# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2022 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:`HassaniAtkinson2018`
"""
import re
import pathlib
import numpy as np
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib.gsim.boore_2014 import BooreEtAl2014
from openquake.hazardlib.gsim.yenier_atkinson_2015 import (
get_fs_SeyhanStewart2014)
TFP = pathlib.Path(__file__).parent.absolute()
def _get_pseudo_depth(mag):
""" Pseudo depth as defined in eq. 17 """
return 10**(-0.405+0.235*mag)
def _get_geometrical_attenuation(rrup, r):
"""
Compute the geometrical attenuation of Fourier amplitudes. See equation
15 at page 5 of ha18.
"""
rt = 50.0
b1 = -1.3
b2 = -0.5
z = np.zeros_like(rrup)
# Direct wave spreading
idx = r <= rt
z[idx] = r[idx]**b1
# Surface-wave spreading
idx = r > rt
z[idx] = rt**b1 * (r[idx]/rt)**b2
return z
def _geometrical_spreading(C, rrup, mag):
""" Geometrical spreading term as per eq. 15 """
h = _get_pseudo_depth(mag)
r = (rrup**2 + h**2)**0.5
z = _get_geometrical_attenuation(rrup, r)
rref = (1 + h**2)**0.5
return np.log10(z) + (C['b3'] + C['b4'] * mag) * np.log10(r/rref)
def _source_scaling(C, mag, d_sigma):
""" Source scaling as per eq. 2 """
return _magnitude_scaling(C, mag) + _stress_scaling(C, d_sigma, mag)
def _magnitude_scaling(C, mag):
""" Magnitude scaling as defined in eq. 3 """
fm = np.zeros_like(mag)
dff = (mag - C['Mh'])
idx = mag <= C['Mh']
fm[idx] = C['e0'] + C['e1'] * dff[idx] + C['e2'] * dff[idx]**2
idx = mag > C['Mh']
fm[idx] = C['e0'] + C['e3'] * dff[idx]
return fm
def _stress_scaling(C, d_sigma, mag):
""" Stress scaling as defined in eq. 3 """
# e_{\Delta,\sigma_1}
keys = [f'g1_{i}' for i in range(0, 5)]
e_d_sigma_1 = sum(C[k]*mag**(i) for i, k in enumerate(keys))
# e_{\Delta,\sigma_2}
keys = [f'g2_{i}' for i in range(0, 5)]
e_d_sigma_2 = sum(C[k]*mag**(i) for i, k in enumerate(keys))
# e_{\Delta,\sigma_0}
e_d_sigma_0 = -2 * e_d_sigma_1 - 4 * e_d_sigma_2
# scaling factor
l_d_sigma = np.log10(d_sigma)
return e_d_sigma_0 + e_d_sigma_1 * l_d_sigma + e_d_sigma_2 * l_d_sigma**2
def _kappa_scaling(C, kappa0, d_sigma, mag):
""" Stress scaling as defined in eq. 3 """
ld = np.log10(d_sigma)
lm = np.log10(mag)
lk = np.log10(kappa0)
p_1_0 = C['d1_0_0'] + C['d1_0_1'] * ld + C['d1_0_2'] * ld**2
p_1_1 = C['d1_1_0'] + C['d1_1_1'] * ld + C['d1_1_2'] * ld**2
p_1_2 = C['d1_2_0'] + C['d1_2_1'] * ld + C['d1_2_2'] * ld**2
p_1_3 = C['d1_3_0'] + C['d1_3_1'] * ld + C['d1_3_2'] * ld**2
e_k_1 = (p_1_0 + p_1_1 * lm + p_1_2 * lm**2 + p_1_3 * lm**3)
p_2_0 = C['d2_0_0'] + C['d2_0_1'] * ld + C['d2_0_2'] * ld**2
p_2_1 = C['d2_1_0'] + C['d2_1_1'] * ld + C['d2_1_2'] * ld**2
p_2_2 = C['d2_2_0'] + C['d2_2_1'] * ld + C['d2_2_2'] * ld**2
p_2_3 = C['d2_3_0'] + C['d2_3_1'] * ld + C['d2_3_2'] * ld**2
e_k_2 = (p_2_0 + p_2_1 * lm + p_2_2 * lm**2 + p_2_3 * lm**3)
p_3_0 = C['d3_0_0'] + C['d3_0_1'] * ld + C['d3_0_2'] * ld**2
p_3_1 = C['d3_1_0'] + C['d3_1_1'] * ld + C['d3_1_2'] * ld**2
p_3_2 = C['d3_2_0'] + C['d3_2_1'] * ld + C['d3_2_2'] * ld**2
p_3_3 = C['d3_3_0'] + C['d3_3_1'] * ld + C['d3_3_2'] * ld**2
e_k_3 = (p_3_0 + p_3_1 * lm + p_3_2 * lm**2 + p_3_3 * lm**3)
p_4_0 = C['d4_0_0'] + C['d4_0_1'] * ld + C['d4_0_2'] * ld**2
p_4_1 = C['d4_1_0'] + C['d4_1_1'] * ld + C['d4_1_2'] * ld**2
p_4_2 = C['d4_2_0'] + C['d4_2_1'] * ld + C['d4_2_2'] * ld**2
p_4_3 = C['d4_3_0'] + C['d4_3_1'] * ld + C['d4_3_2'] * ld**2
e_k_4 = (p_4_0 + p_4_1 * lm + p_4_2 * lm**2 + p_4_3 * lm**3)
e_k_0 = 3 * e_k_1 - 9 * e_k_2 + 27 * e_k_3 - 81 * e_k_4
out = e_k_0 + e_k_1 * lk + e_k_2 * lk**2 + e_k_3 * lk**3 + e_k_4 * lk**4
return out
def _anelastic_attenuation(gamma, rrup):
""" Anelastic attenuation term """
return gamma * rrup
[docs]def get_gm_rock(C, ctx, kappa0, d_sigma, CAE):
""" Compute ground-motion on bedrock """
gm = (_source_scaling(C, ctx.mag, d_sigma) +
_kappa_scaling(C, kappa0, d_sigma, ctx.mag) +
_geometrical_spreading(C, ctx.rrup, ctx.mag)
)
if CAE is not None:
gm += _anelastic_attenuation(CAE, ctx.rrup)
return gm
[docs]class HassaniAtkinson2018(GMPE):
"""
Implements the model of Hassani and Atkinson (2018) as described in the
BSSA paper titled "Adjustable Generic Ground-Motion Prediction Equation
Based on Equivalent Point-Source Simulations: Accounting for Kappa
Effects" (doi: 10.1785/0120170333).
:param d_sigma:
Stress frop [bar]
:param kappa0:
Kappa_0 [s]
:param gamma_fle:
The name of the file containing the anelastic attenuation term.
"""
#: Supported tectonic region type is active shallow crust, see title!
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 tables 4
#: pages 1036
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is orientation-independent
#: average horizontal :attr:`~openquake.hazardlib.const.IMC.RotD50`,
#: see page 1025.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation types are inter-event, intra-event
#: and total, see paragraph "Equations for standard deviations", page
#: 1046.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
#: Required site parameter is Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and hypocenter depth
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'}
#: Required distance measures is Rrup
REQUIRES_DISTANCES = {'rrup'}
def __init__(self, d_sigma, kappa0, gamma_fle=None, **kwargs):
super().__init__(d_sigma=d_sigma, kappa0=kappa0, gamma_fle=gamma_fle,
**kwargs)
self.d_sigma = d_sigma
self.kappa0 = kappa0
# Read the file and create the coefficient table for the anelastic
# attenuation term
if gamma_fle is not None:
with open(gamma_fle, 'rb') as fle:
data = fle.read().decode('utf-8')
self.CAE = CoeffsTable(sa_damping=5, table=data)
else:
self.CAE = None
# Boore et al. coefficients, used in the site model.
self.BEA14 = BooreEtAl2014.COEFFS
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
""" Compute mean """
# Compute PGA on rock. This is used for computing the soil term.
imt = PGA()
C = self.COEFFS[imt]
gamma = None
if self.CAE is not None:
gamma = self.CAE[imt]['gamma']
pga_rock = np.exp(get_gm_rock(C, ctx, self.kappa0, self.d_sigma, gamma))
# Compute ground-motion on soil.
for m, imt in enumerate(imts):
# Get the mean
C = self.COEFFS[imt]
if self.CAE is not None:
gamma = self.CAE[imt]['gamma']
mean[m] = get_gm_rock(C, ctx, self.kappa0, self.d_sigma, gamma)
# Site term
TMP = self.BEA14[imt]
mean[m] += get_fs_SeyhanStewart2014(TMP, imt, pga_rock, ctx.vs30)
# To natural logarithm and [g]
mean[m] /= np.log10(np.exp(1))
if re.search('SA|PGA', str(imt)):
mean[m] = np.log(np.exp(mean[m]) / 980.665)
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT Mh e0 e1 e2 e3 b3 b4 g1_0 g1_1 g1_2 g1_3 g1_4 g2_0 g2_1 g2_2 g2_3 g2_4 d1_0_0 d1_0_1 d1_0_2 d1_1_0 d1_1_1 d1_1_2 d1_2_0 d1_2_1 d1_2_2 d1_3_0 d1_3_1 d1_3_2 d2_0_0 d2_0_1 d2_0_2 d2_1_0 d2_1_1 d2_1_2 d2_2_0 d2_2_1 d2_2_2 d2_3_0 d2_3_1 d2_3_2 d3_0_0 d3_0_1 d3_0_2 d3_1_0 d3_1_1 d3_1_2 d3_2_0 d3_2_1 d3_2_2 d3_3_0 d3_3_1 d3_3_2 d4_0_0 d4_0_1 d4_0_2 d4_1_0 d4_1_1 d4_1_2 d4_2_0 d4_2_1 d4_2_2 d4_3_0 d4_3_1 d4_3_2
PGV 8.8 3.3020832702 0.4389691965 -0.0167235139 0.4146350561 -0.4414468351 0.0394123571 0.4442506135 0.0569722379 0.0036437698 -0.0040458203 0.0003530051 -0.0942034933 0.0533434608 -0.0141633591 0.0019185922 -0.0001002408 -40.8261642212 40.1130392571 -5.1021285604 155.2523126945 -182.3686804039 27.0333494027 -196.6717542861 258.2107952699 -42.3653301122 82.3574790678 -116.4544082139 20.5376093143 -31.5589270744 36.8747740244 -5.7395492329 125.2777710877 -161.3065178224 27.8740449631 -163.4368685527 223.2664465831 -41.3918330682 69.9031574762 -99.2526602356 19.3502214642 -10.376280011 13.0514009303 -2.256508542 41.8677381569 -56.0550276459 10.5303317116 -55.1925939231 76.6960142436 -15.2384616501 23.7760701622 -33.8327130594 6.9969744833 -1.2294334314 1.6040511763 -0.296017448 4.9934816807 -6.816710646 1.3502018879 -6.6090820328 9.2624147354 -1.9246297215 2.8547014114 -4.0664231392 0.87437342
PGA 7.4 4.3737580679 0.330007551 -0.0093950747 0.3015333317 -0.456482013 0.0382499085 0.7096633248 -0.0383918613 0.0130808215 -0.0011379644 0.000023783 -0.0323847716 0.0190432118 -0.0045166161 0.0003745764 -0.000009338 -51.0987175177 32.5787964105 -0.6027113079 193.3769389098 -154.5366560363 8.9701410121 -246.3770135374 224.3093400193 -19.0560387445 103.8674068929 -102.8628006083 10.7674035794 -44.562063396 38.7082792804 -3.9223740867 176.7251880414 -170.7934709018 21.0155290004 -230.9326523974 237.8661600889 -33.0837191768 99.1364594808 -106.2748859661 16.0786467012 -16.4224378175 15.8479312655 -2.16864161 65.9977373822 -67.9730386386 10.3855144404 -87.0701819028 93.033434856 -15.3297368832 37.6386624177 -41.09486034 7.1483955895 -2.1340416665 2.1508934311 -0.3370120058 8.6187576308 -9.0895962533 1.542770572 -11.4166836197 12.3244901435 -2.2132358804 4.9500459039 -5.4101159109 1.0122830622
0.01 7.15 4.6451420678 0.3440412764 -0.0081551718 0.3056467387 -0.432123999 0.0352795984 1.4724155428 -0.541245476 0.1337792132 -0.0136064606 0.0004916184 -0.2222773523 0.1462761965 -0.0353526956 0.0035796845 -0.0001301312 -41.0107982823 20.9848341026 4.3329321558 143.7259148271 -112.5739642323 -8.7987572623 -185.5027172857 174.2625858466 2.1456980236 78.7931994598 -83.1287030049 2.3805087274 -35.565129626 27.7977763589 0.5050803946 130.2847004071 -131.1409418798 4.976748558 -173.6461342678 190.4355184412 -13.8639022128 75.4765505105 -87.5347798957 8.4534629675 -13.145746842 11.6016707688 -0.5525871582 48.0682184483 -52.4511024164 4.4788312726 -64.7659436448 74.3870319334 -8.2074496141 28.3889668495 -33.7045319011 4.3105214888 -1.7158836168 1.5762228316 -0.1320599394 6.2060720835 -6.9773140963 0.7864628056 -8.3878736064 9.7767580547 -1.2952752002 3.688341554 -4.3974049937 0.6448738171
0.0125892541 7.4 4.6977535858 0.3384826092 -0.0082478225 0.3049000591 -0.4334631181 0.0359538028 1.5542238909 -0.5616075335 0.1313999067 -0.0127660208 0.0004433715 -0.2647504161 0.1652033142 -0.0379324038 0.0036832174 -0.000129329 -36.8285222558 19.5692518096 6.1259093932 133.7996869212 -108.9284407922 -14.5794277424 -175.1080288423 171.4375896683 8.4533260504 74.8445969118 -82.5435219825 0.0547346719 -31.1722799717 25.351333991 2.5316521888 118.7523252911 -123.338463955 -1.8054418993 -161.1733562416 182.1538053597 -6.1941164726 70.6651512206 -84.6018148804 5.5292344598 -11.2811780794 10.2045187952 0.3562641019 42.7543021769 -47.6413957823 1.3509704199 -58.8762358324 68.8542430537 -4.5789001237 26.0881979323 -31.5741788193 2.8951491463 -1.4497966017 1.3380674799 0.0036611068 5.4031719146 -6.1290931231 0.3107172861 -7.4856343948 8.7688733438 -0.7343493645 3.3334717308 -3.9973330647 0.4229556198
0.0158489319 7.5 4.6991251896 0.3360164017 -0.0089372225 0.306043905 -0.428188954 0.0351373029 1.7146520875 -0.6426995059 0.1451525465 -0.0136492035 0.0004586999 -0.3499803018 0.2131200216 -0.0476059211 0.0045158963 -0.0001551993 -33.8430866217 21.852771734 6.4156265557 132.5335445804 -119.6575221006 -14.2894251369 -178.4664241493 186.8869254686 6.8355344807 77.8849827279 -89.6021754288 1.1066840508 -28.5771731971 27.5478380522 3.0405208004 118.5562094533 -134.3070025864 -2.2410582856 -166.1464288973 198.5478126675 -7.0358607721 74.4547367079 -92.2926779649 6.3136158245 -10.4091288278 11.0983245447 0.62375221 43.1805091637 -52.2978627131 0.9744495819 -61.6114017509 75.9878984805 -4.7119117615 27.9468069672 -34.9786896007 3.1445023355 -1.3504612482 1.4651275983 0.0464012634 5.5224345322 -6.8079421643 0.2406126264 -7.9489981997 9.8237757891 -0.7349478952 3.6283937608 -4.5057461333 0.4520391597
0.0199526231 7.8 4.7556082962 0.3269384891 -0.010314344 0.3033860929 -0.4209048867 0.0343552884 1.9121433951 -0.751222247 0.1674140149 -0.0156735083 0.0005277542 -0.4478882645 0.2694635191 -0.0596360655 0.0056440975 -0.0001944388 -42.8277325797 41.1075882423 1.7670056326 175.9994852055 -195.1960146988 4.9952066498 -233.844386437 282.7603313271 -18.6047750739 100.4408355511 -129.2075056017 11.9279871025 -36.3622887447 45.1839849821 -0.9145728042 157.3334082243 -204.0219744559 14.5248123577 -216.2043782902 287.5455973403 -29.4581795161 95.0157015348 -129.2263383639 15.9404511618 -13.0410584594 17.5269872765 -0.7135972297 56.7766408002 -77.8755312445 6.7787823282 -79.3772814829 108.7930409071 -12.5851432285 35.2896380599 -48.6391063011 6.556052291 -1.6597774076 2.2800634076 -0.1116247994 7.17850873 -10.0680160362 0.9427128873 -10.1378354947 14.0210536456 -1.7002327916 4.5380100974 -6.2582653091 0.8738869272
0.0251188643 8.95 5.065654626 0.2963765967 -0.0119281989 0.2969373901 -0.4098087961 0.0331186139 2.1539138139 -0.8927591847 0.1982305382 -0.0186268734 0.0006330414 -0.5719792694 0.3427423146 -0.0756752153 0.007182719 -0.000249038 -48.4797219107 55.7785000258 -4.0133993949 203.1744408844 -245.4657543936 25.9385381009 -266.7082108364 340.0759448663 -43.5920265039 113.9342895071 -151.0624029213 21.7937101574 -42.8382826139 60.8412193483 -6.4582542464 188.7203161972 -259.2502197726 35.0071150867 -255.7087778747 352.3306699851 -54.3115830467 111.6496865619 -154.5931007171 25.8987670888 -15.8365807353 23.9817850436 -2.8287849497 70.4391524705 -101.0599279693 14.7120663427 -96.9893067286 136.4572750195 -22.3325442459 42.8120570944 -59.6381792273 10.5030952707 -2.0648079922 3.1842048796 -0.391808802 9.1648695756 -13.3553052991 2.0057140981 -12.7365278013 17.9875948249 -3.0185636914 5.6573769687 -7.8508252878 1.411862961
0.0316227766 8.25 4.8042229815 0.3066648064 -0.013746637 0.3078399835 -0.4074900854 0.0326778324 2.2779443538 -0.9647994178 0.2136928573 -0.0200645 0.0006814478 -0.6822120101 0.407086072 -0.0895727855 0.0084928 -0.000294393 -36.454347243 50.7470670963 -7.8549338548 150.7810895953 -212.7678867723 36.8724293356 -186.1677313642 284.2653730155 -53.1909335756 75.3824228617 -122.5808344289 24.2424134809 -31.5145157956 58.5002431151 -10.4300311739 140.047746542 -237.7623187054 46.9727499486 -180.7645677206 311.4806214509 -65.709208285 75.6530222016 -132.5800920099 29.2516732748 -11.5212403813 23.8157827678 -4.4385318785 52.1262556172 -95.7306291658 19.7452677421 -68.7772422049 124.527904845 -27.3598748843 29.2289366846 -52.75741697 12.0889092726 -1.4922527907 3.2332969498 -0.6141896891 6.7573608264 -12.9297889021 2.71801631 -9.0279043013 16.7643172496 -3.7506979128 3.8689317834 -7.087304533 1.6518175591
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""")