# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2023 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:`Ameri2014Rjb`,
:class:`AmeriEtAl2017Rjb`,
:class:`AmeriEtAl2017Repi`,
:class:`AmeriEtAl2017RjbStressDrop`,
:class:`AmeriEtAl2017RepiStressDrop`
"""
import numpy as np
from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib.gsim import utils
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
g = 9.81 # According to G. Ameri, pers. communication (May 20th, 2019)
CONSTS = {"Mref": 5.5, "Mh": 6.75, "Rref": 1.0}
def _compute_between_events_std(C_SIGMA, mag):
"""
Return between-events standard deviation term. Expression is provided:
- according to eqn. 11 if model is heteroscedastic
(mag parameter is not None);
- or using a constant term if model is homoscedastic
(mag parameter is None).
"""
if mag is None:
# Homoscedastic model:
tau = C_SIGMA['tau']
else:
# Heteroscedastic model:
tau = C_SIGMA['tau1'] + (C_SIGMA['tau2'] - C_SIGMA['tau1'])*(mag-4.0)
tau[mag <= 4.0] = C_SIGMA['tau1']
tau[mag >= 5] = C_SIGMA['tau2']
return tau
def _compute_within_event_std(C_SIGMA):
"""
Return within-event standard deviation
"""
return C_SIGMA['phi']
def _get_distance_scaling_term(C, rval, mag):
"""
Returns the distance scaling term of the GMPE described in equation 2
"""
r_adj = np.sqrt(rval ** 2.0 + C["h"] ** 2.0)
return (C["c1"] + C["c2"] * (mag - CONSTS["Mref"])) * np.log10(
r_adj / CONSTS["Rref"])
def _get_magnitude_scaling_term(C, mag):
"""
Returns the magnitude scaling term of the GMPE described in
equation 3
"""
dmag = mag - CONSTS["Mh"]
return np.where(mag <= CONSTS["Mh"],
C["b1"] * dmag + C["b2"] * dmag**2,
C["b3"] * dmag)
_get_mean = CallableDict()
@_get_mean.add("rjb", "homoscedastic")
def _get_mean_1(kind, stress_drop, C, C_STRESS, ctx):
"""
Returns the mean ground motion (i.e. log10(ground motion in cm/s^2) )
"""
return (C["a"] +
_get_distance_scaling_term(C, ctx.rjb, ctx.mag) +
_get_magnitude_scaling_term(C, ctx.mag) +
_get_site_amplification_term(C, ctx.vs30) +
_get_style_of_faulting_term(C, ctx))
@_get_mean.add("rjb_stress")
def _get_mean_2(kind, stress_drop, C, C_STRESS, ctx):
"""
Returns the mean ground motion
"""
return (C["a"] +
_get_magnitude_scaling_term(C, ctx.mag) +
_get_distance_scaling_term(C, ctx.rjb, ctx.mag) +
_get_style_of_faulting_term(C, ctx) +
_get_site_amplification_term(C, ctx.vs30) +
_get_stress_term(C_STRESS, ctx.mag, stress_drop))
@_get_mean.add("repi")
def _get_mean_3(kind, stress_drop, C, C_STRESS, ctx):
"""
Returns the mean ground motion
"""
return (C["a"] +
_get_magnitude_scaling_term(C, ctx.mag) +
_get_distance_scaling_term(C, ctx.repi, ctx.mag) +
_get_style_of_faulting_term(C, ctx) +
_get_site_amplification_term(C, ctx.vs30))
@_get_mean.add("repi_stress")
def _get_mean_4(kind, stress_drop, C, C_STRESS, ctx):
"""
Returns the mean ground motion
"""
return (C["a"] +
_get_magnitude_scaling_term(C, ctx.mag) +
_get_distance_scaling_term(C, ctx.repi, ctx.mag) +
_get_style_of_faulting_term(C, ctx) +
_get_site_amplification_term(C, ctx.vs30) +
_get_stress_term(C_STRESS, ctx.mag, stress_drop))
def _get_site_amplification_term(C, vs30):
"""
Returns the site amplification given Eurocode 8 site classification
"""
f_s = np.zeros_like(vs30)
# Site class A
idx = vs30 >= 800.0
f_s[idx] = C["e1"]
# Site class B
idx = np.logical_and(vs30 < 800.0, vs30 >= 360.0)
f_s[idx] = C["e2"]
# Site Class C
idx = np.logical_and(vs30 < 360.0, vs30 >= 180.0)
f_s[idx] = C["e3"]
# Site Class D
idx = vs30 < 180.0
f_s[idx] = C["e4"]
return f_s
def _get_stddevs(kind, C_SIGMA, mag):
"""
Return standard deviations
"""
if kind == "homoscedastic":
tau = C_SIGMA["sigmaB"]
phi = C_SIGMA["sigmaW"]
sigma = np.sqrt(tau ** 2 + phi ** 2)
return sigma, tau, phi
if kind not in "rjb repi":
mag = None
tau = _compute_between_events_std(C_SIGMA, mag)
phi = _compute_within_event_std(C_SIGMA)
sigma = np.sqrt(tau**2 + phi**2)
return sigma, tau, phi
def _get_stress_term(C, mag, norm_stress_drop):
"""
Returns the stress parameter-dependent term, based on Yenier and Atkinson
(2015)
"""
if norm_stress_drop <= 1:
e = C['s0'] + C['s1'] * mag + C['s2'] * mag**2 + \
C['s3'] * mag**3 + C['s4'] * mag**4
else:
e = C['s5'] + C['s6'] * mag + C['s7'] * mag**2 + \
C['s8'] * mag**3 + C['s9'] * mag**4
return e * np.log10(norm_stress_drop)
def _get_style_of_faulting_term(C, ctx):
"""
Returns the style-of-faulting term of the GMPE described in equation 4
Fault type (Strike-slip, Normal, Thrust/reverse) is
derived from rake angle.
Rakes angles within 30 of horizontal are strike-slip,
angles from 30 to 150 are reverse, and angles from
-30 to -150 are normal.
Note that the 'Unspecified' case is not considered in this class
as rake is required as an input variable
"""
SS, NS, RS = utils.get_fault_type_dummy_variables(ctx)
return C["f1"] * NS + C["f2"] * RS + C["f3"] * SS
[docs]class AmeriEtAl2017Rjb(GMPE):
"""
Implements the Ameri et al (2017) GMPE for the case where Joyner-Boore
distance is used. Standard deviation uses the heteroscedastic formulation
given in eqn. 11. (for periods T<=1 s.)
Reference:
Ameri, G., Drouet, S., Traversa, P., Bindi, D., Cotton, F., (2017),
Toward an empirical ground motion prediction equation for France:
accounting for regional differences in the source stress parameter,
Bull. Earthquake Eng., 15: 4681-4717.
"""
#: Supported tectonic region type is 'active shallow crust'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Set of :mod:`intensity measure types <openquake.hazardlib.imt>`
#: this GSIM can calculate. A set should contain classes from module
#: :mod:`openquake.hazardlib.imt`.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation types are inter-event, intra-event
#: and total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameter is only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is Rjb (eq. 1).
REQUIRES_DISTANCES = {'rjb'}
kind = "rjb"
def __init__(self, norm_stress_drop=0.1, adjustment_factor=1.0, **kwargs):
super().__init__(norm_stress_drop=norm_stress_drop,
adjustment_factor=adjustment_factor, **kwargs)
self.norm_stress_drop = norm_stress_drop
self.adjustment_factor = np.log(adjustment_factor)
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
C_SIGMA = self.COEFFS_SIGMA[imt]
C_STRESS = self.COEFFS_STRESS[imt]
imean = _get_mean(self.kind, self.norm_stress_drop,
C, C_STRESS, ctx)
# Convert mean to ln(SA) with SA in units of g:
mean[m] = np.log(10.0 ** (imean - 2.0) / g)
mean[m] += self.adjustment_factor
s, t, p = _get_stddevs(self.kind, C_SIGMA, ctx.mag)
sig[m] = np.log(10.0 ** s)
tau[m] = np.log(10.0 ** t)
phi[m] = np.log(10.0 ** p)
#: Coefficients from Table "10518_2017_171_MOESM2_ESM.xlsx" in electronic supplementary material:
COEFFS = CoeffsTable(sa_damping=5, table="""
imt a c1 c2 h b1 b2 b3 e1 e2 e3 e4 f1 f2 f3
pga 3.57937 -1.4864 0.231465 6.65758 -0.0240888 -0.0631411 0 0 0.167762 0.249286 0.223014 -0.0382253 0.013243 0
0.01 3.5972 -1.49427 0.234091 6.79747 -0.0222199 -0.0600105 0 0 0.160126 0.24238 0.218539 -0.0347956 0.0177128 0
0.02 3.63617 -1.50665 0.234304 6.60957 -0.00818666 -0.0545415 0 0 0.149801 0.231588 0.212933 -0.0317685 0.0190783 0
0.03 3.69185 -1.54706 0.253029 6.83552 -0.0212604 -0.0434654 0 0 0.13237 0.210271 0.193703 -0.0248664 0.037243 0
0.04 3.74843 -1.57163 0.254487 6.84157 -0.023062 -0.0368002 0 0 0.13248 0.198745 0.160215 -0.0186509 0.0384935 0
0.05 3.8254 -1.59374 0.244296 6.97997 -0.0265193 -0.038679 0 0 0.135848 0.191212 0.142625 -0.0172171 0.0385044 0
0.075 4.02576 -1.62183 0.195296 7.29363 -0.00942327 -0.0570317 0 0 0.163595 0.202134 0.142641 -0.0238157 0.0230891 0
0.1 4.12894 -1.62321 0.163216 7.62694 -0.00570805 -0.0775024 0 0 0.200864 0.232295 0.173399 -0.0222679 0.0115192 0
0.15 4.14147 -1.55679 0.137411 7.59936 -0.00140059 -0.103665 0 0 0.230128 0.261189 0.229835 -0.0312945 -0.0134991 0
0.2 4.03038 -1.4505 0.122409 6.71189 0.0251505 -0.117975 0 0 0.222592 0.282414 0.254405 -0.0375677 -0.0132365 0
0.26 3.89003 -1.35644 0.112647 6.06462 0.058444 -0.12719 0 0 0.22463 0.318629 0.280155 -0.0438534 -0.0228273 0
0.3 3.79547 -1.29433 0.105082 5.40797 0.0826731 -0.132525 0 0 0.21436 0.330943 0.293392 -0.052228 -0.0249144 0
0.36 3.65477 -1.21655 0.102617 4.6578 0.123373 -0.13208 0 0 0.218341 0.357137 0.336488 -0.0545282 -0.0369904 0
0.4 3.57828 -1.18611 0.105263 4.45728 0.136293 -0.13249 0 0 0.225607 0.373643 0.36356 -0.0575379 -0.0445194 0
0.46 3.50977 -1.15887 0.108003 4.24293 0.159692 -0.131675 0 0 0.225533 0.392129 0.408201 -0.068798 -0.0588553 0
0.5 3.4641 -1.13335 0.106464 3.92775 0.184071 -0.130586 0 0 0.223114 0.401878 0.437158 -0.0755826 -0.0659854 0
0.6 3.35334 -1.09668 0.110251 3.67158 0.215812 -0.129838 0 0 0.221907 0.414504 0.504533 -0.075854 -0.075577 0
0.7 3.24798 -1.06758 0.110992 3.36202 0.2287 -0.132434 0 0 0.217418 0.421098 0.561574 -0.0780016 -0.0913044 0
0.8 3.13832 -1.03218 0.118672 3.15358 0.247122 -0.13043 0 0 0.207333 0.424843 0.594304 -0.0776178 -0.100387 0
0.9 3.07595 -1.00932 0.116383 3.16122 0.277383 -0.130108 0 0 0.20214 0.432693 0.633541 -0.0793058 -0.106253 0
1.0 3.01481 -0.990675 0.114962 3.04105 0.313627 -0.125759 0 0 0.203179 0.434754 0.64753 -0.0734174 -0.10704 0
1.3 2.8491 -0.954153 0.131841 3.03741 0.362253 -0.118367 0 0 0.189662 0.417724 0.679776 -0.0769343 -0.111787 0
1.5 2.79803 -0.949676 0.128459 2.97213 0.417589 -0.111117 0 0 0.190107 0.414214 0.719585 -0.0766813 -0.101168 0
1.8 2.77959 -0.966699 0.125038 3.65762 0.480496 -0.102423 0 0 0.176816 0.39028 0.674517 -0.0860793 -0.103835 0
2.0 2.75262 -0.973361 0.124103 3.78649 0.505881 -0.100896 0 0 0.169768 0.385618 0.6598 -0.0959682 -0.1124 0
2.6 2.5907 -0.964381 0.143781 3.87901 0.541547 -0.0930562 0 0 0.140212 0.33995 0.604624 -0.081575 -0.104082 0
3.0 2.50167 -0.950629 0.164955 4.11679 0.599563 -0.0673578 0 0 0.124967 0.321712 0.607734 -0.0900985 -0.114396 0
""")
# Coefficients from Table "10518_2017_171_MOESM3_ESM.xlsx" in electronic supplementary material:
# NB: Coefficients from the original table have been modified so as to account for the authors'
# advice in the article (p.4707, "we recommend the heteroscedastic model for T<=1 s only,
# and the homoscedastic model for longer periods".
# Accordingly, values for TAU1 and TAU2 have been edited to match TAU values for the following
# periods: 1.3 s., 1.5 s., 1.8 s., 2.0 s., 2.6 s., 3.0 s.
COEFFS_SIGMA = CoeffsTable(sa_damping=5, table="""
imt tau tau1 tau2 phi
pga 0.170688 0.299730 0.177908 0.303741
0.01 0.171851 0.299730 0.177908 0.305812
0.02 0.173021 0.311915 0.186848 0.307893
0.03 0.179043 0.305421 0.189678 0.318609
0.04 0.174265 0.328821 0.194362 0.328130
0.05 0.176014 0.339281 0.199864 0.331423
0.075 0.184290 0.331247 0.214309 0.327946
0.1 0.190709 0.309358 0.210499 0.321737
0.15 0.186913 0.292712 0.199181 0.315332
0.2 0.187804 0.272432 0.192531 0.301156
0.26 0.174769 0.241235 0.179662 0.294844
0.3 0.173561 0.237312 0.171560 0.292807
0.36 0.174919 0.216497 0.167742 0.295097
0.4 0.168289 0.209183 0.161301 0.299473
0.46 0.169701 0.204619 0.162074 0.301986
0.5 0.169913 0.203503 0.162521 0.302362
0.6 0.169173 0.200595 0.162803 0.301045
0.7 0.171074 0.202465 0.165952 0.304429
0.8 0.170979 0.198534 0.157879 0.304259
0.9 0.168764 0.187191 0.155639 0.300318
1.0 0.176172 0.184987 0.154404 0.297212
1.3 0.183978 0.183978 0.183978 0.295022
1.5 0.184155 0.184155 0.184155 0.295306
1.8 0.184885 0.184885 0.184885 0.296476
2.0 0.185435 0.185435 0.185435 0.297357
2.6 0.210376 0.210376 0.210376 0.293109
3.0 0.212859 0.212859 0.212859 0.283812
""")
# Coefficients from Table "10518_2017_171_MOESM4_ESM.xlsx" in electronic supplementary material
# (see also Yenier and Atkinson, 2015):
COEFFS_STRESS = CoeffsTable(sa_damping=5, table="""
imt s0 s1 s2 s3 s4 s5 s6 s7 s8 s9
pga -2.132000000000000000 1.937000000000000000 -0.504000000000000000 0.058240000000000000 -0.002498000000000000 -1.444000000000000000 1.235000000000000000 -0.285100000000000000 0.030210000000000000 -0.001217000000000000
0.01 -2.048000000000000000 1.881000000000000000 -0.490100000000000000 0.056680000000000000 -0.002433000000000000 -1.437000000000000000 1.242000000000000000 -0.289200000000000000 0.030880000000000000 -0.001252000000000000
0.02 -1.160000000000000000 1.274000000000000000 -0.334400000000000000 0.039110000000000000 -0.001700000000000000 -1.272000000000000000 1.254000000000000000 -0.317100000000000000 0.036240000000000000 -0.001550000000000000
0.03 -1.056000000000000000 1.205000000000000000 -0.313200000000000000 0.036150000000000000 -0.001550000000000000 -2.243000000000000000 1.981000000000000000 -0.508600000000000000 0.057820000000000000 -0.002439000000000000
0.04 -0.857100000000000000 1.044000000000000000 -0.267700000000000000 0.030820000000000000 -0.001328000000000000 -3.310000000000000000 2.663000000000000000 -0.668300000000000000 0.074150000000000000 -0.003056000000000000
0.05 -0.962800000000000000 0.982600000000000000 -0.215600000000000000 0.020800000000000000 -0.000742300000000000 -4.228000000000000000 3.293000000000000000 -0.831600000000000000 0.093030000000000000 -0.003873000000000000
0.075 -3.307093622752820000 2.715618872036960000 -0.691461347788890000 0.077930164008379800 -0.003265156851659290 -3.391720419721760000 2.384390298763130000 -0.525460084931779000 0.051464187772421400 -0.001885243731635890
0.10 -4.051000000000000000 3.100000000000000000 -0.762500000000000000 0.083280000000000000 -0.003393000000000000 -2.452000000000000000 1.569000000000000000 -0.289000000000000000 0.023000000000000000 -0.000657300000000000
0.15 -4.135496790484950000 2.990175665924260000 -0.703560572208682000 0.074081088832166700 -0.002926336129704660 -0.559855506733657000 -0.053291402105396500 0.180588831258940000 -0.033835675561780300 0.001817879129878780
0.20 -2.707000000000000000 1.729000000000000000 -0.330200000000000000 0.028160000000000000 -0.000906400000000000 0.819700000000000000 -1.083000000000000000 0.439500000000000000 -0.061050000000000000 0.002846000000000000
0.26 -1.505285261389930000 0.778534841420447000 -0.076457065704366200 -0.000269726890490286 0.000248305753738586 1.899210650769040000 -1.836817196760830000 0.618619194004931000 -0.078935922164824500 0.003491574884857080
0.30 -0.318200000000000000 -0.138600000000000000 0.170400000000000000 -0.028500000000000000 0.001421000000000000 2.245000000000000000 -2.003000000000000000 0.632600000000000000 -0.076990000000000000 0.003268000000000000
0.36 1.111764905130550000 -1.191881353033970000 0.439960248224610000 -0.057764942347499700 0.002573205245872980 2.596970663273000000 -2.161763564108410000 0.643269347166781000 -0.074790329176234400 0.003050023155703400
0.40 2.018000000000000000 -1.857000000000000000 0.611700000000000000 -0.076740000000000000 0.003341000000000000 2.422000000000000000 -1.938000000000000000 0.555800000000000000 -0.061740000000000000 0.002390000000000000
0.46 3.370459349501280000 -2.867857822677980000 0.881282613938582000 -0.107753617606812000 0.004656357005019520 1.511700286086790000 -1.063201044297120000 0.263446359042810000 -0.021599838071486900 0.000449893309699056
0.50 3.956000000000000000 -3.288000000000000000 0.988500000000000000 -0.119600000000000000 0.005142000000000000 0.855500000000000000 -0.452800000000000000 0.064590000000000000 0.005220000000000000 -0.000829900000000000
0.60 4.005249108906740000 -3.183158831926270000 0.917619630870284000 -0.106718967852185000 0.004415895819937990 -0.245407670497777000 0.555351425397322000 -0.256909575045555000 0.047551190466675300 -0.002799950197340630
0.70 3.209976852768910000 -2.406186937090780000 0.654683779233643000 -0.070222093434176500 0.002629549156714740 -1.091578741397200000 1.292319501723110000 -0.479373955359707000 0.075037674525423100 -0.003993830592681950
0.80 2.404000000000000000 -1.652000000000000000 0.408800000000000000 -0.037100000000000000 0.001051000000000000 -2.124000000000000000 2.152000000000000000 -0.730100000000000000 0.105300000000000000 -0.005287000000000000
0.90 1.809528912677510000 -1.104457948914730000 0.235192596243833000 -0.014593092486076200 0.000026650903092806 -3.410479563877170000 3.201765159152890000 -1.033659203023420000 0.142312111204227000 -0.006905803814287950
1.00 1.066000000000000000 -0.455200000000000000 0.037390000000000000 0.010330000000000000 -0.001084000000000000 -4.473000000000000000 4.051000000000000000 -1.274000000000000000 0.171000000000000000 -0.008137000000000000
1.30 -2.508000000000000000 2.523000000000000000 -0.844600000000000000 0.120500000000000000 -0.006024000000000000 -5.494000000000000000 4.766000000000000000 -1.439000000000000000 0.184900000000000000 -0.008458000000000000
1.50 -4.562591209586210000 4.184178885193690000 -1.321626951817460000 0.178297179632034000 -0.008536305641724080 -5.752786034123840000 4.904176324860710000 -1.453760278582560000 0.183165745788638000 -0.008216131058600520
1.80 -6.066252631749060000 5.345315499812140000 -1.635798607735410000 0.213421543697430000 -0.009917991992558870 -6.081700433391410000 5.092342470146320000 -1.481158779327170000 0.182998865017356000 -0.008050251934664040
2.0 -6.642000000000000000 5.767000000000000000 -1.742000000000000000 0.224100000000000000 -0.010280000000000000 -6.010000000000000000 4.985000000000000000 -1.433000000000000000 0.174800000000000000 -0.007587000000000000
2.6 -8.161077047405510000 6.880595832041620000 -2.024661773244400000 0.253463377249699000 -0.011347702706097400 -4.707867446814010000 3.789164702352790000 -1.037841219533240000 0.119381787710041000 -0.004831972404074730
3.0 -7.980000000000000000 6.643000000000000000 -1.924000000000000000 0.236600000000000000 -0.010390000000000000 -4.180000000000000000 3.317000000000000000 -0.886200000000000000 0.098880000000000000 -0.003853000000000000
""")
[docs]class AmeriEtAl2017RjbStressDrop(AmeriEtAl2017Rjb):
"""
Implements the Ameri et al (2017) GMPE for the case where Joyner-Boore
distance is used, and the stress parameter is specified in the
Ground-motion logic-tree.
Example specification of the normalizaed stress parameter::
<uncertaintyModel>
[AmeriEtAl2017RjbStressDrop]
norm_stress_drop = 0.3
</uncertaintyModel>
The stress parameter is normalized according to STRESS_DROP/REF_STRESS_DROP,
where REF_STRESS_DROP varies regionally. The authors used the following
values for reference regional stress estimates: 1 bar for the Swtzerland
(Swiss Alps +Foreland), 10 bars for the French Alps + Rhine Graben, and 100
bars for the Pyrenees events. In this case, the standard deviation
implements a homoscedastic formulation.
Reference:
Ameri, G., Drouet, S., Traversa, P., Bindi, D., Cotton, F., (2017),
Toward an empirical ground motion prediction equation for France:
accounting for regional differences in the source stress parameter,
Bull. Earthquake Eng., 15: 4681-4717.
"""
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
kind = "rjb_stress"
[docs]class AmeriEtAl2017Repi(AmeriEtAl2017Rjb):
"""
Implements the Ameri et al (2017) GMPE for the case where epicentral
distance is used. Standard deviation uses the heteroscedastic formulation
given in eqn. 11. (for periods T<=1 s.)
Reference:
Ameri, G., Drouet, S., Traversa, P., Bindi, D., Cotton, F., (2017),
Toward an empirical ground motion prediction equation for France:
accounting for regional differences in the source stress parameter,
Bull. Earthquake Eng., 15: 4681-4717.
"""
kind = "repi"
#: Required distance measure is Repi (eq. 1).
REQUIRES_DISTANCES = {'repi'}
#: Coefficients from Table "10518_2017_171_MOESM1_ESM.xlsx" in electronic supplementary material:
COEFFS = CoeffsTable(sa_damping=5, table="""
imt a c1 c2 h b1 b2 b3 e1 e2 e3 e4 f1 f2 f3
pga 3.90119 -1.5472 0.203801 6.78654 0.157748 -0.0375241 0 0 0.183962 0.265793 0.223751 -0.0467904 0.0184746 0
0.01 3.91834 -1.55513 0.206695 6.93871 0.158768 -0.0344853 0 0 0.176314 0.258883 0.219586 -0.0433188 0.0229539 0
0.02 3.96778 -1.56944 0.204904 6.71767 0.179572 -0.0283156 0 0 0.166393 0.248523 0.216466 -0.0404006 0.0245037 0
0.03 4.03457 -1.61309 0.221786 6.97123 0.170789 -0.0170738 0 0 0.1495 0.22776 0.198027 -0.033472 0.0429289 0
0.04 4.09161 -1.63695 0.223878 6.93988 0.170856 -0.00977618 0 0 0.149521 0.216085 0.161634 -0.0274375 0.0441535 0
0.05 4.16164 -1.65202 0.213028 6.87221 0.173549 -0.0106632 0 0 0.153353 0.208313 0.142202 -0.0260106 0.0440531 0
0.075 4.33841 -1.6683 0.169004 7.00747 0.189381 -0.0275671 0 0 0.180887 0.218339 0.140321 -0.0334549 0.0279034 0 1
0.10 4.42216 -1.66545 0.142599 7.42062 0.181596 -0.0484681 0 0 0.217184 0.248079 0.169717 -0.0322814 0.0161202 0
0.15 4.41412 -1.59603 0.121696 7.46484 0.172235 -0.075683 0 0 0.245926 0.275714 0.226713 -0.0406154 -0.00923057 0
0.20 4.29143 -1.48937 0.109037 6.66175 0.188457 -0.0912278 0 0 0.237868 0.296127 0.251076 -0.0473502 -0.00965523 0
0.26 4.15414 -1.3971 0.0981806 6.01355 0.222792 -0.100492 0 0 0.240346 0.331854 0.276914 -0.0529457 -0.0200077 0
0.30 4.06715 -1.33781 0.0881106 5.40572 0.249494 -0.106148 0 0 0.229999 0.344676 0.291959 -0.061157 -0.0217789 0
0.36 3.93473 -1.26446 0.082679 4.76415 0.290781 -0.106547 0 0 0.234552 0.371843 0.336232 -0.0634606 -0.0336804 0
0.40 3.86858 -1.2376 0.0824992 4.59994 0.307618 -0.107085 0 0 0.242295 0.388648 0.362821 -0.0660934 -0.0413226 0
0.46 3.80262 -1.2128 0.08412 4.46018 0.329334 -0.106975 0 0 0.241844 0.407015 0.405404 -0.0767804 -0.0551733 0
0.50 3.76231 -1.18977 0.0810918 4.20281 0.354457 -0.106229 0 0 0.239285 0.416952 0.433658 -0.0835497 -0.0619977 0
0.60 3.65478 -1.15523 0.0833905 4.00398 0.385689 -0.106057 0 0 0.237641 0.429496 0.500227 -0.0833572 -0.0718527 0
0.70 3.55408 -1.13019 0.0840393 3.85672 0.396746 -0.108988 0 0 0.232891 0.436872 0.559456 -0.0853279 -0.0872709 0
0.80 3.44534 -1.09309 0.0883406 3.4791 0.419463 -0.10718 0 0 0.223144 0.44086 0.594032 -0.0851173 -0.0969812 0
0.90 3.37653 -1.06841 0.0860723 3.48856 0.446457 -0.107469 0 0 0.217031 0.448439 0.634135 -0.0872213 -0.103167 0
1.0 3.31044 -1.04917 0.085526 3.38282 0.479407 -0.103463 0 0 0.217976 0.449865 0.647 -0.0811993 -0.103835 0
1.3 3.13628 -1.01108 0.101962 3.39674 0.523028 -0.0971368 0 0 0.204172 0.433443 0.680322 -0.085345 -0.108176 0
1.5 3.08483 -1.00615 0.0983393 3.32168 0.580112 -0.0894907 0 0 0.205563 0.430942 0.719757 -0.085572 -0.095703 0
1.8 3.05563 -1.01592 0.0933633 3.5879 0.64878 -0.0794491 0 0 0.191903 0.40723 0.673431 -0.0933542 -0.0975485 0
2.0 3.03188 -1.02463 0.0921217 3.80958 0.673389 -0.0781992 0 0 0.184302 0.40322 0.658312 -0.103371 -0.105662 0
2.6 2.87034 -1.01797 0.111257 4.12602 0.708014 -0.0696517 0 0 0.155283 0.359284 0.603672 -0.0906715 -0.0973401 0
3.0 2.77941 -1.00223 0.130875 4.44146 0.773886 -0.0405902 0 0 0.140958 0.341313 0.606863 -0.0982915 -0.108276 0
""")
# Coefficients from Table "10518_2017_171_MOESM3_ESM.xlsx" in electronic supplementary material:
# NB: Coefficients from the original table have been modified so as to account for the authors'
# advice in the article (p.4707, "we recommend the heteroscedastic model for T<=1 s only,
# and the homoscedastic model for longer periods".
# Accordingly, values for TAU1 and TAU2 have been edited to match TAU values for the following
# periods: 1.3 s., 1.5 s., 1.8 s., 2.0 s., 2.6 s., 3.0 s.
COEFFS_SIGMA = CoeffsTable(sa_damping=5, table="""
imt tau tau1 tau2 phi
pga 0.171510 0.311636 0.180874 0.305205
0.01 0.172616 0.311636 0.180874 0.307173
0.02 0.173732 0.311987 0.182078 0.309158
0.03 0.179536 0.317621 0.184522 0.319487
0.04 0.174760 0.329101 0.188943 0.329062
0.05 0.185622 0.339251 0.193773 0.330316
0.075 0.193894 0.332014 0.207885 0.327110
0.1 0.191344 0.310587 0.212569 0.322807
0.15 0.196745 0.293783 0.201864 0.315493
0.2 0.189696 0.274526 0.196893 0.304190
0.26 0.177025 0.243233 0.177031 0.298652
0.3 0.176062 0.239891 0.176732 0.297027
0.36 0.177392 0.219213 0.164453 0.299269
0.4 0.170361 0.211530 0.165739 0.303160
0.46 0.171621 0.206189 0.166153 0.305402
0.5 0.171776 0.205112 0.166378 0.305678
0.6 0.171188 0.202812 0.158203 0.304631
0.7 0.173219 0.204808 0.161272 0.308245
0.8 0.172734 0.200690 0.161046 0.307382
0.9 0.170475 0.196917 0.149874 0.303362
1.0 0.177982 0.185807 0.157426 0.300265
1.3 0.185666 0.185666 0.185666 0.297728
1.5 0.185940 0.185940 0.185940 0.298167
1.8 0.186799 0.186799 0.186799 0.299545
2.0 0.187335 0.187335 0.187335 0.300404
2.6 0.204828 0.204828 0.204828 0.298586
3.0 0.216272 0.216272 0.216272 0.288363
""")
[docs]class AmeriEtAl2017RepiStressDrop(AmeriEtAl2017Repi):
"""
Implements the Ameri et al (2017) GMPE for the case where epicentral
distance is used, and the stress parameter is specified in the
Ground-motion logic-tree.
Example specification of the normalized stress parameter::
<uncertaintyModel>
[AmeriEtAl2017RepiStressDrop]
norm_stress_drop = 0.3
</uncertaintyModel>
The stress parameter is normalized according to
STRESS_DROP/REF_STRESS_DROP, where REF_STRESS_DROP varies regionally.
The authors used the following values for reference regional stress
estimates: 1 bar for the Swtzerland (Swiss Alps+ Foreland), 10 bars
for the French Alps + Rhine Graben, and 100 bars for the Pyrenees events.
In this case, the standard deviation implements a homoscedastic formulation
Reference:
Ameri, G., Drouet, S., Traversa, P., Bindi, D., Cotton, F., (2017),
Toward an empirical ground motion prediction equation for France:
accounting for regional differences in the source stress parameter,
Bull. Earthquake Eng., 15: 4681-4717.
"""
kind = "repi_stress"
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
def __init__(self, norm_stress_drop=1.1, adjustment_factor=1.0):
super().__init__(adjustment_factor=adjustment_factor)
self.norm_stress_drop = norm_stress_drop
[docs]class Ameri2014Rjb(AmeriEtAl2017Rjb):
"""
Implementation of Ameri (2014), an early version of the Ameri et al. (2017)
GMM published in:
Ameri (2014) "Empirical Ground Motion Model Adapted to the French Context",
Seismic Ground Motion Assessment (SIGMA) Deliverable SIGMA-2014-D2-131
However, the model is adopted in favour of the Ameri et al. (2017) model
within the 2020 seismic hazard model of France published by Drouet et al.
(2020):
Drouet S, Ameri G, Le Dortz, K, Sevanell R, Senfaute G. (2020)
"A probabilistic seismic hazard map for the metropolitan France",
Bulletin of Earthquake Engineering, 18: 1865 - 1898
Adopts a homoscedastic standard deviation model.
"""
kind = "homoscedastic"
#: Coefficients from xls file "coeff_AMERI2014_Rjb_generic.xls":
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt a c1 c2 h b1 b2 b3 e1 e2 e3 e4 f1 f2 f3
pga 3.4299200 -1.4186000 0.2155010 6.9348200 -0.1344920 -0.1021380 0.00 0.00 0.1662230 0.2201900 0.2073030 -0.0259315 0.0575387 0.00
0.010 3.4445000 -1.4249900 0.2181910 7.0431800 -0.1319270 -0.0983586 0.00 0.00 0.1609590 0.2139220 0.2046230 -0.0250589 0.0628565 0.00
0.020 3.4780800 -1.4342900 0.2169050 6.8457100 -0.1211040 -0.0944366 0.00 0.00 0.1511240 0.2018620 0.2011810 -0.0211561 0.0650619 0.00
0.030 3.5340800 -1.4724500 0.2327950 7.0594700 -0.1335990 -0.0846513 0.00 0.00 0.1344390 0.1799090 0.1822870 -0.0140633 0.0846879 0.00
0.040 3.5845300 -1.4965000 0.2364990 7.0683300 -0.1410750 -0.0786815 0.00 0.00 0.1338950 0.1680250 0.1454330 -0.0085579 0.0868674 0.00
0.050 3.6592600 -1.5159600 0.2257250 7.1327700 -0.1401910 -0.0795892 0.00 0.00 0.1372460 0.1604960 0.1270730 -0.0065000 0.0867504 0.00
0.075 3.8433500 -1.5442900 0.1855380 7.3996300 -0.1322830 -0.0960448 0.00 0.00 0.1623400 0.1702940 0.1255480 -0.0137204 0.0725592 0.00
0.100 3.9491600 -1.5521700 0.1589970 7.8753900 -0.1304940 -0.1137860 0.00 0.00 0.1977650 0.2014370 0.1558740 -0.0124134 0.0602458 0.00
0.150 3.9690700 -1.4935600 0.1398220 7.8395000 -0.1230940 -0.1358840 0.00 0.00 0.2241600 0.2314580 0.2126800 -0.0229505 0.0324183 0.00
0.200 3.8815600 -1.4021600 0.1295530 7.1482300 -0.0907246 -0.1459470 0.00 0.00 0.2155400 0.2565140 0.2432830 -0.0323343 0.0270226 0.00
0.260 3.7621300 -1.3151300 0.1198170 6.4311000 -0.0411302 -0.1506240 0.00 0.00 0.2172770 0.2952000 0.2687630 -0.0390729 0.0133672 0.00
0.300 3.6809100 -1.2603400 0.1131640 5.9062600 -0.0132164 -0.1543630 0.00 0.00 0.2066750 0.3094220 0.2870460 -0.0481329 0.0088210 0.00
0.360 3.5548100 -1.1894500 0.1104210 5.2933300 0.0334797 -0.1522850 0.00 0.00 0.2112730 0.3385730 0.3324460 -0.0510757 -0.0059703 0.00
0.400 3.4885400 -1.1623200 0.1119970 5.1330600 0.0530004 -0.1514720 0.00 0.00 0.2194750 0.3560050 0.3595690 -0.0536326 -0.0149397 0.00
0.460 3.4207700 -1.1375300 0.1165370 4.9782100 0.0763429 -0.1497750 0.00 0.00 0.2199700 0.3761570 0.4020090 -0.0648424 -0.0315718 0.00
0.500 3.3758300 -1.1137300 0.1160610 4.7366800 0.0996337 -0.1484540 0.00 0.00 0.2175090 0.3866420 0.4309080 -0.0721233 -0.0397411 0.00
0.600 3.2676500 -1.0768700 0.1191360 4.4259300 0.1355550 -0.1469930 0.00 0.00 0.2165190 0.3998460 0.4989120 -0.0726062 -0.0517600 0.00
0.700 3.1724200 -1.0534700 0.1199620 4.2476000 0.1504170 -0.1489880 0.00 0.00 0.2126620 0.4083170 0.5600450 -0.0752202 -0.0684885 0.00
0.800 3.0660600 -1.0182000 0.1268360 3.9563300 0.1726660 -0.1464220 0.00 0.00 0.2032800 0.4128690 0.5960230 -0.0758408 -0.0794567 0.00
0.900 2.9964500 -0.9942510 0.1280420 3.9208300 0.1979320 -0.1457170 0.00 0.00 0.1955140 0.4193100 0.6355290 -0.0792907 -0.0870377 0.00
1.000 2.9350300 -0.9752740 0.1264460 3.8208500 0.2339080 -0.1415580 0.00 0.00 0.1966170 0.4212260 0.6486290 -0.0737010 -0.0878048 0.00
1.300 2.7827900 -0.9400810 0.1392110 3.8020600 0.2942740 -0.1332020 0.00 0.00 0.1832300 0.4053710 0.6727040 -0.0754954 -0.0903559 0.00
1.500 2.7402500 -0.9350050 0.1326680 3.8021500 0.3559020 -0.1261410 0.00 0.00 0.1809680 0.3976890 0.7102410 -0.0729895 -0.0783815 0.00
1.800 2.6933600 -0.9415820 0.1345680 4.2154000 0.4141180 -0.1148970 0.00 0.00 0.1632190 0.3692440 0.6611440 -0.0791300 -0.0768855 0.00
2.000 2.6643400 -0.9479680 0.1337100 4.4291100 0.4369840 -0.1139270 0.00 0.00 0.1558270 0.3645580 0.6458130 -0.0888361 -0.0845512 0.00
2.600 2.5117100 -0.9447250 0.1570700 4.6118900 0.4858550 -0.0985749 0.00 0.00 0.1209170 0.3188600 0.5885730 -0.0735028 -0.0659589 0.00
3.000 2.4565500 -0.9442740 0.1724760 5.1844600 0.5461080 -0.0768508 0.00 0.00 0.1099650 0.3089590 0.5937220 -0.0879513 -0.0845897 0.00
""")
# Homoscedastic sigma model
COEFFS_SIGMA = CoeffsTable(sa_damping=5, table="""\
imt sigmaB sigmaW sigmaT
pga 0.2269060 0.3025410 0.3781770
0.010 0.2286200 0.3048270 0.3810330
0.020 0.2300070 0.3066760 0.3833450
0.030 0.2335220 0.3182370 0.3947250
0.040 0.2402440 0.3273970 0.4060860
0.050 0.2476110 0.3301480 0.4126840
0.075 0.2553120 0.3261180 0.4141700
0.100 0.2455130 0.3203650 0.4036210
0.150 0.2342130 0.3122840 0.3903550
0.200 0.2240930 0.2987910 0.3734880
0.260 0.2050650 0.2921950 0.3569730
0.300 0.1996860 0.2910900 0.3529980
0.360 0.1967460 0.2935280 0.3533660
0.400 0.1901640 0.2975480 0.3531250
0.460 0.1875050 0.3006780 0.3543520
0.500 0.1875000 0.3006690 0.3543420
0.600 0.1863500 0.2988250 0.3521690
0.700 0.1882750 0.3019110 0.3558050
0.800 0.1879880 0.3014520 0.3552650
0.900 0.1816910 0.2987540 0.3496650
1.000 0.1804730 0.2967510 0.3473210
1.300 0.1921380 0.2934950 0.3507940
1.500 0.1878810 0.2939760 0.3488860
1.800 0.1888490 0.2954910 0.3506840
2.000 0.1894050 0.2963620 0.3517170
2.600 0.2007940 0.2927050 0.3549570
3.000 0.2076440 0.2829710 0.3509820
""")