Source code for openquake.hazardlib.gsim.zalachoris_rathje_2019

# -*- 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.
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# 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:'ZalachorisRathje2019'
"""
import numpy as np
from openquake.hazardlib.gsim.base import CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
from openquake.hazardlib.gsim.boore_2014 import BooreEtAl2014


[docs]class ZalachorisRathje2019(BooreEtAl2014): """ Implements the Induced Seismicity GMPE of Zalachoris & Rathje (2019) for Texas, Oklahoma and Kansas. Ground Motion Model for Small-to-Moderate Earthquakes in Texas, Oklahoma, and Kansas. Earthquake Spectra. Data: 4528 observations from 376 EQs of Mw 3.0-5.8 in Texas, Oklahoma and Kansas, distances between 4 and 500km. PGA, PGV, SA(0-10s) version: Apr 28, 2020. Verified with margin 1% """ #: The GMPE is derived from induced earthquakes DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.INDUCED #: Supported intensity measure types are spectral acceleration, #: peak ground velocity and peak ground acceleration DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA} #: Supported intensity measure component is orientation-independent #: measure :attr:`~openquake.hazardlib.const.IMC.RotD50` DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50 #: 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 REQUIRES_SITES_PARAMETERS = {'vs30'} #: Required rupture parameters are magnitude, and rake. REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'} #: Required distance measure is Rjb REQUIRES_DISTANCES = {'rjb', 'rhypo'} #: GMPE not tested against independent implementation so raise #: not verified warning non_verified = False
[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_BSSA14[imt] C_PGA = self.COEFFS_BSSA14[PGA()] Cadj = self.COEFFS_HA15[imt] C_ZR19 = self.COEFFS_ZR19[imt] imt_per = 0 if imt.name == 'PGV' else imt.period pga_rock = self._get_pga_on_rock(C_PGA, rup, dists) mean_BSSA14 = ( self._get_magnitude_scaling_term(C, rup) + self._get_path_scaling(C, dists, rup.mag) + self._get_site_scaling(C, pga_rock, sites, imt_per, dists.rjb)) FZR19 = (self._get_ZR19_magnitude_term(C_ZR19, rup.mag) + self._get_ZR19_distance_term(C_ZR19, dists.rhypo) + self._get_ZR19_site_term(C_ZR19, sites)) # add HA15, all in ln units mean = mean_BSSA14 + self.get_FENA(Cadj, rup, dists, imt) # add ZR19, all in ln units mean = mean + FZR19 stddevs = self._get_stddevs(C_ZR19, len(dists.rjb), stddev_types) return mean, stddevs
#: terms for HA15 def _get_C2_term(self, Cadj, rjb): """ distance term, C2, from HA15 """ F2 = Cadj["C2"] * rjb return F2 def _get_C3_term(self, Cadj, rjb): """ anelastic attenuation, C3, from HA15 """ F3 = Cadj["C3"] * np.maximum(0, np.log10(np.minimum(rjb, 150)/50)) return F3
[docs] def get_FENA(self, Cadj, rup, dists, imt): """ See :meth:`superclass method <.base.GroundShakingIntensityModel.get_mean_and_stddevs>` for spec of input and result values. """ imean = (Cadj["C1"] + self._get_C2_term(Cadj, dists.rjb) + self._get_C3_term(Cadj, dists.rjb)) # Convert from log10 to ln if imt.name in "SA PGA": FENA = np.log(10.0 ** imean) else: FENA = np.log(10.0 ** imean) return FENA
def _get_stddevs(self, C_ZR19, num_sites, stddev_types): """ Return standard deviations, in ln units [g] """ # the units for PGV are not clearly stated in the paper, # assumed here cm/s stddevs = [] for stddev_type in stddev_types: assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES if stddev_type == const.StdDev.TOTAL: stddevs.append(C_ZR19["sigma"] + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTER_EVENT: stddevs.append(C_ZR19["tau"] + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTRA_EVENT: stddevs.append(C_ZR19["phi"] + np.zeros(num_sites)) return stddevs #: terms for ZR19 def _get_ZR19_magnitude_term(self, C_ZR19, mag): """ Returns the magnitude scaling term """ Mb_ = C_ZR19["Mb"] if mag < Mb_: FM = C_ZR19["b0"] + C_ZR19["Cadj"] elif mag > Mb_ and mag < 5.8: FM = C_ZR19["b0"] + C_ZR19["b1"] * (mag - Mb_) + C_ZR19["Cadj"] else: FM = C_ZR19["b0"] + C_ZR19["b1"] * (5.8 - Mb_) + C_ZR19["Cadj"] return FM def _get_ZR19_distance_term(self, C_ZR19, rhypo): """ Returns the distance scaling term """ Rb_ = C_ZR19["Rb"] FR = np.zeros_like(rhypo) FR[(rhypo < Rb_) & (rhypo >= 4)] = (C_ZR19["a"] * np.log(rhypo[(rhypo < Rb_) & (rhypo >= 4)]/Rb_)) FR[rhypo < 4] = C_ZR19["a"] * np.log(4/Rb_) return FR def _get_ZR19_site_term(self, C_ZR19, sites): """ Returns the amplification factor, based on vs30 """ Vc_ = C_ZR19["Vc"] FS = np.zeros_like(sites.vs30) FS[sites.vs30 < Vc_] = (C_ZR19["c"] * np.log(sites.vs30[sites.vs30 < Vc_]/Vc_)) return FS #: coeffs for BSSA14 #: fewer decimals used for BSSA14 by Zalachoris compared to the original #: values COEFFS_BSSA14 = CoeffsTable(sa_damping=5, table="""\ IMT e0 e1 e2 e3 e4 e5 e6 Mh c1 c2 c3 h Dc3 c Vc f4 f5 f6 f7 R1 R2 DfR DfV f1 f2 t1 t2 pgv 5.0400000 5.0800000 4.8500000 5.0300000 1.0700000 -0.1540000 0.2250000 6.2000000 -1.2400000 0.1490000 -0.0034400 5.3000000 0.0000000 -0.8400000 1300.0000000 -0.1000000 -0.0084400 -9.9000000 -9.9000000 105.0000000 272.0000000 0.0820000 0.0800000 0.6440000 0.5520000 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130.7100000 238.1300000 0.0590000 0.0000000 0.5090000 0.6220000 0.5030000 0.2650000 9.000 -2.8800000 -2.7700000 -3.1700000 -2.9800000 1.9600000 -0.1340000 1.0500000 6.2000000 -1.3000000 0.1430000 0.0000000 9.6600000 0.0000000 -0.7020000 768.0700000 -0.0001080 -0.0013700 1.2500000 0.7540000 130.5000000 229.5600000 0.0600000 0.0000000 0.5090000 0.6130000 0.4980000 0.2520000 9.500 -2.9800000 -2.8600000 -3.2800000 -3.0800000 1.9200000 -0.1440000 1.0600000 6.2000000 -1.3100000 0.1480000 0.0000000 9.6600000 0.0000000 -0.6790000 771.5500000 -0.0000600 -0.0013600 1.2200000 0.7290000 130.2600000 220.0200000 0.0600000 0.0000000 0.5090000 0.6040000 0.4920000 0.2390000 10.000 -3.0700000 -2.9500000 -3.3800000 -3.1700000 1.8800000 -0.1510000 1.0700000 6.2000000 -1.3300000 0.1520000 0.0000000 9.6600000 0.0000000 -0.6560000 775.0000000 0.0000000 -0.0013600 1.1800000 0.7030000 130.0000000 210.0000000 0.0600000 0.0000000 0.5100000 0.6040000 0.4870000 0.2390000 """) CONSTS = { "Mref": 4.5, "Rref": 1.0, "Vref": 760.0, "f1": 0.0, "f3": 0.1, "v1": 225.0, "v2": 300.0} #: coeffs for HA15 COEFFS_HA15 = CoeffsTable(sa_damping=5, table=""" IMT C1 C2 C3 sigma tau phi pgv 0.166 0.0007 0.73 0.33 0.28 0.18 pga 0.384 0.0017 0.63 0.41 0.30 0.27 0.05 0.472 0.0022 0.44 0.47 0.36 0.32 0.063 0.439 0.0023 0.52 0.45 0.33 0.30 0.079 0.37 0.0024 0.61 0.42 0.32 0.28 0.1 0.264 0.0023 0.71 0.40 0.31 0.25 0.126 0.158 0.0022 0.81 0.38 0.30 0.22 0.158 0.074 0.0021 0.88 0.36 0.30 0.20 0.199 0.014 0.0020 0.89 0.35 0.30 0.18 0.251 -0.016 0.0018 0.86 0.34 0.29 0.17 0.316 -0.036 0.0016 0.80 0.33 0.29 0.15 0.398 -0.053 0.0015 0.71 0.31 0.28 0.14 0.5 -0.068 0.0014 0.63 0.30 0.27 0.14 0.633 -0.077 0.0013 0.59 0.29 0.26 0.13 0.794 -0.067 0.0011 0.57 0.28 0.25 0.12 1. -0.043 0.0009 0.54 0.28 0.25 0.13 1.266 -0.009 0.0006 0.50 0.28 0.25 0.14 1.587 0.02 0.0005 0.48 0.29 0.24 0.15 2. 0.041 0.0004 0.44 0.28 0.24 0.15 2.5 0.061 0.0004 0.36 0.28 0.23 0.16 3.125 0.067 0.0005 0.27 0.28 0.23 0.16 4. 0.052 0.0006 0.21 0.28 0.23 0.17 5. 0.025 0.0006 0.22 0.29 0.22 0.18 6.25 0.010 0.0006 0.27 0.29 0.22 0.20 7.692 0.029 0.0006 0.27 0.28 0.21 0.19 10. 0.065 0.0006 0.22 0.25 0.21 0.14 """) # coeffs for ZR19 (more IMT values compared to the published paper) COEFFS_ZR19 = CoeffsTable(sa_damping=5, table=""" IMT a Rb Mb b0 b1 c Vc Cadj tau phi sigma pgv -0.5339 13.94 2.925 0.2018 -0.2865 0.8682 515.96 0.1751 0.2716 0.513 0.5804 pga -0.6347 16.73 3.393 0.0908 -0.3217 0.4779 638.08 -0.2208 0.2959 0.5443 0.6195 0.05 -0.7112 18.2 3.4 0.0854 -0.3108 0.1668 945.8 -0.2267 0.3147 0.5785 0.6586 0.055 -0.6822 18.43 3.4 0.0867 -0.3146 0.2176 886.9 -0.2007 0.3156 0.5813 0.6614 0.06 -0.6581 18.51 3.4 0.0876 -0.3167 0.2657 831.6 -0.1727 0.3146 0.5833 0.6627 0.065 -0.6385 18.45 3.4 0.088 -0.3166 0.3088 783 -0.1414 0.3114 0.5844 0.6622 0.07 -0.6164 18.45 3.4 0.0879 -0.3148 0.346 742.7 -0.1067 0.3072 0.5847 0.6605 0.075 -0.5864 18.69 3.4 0.0872 -0.312 0.3777 710.8 -0.0697 0.3035 0.5843 0.6584 0.08 -0.5478 19.21 3.4 0.086 -0.3088 0.4052 686.4 -0.0321 0.3011 0.5832 0.6564 0.085 -0.507 19.81 3.4 0.0852 -0.3056 0.4306 667.5 0.0052 0.3 0.5819 0.6546 0.09 -0.4712 20.28 3.39 0.086 -0.3029 0.4561 652 0.0423 0.2996 0.5809 0.6536 0.095 -0.4467 20.42 3.37 0.0905 -0.3017 0.4838 637.8 0.0811 0.2995 0.5807 0.6534 0.1 -0.4351 20.16 3.34 0.0986 -0.3019 0.5151 623.8 0.1222 0.2993 0.5817 0.6541 0.133 -0.4354 19.48 3.3 0.1077 -0.3031 0.5509 609.3 0.1653 0.2986 0.5838 0.6557 0.15 -0.4418 18.45 3.28 0.1135 -0.3032 0.5854 593.2 0.2079 0.2971 0.5869 0.6578 0.2 -0.4515 17.13 3.27 0.1138 -0.3009 0.6158 563 0.248 0.2944 0.5897 0.6591 0.25 -0.4627 15.69 3.29 0.1091 -0.2976 0.638 542.5 0.2818 0.2907 0.5894 0.6572 0.3 -0.4789 14.27 3.36 0.0998 -0.3011 0.6878 527.8 0.3069 0.2865 0.5839 0.6504 0.35 -0.5019 13.01 3.5 0.0848 -0.3225 0.7734 517 0.3249 0.2821 0.5729 0.6386 0.4 -0.5353 11.92 3.73 0.0643 -0.3655 0.8714 510.8 0.3413 0.2773 0.5588 0.6239 0.45 -0.581 10.97 4 0.0421 -0.4214 0.9505 510.9 0.3617 0.2714 0.5447 0.6085 0.5 -0.6371 10.15 4.21 0.0244 -0.4728 0.9996 515 0.3861 0.264 0.5323 0.5942 0.55 -0.6923 9.51 4.35 0.0142 -0.5134 1.0257 519.9 0.4107 0.2554 0.5224 0.5815 0.6 -0.733 9.09 4.42 0.0104 -0.5482 1.0382 523.7 0.4307 0.2467 0.5148 0.5709 0.65 -0.7523 8.87 4.47 0.0094 -0.5887 1.0429 526.3 0.4448 0.2389 0.5092 0.5625 0.667 -0.7561 8.76 4.52 0.0091 -0.6355 1.0417 528.5 0.4542 0.2325 0.5051 0.556 0.7 -0.7524 8.7 4.58 0.0087 -0.6825 1.0391 530.4 0.4616 0.2271 0.502 0.551 0.75 -0.7452 8.64 4.62 0.0084 -0.7204 1.0398 531.8 0.4694 0.2226 0.4993 0.5466 0.8 -0.7325 8.6 4.64 0.0083 -0.7468 1.0465 532.6 0.4785 0.2188 0.4963 0.5423 0.85 -0.7131 8.58 4.66 0.0082 -0.7624 1.0576 533.2 0.4888 0.2161 0.4925 0.5379 0.9 -0.687 8.62 4.67 0.008 -0.7724 1.0696 534 0.499 0.2153 0.4879 0.5333 0.95 -0.6509 8.76 4.71 0.0076 -0.7704 1.081 534.9 0.5076 0.2176 0.4825 0.5293 1 -0.603 9.02 4.69 0.0078 -0.7923 1.0909 536 0.5118 0.2242 0.4759 0.526 1.5 -0.547 9.35 4.78 0.0059 -0.7244 1.0997 536.5 0.5093 0.2368 0.4677 0.5243 2 -0.4981 9.59 4.89 0.0056 -0.5086 1.105 535.8 0.499 0.2548 0.459 0.525 2.5 -0.4738 9.63 5.8 0 0 1.1049 533.5 0.4836 0.2754 0.4525 0.5297 3 -0.4847 9.46 5.8 0 0 1.0961 530.3 0.4659 0.2926 0.4505 0.5372 3.5 -0.5269 9.21 5.8 0 0 1.077 527.4 0.4487 0.3012 0.4535 0.5444 4.0 -0.5844 9.06 5.8 0 0 1.0462 525.6 0.4316 0.2989 0.4589 0.5476 4.4 -0.6387 9.14 5.8 0 0 1.0049 525 0.4151 0.2879 0.4634 0.5455 5 -0.6766 9.45 5.8 0 0 0.9561 525.1 0.399 0.2726 0.4652 0.5392 5.5 -0.6954 9.89 4.91 -0.0003 -0.0711 0.9036 525.4 0.3848 0.2573 0.4642 0.5308 6 -0.6983 10.36 4.51 0.0042 -0.1059 0.8507 525.5 0.3732 0.2449 0.4614 0.5224 6.5 -0.693 10.73 4.16 0.0151 -0.1418 0.7992 525.3 0.3653 0.2363 0.4582 0.5155 7 -0.6839 10.95 3.86 0.0312 -0.1693 0.7499 525.1 0.3619 0.2311 0.4556 0.5108 7.5 -0.676 11.03 3.63 0.0505 -0.1954 0.7043 524.8 0.3631 0.2284 0.4542 0.5084 8 -0.6704 11.03 3.48 0.0684 -0.2226 0.6642 524.7 0.3681 0.227 0.4543 0.5078 8.5 -0.6711 11.03 3.41 0.0846 -0.2569 0.6311 524.6 0.3755 0.226 0.4554 0.5084 9 -0.6787 11.09 3.39 0.0982 -0.2937 0.6043 524.6 0.3831 0.2247 0.4572 0.5094 9.5 -0.6941 11.22 3.39 0.1105 -0.3295 0.5816 524.6 0.3897 0.2227 0.4594 0.5106 10 -0.7138 11.39 3.4 0.1218 -0.3627 0.5605 524.5 0.3951 0.2201 0.4618 0.5116 """)