc1
if mag > dmag:
f_mag = (C['theta5'] * (mag - dmag)) +\
C['theta13'] * ((10. - mag) ** 2.)
else:
f_mag = (C['theta4'] * (mag - dmag)) +\
C['theta13'] * ((10. - mag) ** 2.)
return base + f_mag
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1)
"""
return (C['theta2'] + C['theta3'] * (mag - 7.8)) *\
np.log(dists.rrup + self.CONSTS['c4'] * np.exp((mag - 6.) *
self.CONSTS['theta9'])) + (C['theta6'] * dists.rrup)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt DC1 vlin b theta1 theta2 theta3 theta4 theta5 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma phi_s2s
pga 0.200000000 865.1 -1.186 4.935754758 -1.319716122 0.156954813 -1.038307042 -0.200134154 -0.002064757 1.0988 -1.42 4.559632568 0.004375202 0.914271114 -0.203185487 -0.694459960 0.9969 -1.00 0.676804137 0.436356919 0.805277096 0.547434071
0.010 0.200000000 865.1 -1.186 4.935754758 -1.319716122 0.156954813 -1.038307042 -0.200134154 -0.002064757 1.0988 -1.42 4.559632568 0.004375202 0.914271114 -0.203185487 -0.694459960 0.9969 -1.00 0.676804137 0.436356919 0.805277096 0.547434071
0.020 0.200000000 865.1 -1.186 4.963548267 -1.321501153 0.142973041 -0.925888135 -0.148739101 -0.002188725 1.0988 -1.42 4.654806348 0.004263109 0.934182754 -0.197899904 -0.710342148 0.9969 -1.00 0.683243196 0.430880779 0.807762039 0.554691749
0.050 0.200000000 1053.5 -1.346 7.358115618 -1.825715240 0.093914961 -0.555849306 0.129797026 -0.000431630 1.2536 -1.65 5.105622455 0.005100764 1.188485184 -0.183201116 -0.737586413 1.1030 -1.18 0.671606746 0.483036109 0.827272328 0.545045472
0.075 0.200000000 1085.7 -1.471 7.558603177 -1.810050104 0.103239851 -0.561904402 0.151637804 -0.001102941 1.4175 -1.80 4.514166186 0.005820798 1.395007124 -0.174729372 -0.615517435 1.2732 -1.36 0.697383068 0.508098624 0.862848397 0.582340972
0.100 0.200000000 1032.5 -1.624 7.027657583 -1.633492535 0.088844200 -0.525502325 0.265136034 -0.002397453 1.3997 -1.80 3.827080246 0.004236026 1.560949356 -0.176264079 -0.487079351 1.3042 -1.36 0.722361027 0.504635520 0.881171074 0.616096154
0.150 0.200000000 877.6 -1.931 6.049355161 -1.335645478 0.073754755 -0.567044631 0.294956394 -0.003942231 1.3582 -1.69 2.880273890 0.002951253 1.824536435 -0.193149712 -0.343522351 1.2600 -1.30 0.741411715 0.475224629 0.880641687 0.629331025
0.200 0.200000000 748.2 -2.188 4.179750788 -0.885470585 0.065604603 -0.659648456 0.359088006 -0.005638198 1.1648 -1.49 3.257747522 0.002516425 1.976696142 -0.214467130 -0.452888442 1.2230 -1.25 0.759426634 0.429788781 0.872609425 0.637577298
0.250 0.200000000 654.3 -2.381 3.999581211 -0.821066204 0.055367666 -0.643078011 0.352583884 -0.005484494 0.9940 -1.30 3.545595708 0.000888426 2.152539829 -0.226122818 -0.531334245 1.1600 -1.17 0.743380316 0.401651257 0.844948535 0.606641527
0.300 0.200000000 587.1 -2.518 3.343521294 -0.678019870 0.070313635 -0.816717363 0.236089761 -0.005490803 0.8821 -1.18 3.711884196 0.001562756 2.179000482 -0.238785185 -0.601073843 1.0500 -1.06 0.750620673 0.389053205 0.845454783 0.609833032
0.400 0.143682921 503.0 -2.657 3.342528747 -0.674981502 0.071624870 -1.123522692 0.103008688 -0.004346784 0.7046 -0.98 4.125701638 -0.001119565 2.225720730 -0.284536574 -0.702111182 0.8000 -0.78 0.741503989 0.383488689 0.834800419 0.589961066
0.500 0.100000000 456.6 -2.669 3.714706072 -0.770820923 0.073623537 -1.330962172 -0.019664088 -0.003028097 0.5799 -0.82 4.507163580 -0.000434645 2.265272475 -0.318116722 -0.800834677 0.6620 -0.62 0.688862082 0.384159164 0.788739014 0.513251109
0.600 0.073696559 430.3 -2.599 4.425108150 -0.939459680 0.062188731 -1.569443919 -0.014606735 -0.001675340 0.5021 -0.70 5.255072487 -0.000097416 2.200898990 -0.365330018 -0.966147926 0.5800 -0.50 0.665479640 0.394271020 0.773506812 0.486626176
0.750 0.041503750 410.5 -2.401 4.372165283 -0.933761671 0.053771754 -1.730788918 -0.031408137 -0.001524349 0.3687 -0.54 5.074522171 -0.001350443 1.918279398 -0.401223910 -0.937019824 0.4800 -0.34 0.637244299 0.414109647 0.759978352 0.443006934
1.000 0.000000000 400.0 -1.955 4.021211151 -0.924917589 0.054326150 -1.908027335 -0.138131804 -0.001101517 0.1746 -0.34 5.211831136 -0.002283504 1.509910061 -0.433435346 -0.964846571 0.3300 -0.14 0.611337571 0.442015583 0.754394725 0.421636418
1.500 -0.058496250 400.0 -1.025 3.946972058 -1.002244695 0.049918773 -2.307833569 -0.412376757 -0.000261255 -0.0820 -0.05 5.561359279 -0.000996882 0.656237153 -0.502990059 -1.057548381 0.3100 0.00 0.617840247 0.436708751 0.756598377 0.448028967
2.000 -0.100000000 400.0 -0.299 3.763370770 -1.048406811 0.049945027 -2.218316295 -0.488347011 -0.000156404 -0.2821 0.12 5.310311721 -0.000289011 -0.148288073 -0.501824964 -1.007661553 0.3000 0.00 0.586452050 0.429957558 0.727179144 0.424207890
2.500 -0.155033971 400.0 0.000 3.279573476 -0.991842986 0.095212751 -2.496506471 -0.770828569 -0.000738153 -0.4108 0.25 4.764778613 -0.001039535 -0.459995635 -0.517128864 -0.886704977 0.3000 0.00 0.567864698 0.442678828 0.720024208 0.416230786
3.000 -0.200000000 400.0 0.000 3.407135085 -1.079312405 0.092359656 -2.425045547 -0.883889211 -0.000357658 -0.4466 0.30 4.800502846 -0.000395577 -0.450645670 -0.514638813 -0.901051441 0.3000 0.00 0.559253514 0.420099114 0.699462478 0.418794658
4.000 -0.200000000 400.0 0.000 2.789669400 -1.072279505 0.148258197 -2.792416051 -1.282315047 0.000409730 -0.4344 0.30 5.011985606 -0.000308830 -0.512937685 -0.529022902 -0.939796651 0.3000 0.00 0.569097474 0.408117852 0.700308586 0.435934346
5.000 -0.200000000 400.0 0.000 2.700791140 -1.202536653 0.172625283 -2.741020801 -1.141773134 0.001833647 -0.4368 0.30 5.457710792 0.000255165 -0.503538042 -0.504799612 -1.025705989 0.3000 0.00 0.558540211 0.387890193 0.680019095 0.418174855
6.000 -0.200000000 400.0 0.000 2.630174552 -1.303101604 0.127044195 -1.863112205 -0.727779859 0.002185845 -0.4586 0.30 5.826483564 0.001637500 -0.497674025 -0.423978007 -1.110103433 0.3000 0.00 0.502062640 0.394614799 0.638582598 0.346222778
7.500 -0.200000000 400.0 0.000 2.520418211 -1.399368154 0.084904399 -0.930694380 -0.212014425 0.002325451 -0.4433 0.30 6.332273436 0.001046880 -0.481585300 -0.334701563 -1.195826518 0.3000 0.00 0.482570602 0.373377912 0.610151990 0.321745366
10.00 -0.200000000 400.0 0.000 3.266979586 -1.707902316 0.068210457 -0.967817098 0.253077379 0.004736644 -0.4828 0.30 7.382937906 0.000738462 -0.423369635 -0.347713953 -1.409670235 0.3000 0.00 0.466924628 0.376696614 0.599932452 0.300789811
""")
CONSTS = {
# Period-Independent Coefficients (Table 2)
'n': 1.18,
'c': 1.88,
'c4': 10.0,
'C1': 7.8,
'theta9': 0.4
}
[docs]class MontalvaEtAl2016SSlab(AbrahamsonEtAl2015SSlab):
"""
Adaptation of the Abrahamson et al. (2015) BC Hydro subduction in-slab
GMPE, calibrated to Chilean strong motion data
"""
[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.
"""
# extract dictionaries of coefficients specific to required
# intensity measure type and for PGA
C = self.COEFFS[imt]
# For inslab GMPEs the correction term is fixed at -0.3
dc1 = -0.3
C_PGA = self.COEFFS[PGA()]
# compute median pga on rock (vs30=1000), needed for site response
# term calculation
pga1000 = np.exp(
self._compute_pga_rock(C_PGA, dc1, sites, rup, dists))
mean = (self._compute_magnitude_term(C, dc1, rup.mag) +
self._compute_distance_term(C, rup.mag, dists) +
self._compute_focal_depth_term(C, rup) +
self._compute_forearc_backarc_term(C, sites, dists) +
self._compute_site_response_term(C, sites, pga1000))
stddevs = self._get_stddevs(C, stddev_types, len(sites.vs30))
return mean, stddevs
def _compute_magnitude_term(self, C, dc1, mag):
"""
Computes the magnitude scaling term given by equation (2)
corrected by a local adjustment factor
"""
base = C['theta1'] + (C['theta4'] * dc1)
dmag = self.CONSTS["C1"] + dc1
if mag > dmag:
f_mag = (C['theta5'] * (mag - dmag)) +\
C['theta13'] * ((10. - mag) ** 2.)
else:
f_mag = (C['theta4'] * (mag - dmag)) +\
C['theta13'] * ((10. - mag) ** 2.)
return base + f_mag
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1b)
"""
return ((C['theta2'] + C['theta14'] + C['theta3'] *
(mag - 7.8)) * np.log(dists.rhypo + self.CONSTS['c4'] *
np.exp((mag - 6.) * self.CONSTS['theta9'])) +
(C['theta6'] * dists.rhypo)) + C["theta10"]
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt DC1 vlin b theta1 theta2 theta3 theta4 theta5 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma phi_s2s
pga -0.300000000 865.1 -1.186 4.935754758 -1.319716122 0.156954813 -1.038307042 -0.200134154 -0.002064757 1.0988 -1.42 4.559632568 0.004375202 0.914271114 -0.203185487 -0.694459960 0.9969 -1.00 0.676804137 0.436356919 0.805277096 0.547434071
0.010 -0.300000000 865.1 -1.186 4.935754758 -1.319716122 0.156954813 -1.038307042 -0.200134154 -0.002064757 1.0988 -1.42 4.559632568 0.004375202 0.914271114 -0.203185487 -0.694459960 0.9969 -1.00 0.676804137 0.436356919 0.805277096 0.547434071
0.020 -0.300000000 865.1 -1.186 4.963548267 -1.321501153 0.142973041 -0.925888135 -0.148739101 -0.002188725 1.0988 -1.42 4.654806348 0.004263109 0.934182754 -0.197899904 -0.710342148 0.9969 -1.00 0.683243196 0.430880779 0.807762039 0.554691749
0.050 -0.300000000 1053.5 -1.346 7.358115618 -1.825715240 0.093914961 -0.555849306 0.129797026 -0.000431630 1.2536 -1.65 5.105622455 0.005100764 1.188485184 -0.183201116 -0.737586413 1.1030 -1.18 0.671606746 0.483036109 0.827272328 0.545045472
0.075 -0.300000000 1085.7 -1.471 7.558603177 -1.810050104 0.103239851 -0.561904402 0.151637804 -0.001102941 1.4175 -1.80 4.514166186 0.005820798 1.395007124 -0.174729372 -0.615517435 1.2732 -1.36 0.697383068 0.508098624 0.862848397 0.582340972
0.100 -0.300000000 1032.5 -1.624 7.027657583 -1.633492535 0.088844200 -0.525502325 0.265136034 -0.002397453 1.3997 -1.80 3.827080246 0.004236026 1.560949356 -0.176264079 -0.487079351 1.3042 -1.36 0.722361027 0.504635520 0.881171074 0.616096154
0.150 -0.300000000 877.6 -1.931 6.049355161 -1.335645478 0.073754755 -0.567044631 0.294956394 -0.003942231 1.3582 -1.69 2.880273890 0.002951253 1.824536435 -0.193149712 -0.343522351 1.2600 -1.30 0.741411715 0.475224629 0.880641687 0.629331025
0.200 -0.300000000 748.2 -2.188 4.179750788 -0.885470585 0.065604603 -0.659648456 0.359088006 -0.005638198 1.1648 -1.49 3.257747522 0.002516425 1.976696142 -0.214467130 -0.452888442 1.2230 -1.25 0.759426634 0.429788781 0.872609425 0.637577298
0.250 -0.300000000 654.3 -2.381 3.999581211 -0.821066204 0.055367666 -0.643078011 0.352583884 -0.005484494 0.9940 -1.30 3.545595708 0.000888426 2.152539829 -0.226122818 -0.531334245 1.1600 -1.17 0.743380316 0.401651257 0.844948535 0.606641527
0.300 -0.300000000 587.1 -2.518 3.343521294 -0.678019870 0.070313635 -0.816717363 0.236089761 -0.005490803 0.8821 -1.18 3.711884196 0.001562756 2.179000482 -0.238785185 -0.601073843 1.0500 -1.06 0.750620673 0.389053205 0.845454783 0.609833032
0.400 -0.300000000 503.0 -2.657 3.342528747 -0.674981502 0.071624870 -1.123522692 0.103008688 -0.004346784 0.7046 -0.98 4.125701638 -0.001119565 2.225720730 -0.284536574 -0.702111182 0.8000 -0.78 0.741503989 0.383488689 0.834800419 0.589961066
0.500 -0.300000000 456.6 -2.669 3.714706072 -0.770820923 0.073623537 -1.330962172 -0.019664088 -0.003028097 0.5799 -0.82 4.507163580 -0.000434645 2.265272475 -0.318116722 -0.800834677 0.6620 -0.62 0.688862082 0.384159164 0.788739014 0.513251109
0.600 -0.300000000 430.3 -2.599 4.425108150 -0.939459680 0.062188731 -1.569443919 -0.014606735 -0.001675340 0.5021 -0.70 5.255072487 -0.000097416 2.200898990 -0.365330018 -0.966147926 0.5800 -0.50 0.665479640 0.394271020 0.773506812 0.486626176
0.750 -0.300000000 410.5 -2.401 4.372165283 -0.933761671 0.053771754 -1.730788918 -0.031408137 -0.001524349 0.3687 -0.54 5.074522171 -0.001350443 1.918279398 -0.401223910 -0.937019824 0.4800 -0.34 0.637244299 0.414109647 0.759978352 0.443006934
1.000 -0.300000000 400.0 -1.955 4.021211151 -0.924917589 0.054326150 -1.908027335 -0.138131804 -0.001101517 0.1746 -0.34 5.211831136 -0.002283504 1.509910061 -0.433435346 -0.964846571 0.3300 -0.14 0.611337571 0.442015583 0.754394725 0.421636418
1.500 -0.300000000 400.0 -1.025 3.946972058 -1.002244695 0.049918773 -2.307833569 -0.412376757 -0.000261255 -0.0820 -0.05 5.561359279 -0.000996882 0.656237153 -0.502990059 -1.057548381 0.3100 0.00 0.617840247 0.436708751 0.756598377 0.448028967
2.000 -0.300000000 400.0 -0.299 3.763370770 -1.048406811 0.049945027 -2.218316295 -0.488347011 -0.000156404 -0.2821 0.12 5.310311721 -0.000289011 -0.148288073 -0.501824964 -1.007661553 0.3000 0.00 0.586452050 0.429957558 0.727179144 0.424207890
2.500 -0.300000000 400.0 0.000 3.279573476 -0.991842986 0.095212751 -2.496506471 -0.770828569 -0.000738153 -0.4108 0.25 4.764778613 -0.001039535 -0.459995635 -0.517128864 -0.886704977 0.3000 0.00 0.567864698 0.442678828 0.720024208 0.416230786
3.000 -0.300000000 400.0 0.000 3.407135085 -1.079312405 0.092359656 -2.425045547 -0.883889211 -0.000357658 -0.4466 0.30 4.800502846 -0.000395577 -0.450645670 -0.514638813 -0.901051441 0.3000 0.00 0.559253514 0.420099114 0.699462478 0.418794658
4.000 -0.300000000 400.0 0.000 2.789669400 -1.072279505 0.148258197 -2.792416051 -1.282315047 0.000409730 -0.4344 0.30 5.011985606 -0.000308830 -0.512937685 -0.529022902 -0.939796651 0.3000 0.00 0.569097474 0.408117852 0.700308586 0.435934346
5.000 -0.300000000 400.0 0.000 2.700791140 -1.202536653 0.172625283 -2.741020801 -1.141773134 0.001833647 -0.4368 0.30 5.457710792 0.000255165 -0.503538042 -0.504799612 -1.025705989 0.3000 0.00 0.558540211 0.387890193 0.680019095 0.418174855
6.000 -0.300000000 400.0 0.000 2.630174552 -1.303101604 0.127044195 -1.863112205 -0.727779859 0.002185845 -0.4586 0.30 5.826483564 0.001637500 -0.497674025 -0.423978007 -1.110103433 0.3000 0.00 0.502062640 0.394614799 0.638582598 0.346222778
7.500 -0.300000000 400.0 0.000 2.520418211 -1.399368154 0.084904399 -0.930694380 -0.212014425 0.002325451 -0.4433 0.30 6.332273436 0.001046880 -0.481585300 -0.334701563 -1.195826518 0.3000 0.00 0.482570602 0.373377912 0.610151990 0.321745366
10.00 -0.300000000 400.0 0.000 3.266979586 -1.707902316 0.068210457 -0.967817098 0.253077379 0.004736644 -0.4828 0.30 7.382937906 0.000738462 -0.423369635 -0.347713953 -1.409670235 0.3000 0.00 0.466924628 0.376696614 0.599932452 0.300789811
""")