# -*- 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:`KothaEtAl2020`,
:class:`KothaEtAl2020Site`,
:class:`KothaEtAl2020Slope`,
:class:`KothaEtAl2020ESHM20`,
:class:`KothaEtAl2020ESHM20SlopeGeology`
:class:`KothaEtAl2020regional`
"""
import os
import numpy as np
from scipy.constants import g
from shapely.geometry import Point, shape
from shapely.prepared import prep
from openquake.baselib.general import CallableDict
from openquake.hazardlib.geo.packager import fiona
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable, add_alias
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA, from_string
from openquake.hazardlib.gsim.nga_east import (get_tau_at_quantile, ITPL,
TAU_EXECUTION, TAU_SETUP)
DATA_FOLDER = os.path.join(os.path.dirname(__file__), 'Kotha_2020')
CONSTANTS = {"Mref": 4.5, "Rref": 30., "Mh": 5.7,
"h_D10": 4.0, "h_10D20": 8.0, "h_D20": 12.0}
# The large-magnitude statistical standard deviation values are taken from data
# supplied by Kotha et al. (2020)
SIGMA_MU_COEFFS = CoeffsTable(sa_damping=5, table="""\
imt sigma_mu_m8_shallow sigma_mu_m8_intermediate sigma_mu_m8_deep sigma_mu_m7p4_shallow sigma_mu_m7p4_intermediate sigma_mu_m7p4_deep
pgv 0.2865 0.2829 0.2814 0.2108 0.2072 0.2057
pga 0.3040 0.3003 0.2986 0.2250 0.2213 0.2197
0.010 0.3039 0.3002 0.2986 0.2250 0.2213 0.2197
0.025 0.3026 0.2988 0.2972 0.2243 0.2205 0.2189
0.040 0.3010 0.2972 0.2955 0.2241 0.2203 0.2186
0.050 0.3053 0.3014 0.2997 0.2278 0.2239 0.2222
0.070 0.3133 0.3093 0.3076 0.2340 0.2301 0.2284
0.100 0.3219 0.3179 0.3162 0.2403 0.2364 0.2346
0.150 0.3199 0.3159 0.3141 0.2377 0.2337 0.2319
0.200 0.3174 0.3134 0.3117 0.2343 0.2303 0.2285
0.250 0.3118 0.3078 0.3061 0.2297 0.2257 0.2240
0.300 0.3094 0.3055 0.3038 0.2275 0.2236 0.2220
0.350 0.3038 0.2999 0.2982 0.2230 0.2191 0.2174
0.400 0.2989 0.2950 0.2933 0.2197 0.2157 0.2140
0.450 0.2964 0.2926 0.2909 0.2180 0.2142 0.2125
0.500 0.2916 0.2878 0.2861 0.2145 0.2106 0.2090
0.600 0.2897 0.2860 0.2844 0.2131 0.2094 0.2078
0.700 0.2888 0.2852 0.2836 0.2124 0.2088 0.2072
0.750 0.2902 0.2867 0.2851 0.2134 0.2098 0.2083
0.800 0.2923 0.2888 0.2873 0.2147 0.2112 0.2097
0.900 0.2948 0.2915 0.2900 0.2165 0.2132 0.2117
1.000 0.2964 0.2932 0.2918 0.2175 0.2142 0.2128
1.200 0.2961 0.2930 0.2917 0.2170 0.2139 0.2126
1.400 0.3019 0.2990 0.2977 0.2211 0.2182 0.2169
1.600 0.3041 0.3013 0.3000 0.2225 0.2197 0.2184
1.800 0.3060 0.3032 0.3020 0.2235 0.2207 0.2195
2.000 0.3094 0.3067 0.3055 0.2258 0.2231 0.2219
2.500 0.3121 0.3095 0.3083 0.2275 0.2249 0.2237
3.000 0.3279 0.3254 0.3243 0.2392 0.2366 0.2355
3.500 0.3256 0.3230 0.3219 0.2378 0.2351 0.2339
4.000 0.3269 0.3243 0.3232 0.2386 0.2359 0.2348
4.500 0.3483 0.3456 0.3444 0.2537 0.2510 0.2498
5.000 0.3525 0.3498 0.3486 0.2567 0.2539 0.2527
6.000 0.3458 0.3422 0.3406 0.2514 0.2478 0.2462
7.000 0.3453 0.3417 0.3402 0.2513 0.2477 0.2461
8.000 0.3428 0.3392 0.3376 0.2497 0.2460 0.2444
""")
AVGSA_SIGMA_MU_COEFFS = CoeffsTable(sa_damping=5, table="""\
imt sigma_mu_m8_shallow sigma_mu_m8_intermediate sigma_mu_m8_deep sigma_mu_m7p4_shallow sigma_mu_m7p4_intermediate sigma_mu_m7p4_deep
AvgSA(0.050) 0.36237117 0.36194128 0.36153721 0.26814685 0.26770184 0.26728207
AvgSA(0.100) 0.37100348 0.37058454 0.37019017 0.27464169 0.27420650 0.27379506
AvgSA(0.150) 0.37113960 0.37073150 0.37034714 0.27399830 0.27357286 0.27317036
AvgSA(0.200) 0.36853324 0.36813709 0.36776392 0.27144161 0.27102774 0.27063616
AvgSA(0.250) 0.36438013 0.36399264 0.36362762 0.26790615 0.26750087 0.26711746
AvgSA(0.300) 0.36004639 0.35966739 0.35931043 0.26444337 0.26404673 0.26367159
AvgSA(0.400) 0.34960757 0.34924208 0.34889809 0.25636041 0.25597756 0.25561573
AvgSA(0.500) 0.34196320 0.34160761 0.34127316 0.25046920 0.25009644 0.24974445
AvgSA(0.600) 0.33628994 0.33594377 0.33561851 0.24613837 0.24577525 0.24543272
AvgSA(0.700) 0.33265779 0.33232082 0.33200448 0.24327786 0.24292413 0.24259077
AvgSA(0.800) 0.33080518 0.33047781 0.33017078 0.24172055 0.24137672 0.24105304
AvgSA(0.900) 0.33028960 0.32997162 0.32967376 0.24123027 0.24089610 0.24058191
AvgSA(1.000) 0.33118486 0.33087499 0.33058504 0.24174675 0.24142106 0.24111520
AvgSA(1.250) 0.33684608 0.33655872 0.33629100 0.24552957 0.24522646 0.24494296
AvgSA(1.500) 0.34131151 0.34103635 0.34078037 0.24857633 0.24828558 0.24801406
AvgSA(1.750) 0.34468757 0.34442002 0.34417138 0.25099193 0.25070866 0.25044432
AvgSA(2.000) 0.34962212 0.34936230 0.34912098 0.25441729 0.25414208 0.25388544
AvgSA(2.500) 0.35772559 0.35748828 0.35726965 0.25993600 0.25968178 0.25944620
AvgSA(3.000) 0.38024588 0.38006170 0.37989860 0.27645421 0.27624724 0.27606079
AvgSA(3.500) 0.37303807 0.37283697 0.37265703 0.27159333 0.27137037 0.27116809
AvgSA(4.000) 0.37757969 0.37738041 0.37720210 0.27464125 0.27442015 0.27421954
AvgSA(4.500) 0.39949828 0.39927571 0.39907300 0.29012395 0.28988040 0.28965658
AvgSA(5.000) 0.40186133 0.40163856 0.40143559 0.29173110 0.29148734 0.29126324
""")
def _get_h(C, hypo_depth):
"""
Returns the depth-specific coefficient
"""
return np.where(
hypo_depth <= 10.,
CONSTANTS["h_D10"],
np.where(hypo_depth > 20., CONSTANTS["h_D20"], CONSTANTS["h_10D20"]))
get_distance_coefficients = CallableDict()
[docs]@get_distance_coefficients.add("base", "site", "slope", "avgsa_base")
def get_distance_coefficients_1(kind, c3, c3_epsilon, C, imt, sctx):
"""
Returns either the directly specified c3 value or the c3 from the
existing tau_c3 distribution
"""
if c3:
# Use the c3 that has been defined on input
return c3
else:
# Define the c3 as a number of standard deviation multiplied
# by tau_c3
return C["c3"] + (c3_epsilon * C["tau_c3"])
[docs]@get_distance_coefficients.add("ESHM20", "geology", "avgsa_ESHM20",
"avgsa_ESHM20_geology",
"avgsa_ESHM20_homoskedastic")
def get_distance_coefficients_2(kind, c3, c3_epsilon, C, imt, sctx):
"""
Returns the c3 term. If c3 was input directly into the GMPE then
this over-rides the c3 regionalisation. Otherwise the c3 and tau_c3
are determined according to the region to which each site is assigned.
Note that no regionalisation is defined for PGV and hence the
default values from Kotha et al. (2020) are taken unless defined
otherwise in the input c3
"""
if c3:
# If c3 is input then this over-rides the regionalisation
# assumed within this model
return c3[imt]["c3"] * np.ones(sctx.region.shape)
# Default c3 and tau values to the original GMPE c3 and tau
c3_ = C["c3"] + np.zeros(sctx.region.shape)
tau_c3 = C["tau_c3"] + np.zeros(sctx.region.shape)
if not np.any(sctx.region) or ("PGV" in str(imt)):
# No regionalisation - take the default C3 and multiply tau_c3
# by the original epsilon
return (c3_ + c3_epsilon * tau_c3) + np.zeros(sctx.region.shape)
# Some ctx belong to the calibrated regions - loop through them
C3_R = C3_REGIONS_AVGSA[imt] if kind.startswith("avgsa") else C3_REGIONS[imt]
for i in range(1, 6):
idx = sctx.region == i
c3_[idx] = C3_R["region_{:s}".format(str(i))]
tau_c3[idx] = C3_R["tau_region_{:s}".format(str(i))]
return c3_ + c3_epsilon * tau_c3
[docs]def get_distance_coefficients_3(att, delta_c3_epsilon, C, imt, sctx):
"""
Return site-specific coefficient 'C3'. The function retrieves the
value of delta_c3 and the standard error of delta_c3 from the 'att'
geojson file depending on the location of site. This delta_c3 is
added to the generic coefficient 'c3' from the GMPE. A delta_c3_epsilon
value of +/- 1.6 gives the 95% confidence interval for delta_c3.
"""
s = [(Point(lon, lat)) for lon, lat in zip(sctx.lon, sctx.lat)]
delta_c3 = np.zeros((len(sctx.lat), 2), dtype=float)
for i, feature in enumerate(att):
prepared_polygon = prep(shape(feature['geometry']))
contained = list(filter(prepared_polygon.contains, s))
if contained:
ll = np.concatenate([
np.where((sctx['lon'] == p.x) &
(sctx['lat'] == p.y))[0] for p in contained])
delta_c3[ll, 0] = feature['properties'][str(imt)]
delta_c3[ll, 1] = feature['properties'][str(imt)+'_se']
return C["c3"] + delta_c3[:, 0] + delta_c3_epsilon * delta_c3[:, 1]
[docs]def get_distance_term(kind, c3, c3_epsilon, C, ctx, imt):
"""
Returns the distance attenuation factor
"""
h = _get_h(C, ctx.hypo_depth)
rval = np.sqrt(ctx.rjb ** 2. + h ** 2.)
rref_val = np.sqrt(CONSTANTS["Rref"] ** 2. + h ** 2.)
if kind != 'regional':
c3 = get_distance_coefficients(kind, c3, c3_epsilon, C, imt, ctx)
f_r = (C["c1"] + C["c2"] * (ctx.mag - CONSTANTS["Mref"])) *\
np.log(rval / rref_val) + (c3 * (rval - rref_val) / 100.)
return f_r
[docs]def get_magnitude_scaling(C, mag):
"""
Returns the magnitude scaling term
"""
d_m = mag - CONSTANTS["Mh"]
return np.where(mag <= CONSTANTS["Mh"],
C["e1"] + C["b1"] * d_m + C["b2"] * d_m ** 2.0,
C["e1"] + C["b3"] * d_m)
[docs]def get_dl2l(tec, ctx, imt, delta_l2l_epsilon):
"""
Returns rupture source specific delta_l2l values. The method
retrieves the delta_l2l and standard error of delta_l2l values.
if delta_l2l_epsilon is provided, standard error of delta_c3
will be included. A delta_l2l_epsilon value of +/- 1.6 gives
the 95% confidence interval for delta_l2l.
"""
f = [(Point(lon, lat)) for lon, lat in zip(ctx.hypo_lon, ctx.hypo_lat)]
dl2l = np.zeros((len(ctx.hypo_lon), 2), dtype=float)
for i, feature in enumerate(tec):
prepared_polygon = prep(shape(feature['geometry']))
contained = list(filter(prepared_polygon.contains, f))
if contained:
ll = np.concatenate([
np.where((ctx['hypo_lon'] == p.x) &
(ctx['hypo_lat'] == p.y))[0] for p in contained])
dl2l[ll, 0] = feature['properties'][str(imt)]
dl2l[ll, 1] = feature['properties'][str(imt)+'_se']
return dl2l[:, 0] + delta_l2l_epsilon * dl2l[:, 1]
[docs]def get_sigma_mu_adjustment(kind, C, imt, ctx):
"""
Returns the sigma_mu adjusment factor, which is taken as the
maximum of tau_L2L and the sigma_mu. For M < 7.4
the sigma statistical does not exceed tau_L2L at any period or
distance. For M > 7.4, sigma_mu is approximately linear up to M 8.0
so we interpolate between the two values and cap sigma statistical
at M 8.0
"""
C_SIG_MU = AVGSA_SIGMA_MU_COEFFS[imt] if kind.startswith("avgsa") else\
SIGMA_MU_COEFFS[imt]
uf = np.full_like(ctx.mag, C_SIG_MU["sigma_mu_m8_intermediate"])
lf = np.full_like(ctx.mag, C_SIG_MU["sigma_mu_m7p4_intermediate"])
idx = ctx.hypo_depth < 10.0
uf[idx] = C_SIG_MU["sigma_mu_m8_shallow"]
lf[idx] = C_SIG_MU["sigma_mu_m7p4_shallow"]
idx = ctx.hypo_depth >= 20.0
uf[idx] = C_SIG_MU["sigma_mu_m8_deep"]
lf[idx] = C_SIG_MU["sigma_mu_m7p4_deep"]
adj = np.maximum(C["tau_l2l"], ITPL(ctx.mag, uf, lf, 7.4, 0.6))
# Below M 7.4 tau_L2L is always larger than sigma mu
adj[ctx.mag < 7.4] = C["tau_l2l"]
# Cap the sigma mu as the value for M 8.0
adj[ctx.mag >= 8.0] = np.maximum(C["tau_l2l"], uf[ctx.mag >= 8.0])
return adj
[docs]def get_site_amplification(kind, extra, C, ctx, imt):
"""
Apply the correct site amplification depending on the kind of GMPE
"""
if kind in {"base", "avgsa_base"}: # no site amplification
ampl = 0.
elif kind in {"site", "regional"}:
# Render with respect to 800 m/s reference Vs30
sref = np.log(ctx.vs30 / 800.)
ampl = (C["g0_vs30"] + C["g1_vs30"] * sref +
C["g2_vs30"] * (sref ** 2.))
elif kind == "slope":
# Render with respect to 0.1 m/m reference slope
sref = np.log(ctx.slope / 0.1)
ampl = (C["g0_slope"] + C["g1_slope"] * sref +
C["g2_slope"] * (sref ** 2.))
elif kind in {"ESHM20", "avgsa_ESHM20", "avgsa_ESHM20_homoskedastic"}:
vs30 = np.copy(ctx.vs30)
vs30[vs30 > 1100.] = 1100.
ampl = np.zeros(vs30.shape)
# For observed vs30 ctx
ampl[ctx.vs30measured] = (C["d0_obs"] + C["d1_obs"] *
np.log(vs30[ctx.vs30measured]))
# For inferred Vs30 ctx
idx = np.logical_not(ctx.vs30measured)
ampl[idx] = (C["d0_inf"] + C["d1_inf"] * np.log(vs30[idx]))
elif kind in {"geology", "avgsa_ESHM20_geology"}:
C_AMP_FIXED = extra['COEFFS_FIXED'][imt]
C_AMP_RAND_INT = extra['COEFFS_RANDOM_INT'][imt]
C_AMP_RAND_GRAD = extra['COEFFS_RANDOM_GRAD'][imt]
ampl = np.zeros(ctx.slope.shape)
geol_units = np.unique(ctx.geology)
t_slope = np.copy(ctx.slope)
t_slope[t_slope > 0.3] = 0.3
# Slope lower than 0.0005 m/m takes value for 0.0005 m/m
t_slope[t_slope < 0.0005] = 0.0005
for geol_unit in geol_units:
idx = ctx.geology == geol_unit
if geol_unit in extra['GEOLOGICAL_UNITS']:
unit = geol_unit.decode()
# Supported geological unit, use the random effects model
v1 = C_AMP_FIXED["V1"] + C_AMP_RAND_INT[unit]
v2 = C_AMP_FIXED["V2"] + C_AMP_RAND_GRAD[unit]
else:
# Unrecognised geological unit, use the fixed effects model
v1 = C_AMP_FIXED["V1"]
v2 = C_AMP_FIXED["V2"]
ampl[idx] = v1 + v2 * np.log(t_slope[idx])
return ampl
[docs]def get_stddevs(kind, ergodic, phi_s2s, C, ctx, imt):
"""
Returns the homoskedastic standard deviation model
"""
mag = ctx.mag
if kind in {"ESHM20", "geology"}:
# Get the heteroskedastic tau and phi0
tau = get_tau(imt, mag)
phi = get_phi_ss(imt, mag)
elif kind in {'avgsa_ESHM20', "avgsa_ESHM20_geology"}:
# Get the heteroskedastic tau and phi0 for AvgSA
tau, phi = get_heteroskedastic_tau_phi0_avgsa(imt, ctx.mag)
else:
# Get the homoskedastic tau and phi0
tau = C["tau_event_0"]
phi = C["phi_0"]
if ergodic:
if kind in {'ESHM20', "geology", "avgsa_ESHM20_geology",
"avgsa_ESHM20", "avgsa_ESHM20_homoskedastic"}:
# phi_s2s retrieved in the compute() function of the GMM
phi = np.sqrt(phi ** 2. + phi_s2s ** 2.)
elif kind in {"site", "regional"}:
phi = np.sqrt(phi ** 2.0 + C["phi_s2s_vs30"] ** 2.)
elif kind == 'slope':
phi = np.sqrt(phi ** 2.0 + C["phi_s2s_slope"] ** 2.)
else:
phi = np.sqrt(phi ** 2. + C["phis2s"] ** 2.)
return [np.sqrt(tau ** 2. + phi ** 2.), tau, phi]
[docs]class KothaEtAl2020(GMPE):
"""
Implements the first complete version of the newly derived GMPE
for Shallow Crustal regions using the Engineering Strong Motion Flatfile.
Kotha, S. R., Weatherill, G., Bindi, D., Cotton F. (2020) "A regionally-
adaptable ground-motion model for shallow crustal earthquakes in Europe.
Bulletin of Earthquake Engineering, 18:4091-4125
The GMPE is desiged for regional adaptation within a logic-tree framework,
and as such contains several parameters that can be calibrated on input:
1) Source-region scaling, a simple scalar factor that defines how much
to increase or decrease the "regional average" ground motion in the region.
This value is taken as the maximum of the source-region variability term
(tau_l2l) and the statistical uncertainty (sigma_mu). The latter defines
the within-model uncertainty owing to the data set from which the model is
derived and only exceeds the former at large magnitudes
2) Residual attenuation scaling "c3", a factor that controls the residual
attenuation part of the model to make the ground motion decay more or less
rapidly with distance than the regional average.
Both factors are period dependent.
The two adaptable factors can be controlled either by direct specification
at input (in the form of an imt-dependent dictionary) or by a number of
standard deviations multiplying the existing variance terms. The two
approaches are mutually exclusive, with the directly specified parameters
always being used if defined on input.
In the core form of the GMPE no site term is included. This is added in the
subclasses.
:param float sigma_mu_epsilon:
Parameter to control the source-region scaling as a number of
standard deviations by which to multiply the source-region to source-
region variance, max(tau_l2l, sigma_mu)
:param float c3_epsilon:
Parameter to control the residual attenuation scaling as a number
of standard deviations by which to multiply the attenuation-region
variance, tau_c3.
User supplied table for the coefficient c3 controlling the anelastic
attenuation as an instance of :class:
`openquake.hazardlib.gsim.base.CoeffsTable`. If absent, the value is
taken from the normal coefficients table.
:param bool ergodic:
Use the ergodic standard deviation (True) or non-ergodic standard
deviation (False)
:param dict dl2l:
If specifying the source-region scaling directly, defines the
increase or decrease of the ground motion in the form of an imt-
dependent dictionary of delta L2L factors
:param dict c3:
If specifying the residual attenuation scaling directly, defines the
apparent anelastic attenuation term, c3, as an imt-dependent
dictionary
"""
kind = "base"
#: 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, PGV, SA}
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: 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 not set
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude and hypocentral depth
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'}
#: Required distance measure is Rjb (eq. 1).
REQUIRES_DISTANCES = {'rjb'}
def __init__(self, sigma_mu_epsilon=0.0, c3_epsilon=0.0, ergodic=True,
dl2l=None, c3=None, **kwargs):
"""
Instantiate setting the sigma_mu_epsilon and c3 terms
"""
super().__init__(sigma_mu_epsilon=sigma_mu_epsilon,
c3_epsilon=c3_epsilon, ergodic=ergodic, **kwargs)
self.sigma_mu_epsilon = sigma_mu_epsilon
self.c3_epsilon = c3_epsilon
self.ergodic = ergodic
if dl2l:
# Check that the input is a dictionary and p
if not isinstance(dl2l, dict):
raise IOError("For Kotha et al. (2020) GMM, source-region "
"scaling parameter (dl2l) must be input in the "
"form of a dictionary, if specified")
self.dl2l = {}
for key in dl2l:
self.dl2l[from_string(key)] = {"dl2l": dl2l[key]}
self.dl2l = CoeffsTable.fromdict(self.dl2l)
else:
self.dl2l = None
if c3:
if not isinstance(c3, dict):
raise IOError("For Kotha et al. (2020) GMM, residual "
"attenuation scaling (c3) must be input in the "
"form of a dictionary, if specified")
self.c3 = {}
for key in c3:
self.c3[from_string(key)] = {"c3": c3[key]}
self.c3 = CoeffsTable.fromdict(self.c3)
else:
self.c3 = None
[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]
extra = {}
if self.kind in {'ESHM20', "avgsa_ESHM20",
"avgsa_ESHM20_homoskedastic"}:
phi_s2s = np.zeros(ctx.vs30measured.shape, dtype=float)
phi_s2s[ctx.vs30measured] += C["phi_s2s_obs"]
phi_s2s[np.logical_not(ctx.vs30measured)] += C["phi_s2s_inf"]
elif self.kind in {'geology', "avgsa_ESHM20_geology"}:
phi_s2s = self.COEFFS_FIXED[imt]["phi_s2s"]
extra['COEFFS_FIXED'] = self.COEFFS_FIXED
extra['COEFFS_RANDOM_INT'] = self.COEFFS_RANDOM_INT
extra['COEFFS_RANDOM_GRAD'] = self.COEFFS_RANDOM_GRAD
extra['GEOLOGICAL_UNITS'] = self.GEOLOGICAL_UNITS
else:
phi_s2s = None
if self.kind == 'regional':
c3 = get_distance_coefficients_3(self.att,
self.delta_c3_epsilon,
C, imt, ctx)
else:
c3 = self.c3
fp = get_distance_term(self.kind, c3, self.c3_epsilon,
C, ctx, imt)
mean[m] = (get_magnitude_scaling(C, ctx.mag) + fp +
get_site_amplification(self.kind, extra, C, ctx, imt))
# GMPE originally in cm/s/s - convert to g
if imt.string.startswith(('PGA', 'SA', 'AvgSA')):
mean[m] -= np.log(100.0 * g)
sig[m], tau[m], phi[m] = get_stddevs(
self.kind, self.ergodic, phi_s2s, C, ctx, imt)
if self.dl2l:
# The source-region parameter is specified explicity
mean[m] += self.dl2l[imt]["dl2l"]
elif self.kind == 'regional':
dl2l = get_dl2l(self.tec, ctx, imt, self.delta_l2l_epsilon)
mean[m] += dl2l
elif self.sigma_mu_epsilon:
# epistemic uncertainty factor (sigma_mu) multiplied by
# the number of standard deviations
sigma_mu = get_sigma_mu_adjustment(self.kind, C, imt, ctx)
mean[m] += self.sigma_mu_epsilon * sigma_mu
# Coefficients obtained direclty from the regression outputs of
# Kotha et al. (2020)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt e1 b1 b2 b3 c1 c2 c3 tau_c3 phis2s tau_event_0 tau_l2l phi_0 g0_vs30 g1_vs30 g2_vs30 phi_s2s_vs30 g0_slope g1_slope g2_slope phi_s2s_slope
pgv 1.11912161648479 2.55771078860152 0.353267224391297 0.879839839344054 -1.41931258132547 0.2706807258213520 -0.304426142175370 0.178233997535235 0.560627759977840 0.422935885699239 0.258560350227890 0.446525247049620 -0.232891265610189 -0.492356618589364 0.0247963168536102 0.366726744441574 -0.0550827970556740 -0.1469535974165200 -0.00893120461876375 0.434256033254051
pga 3.93782347219377 2.06573167101440 0.304988012209292 0.444773874960317 -1.49787542346412 0.2812414746313380 -0.609876182476899 0.253818777234181 0.606771946180224 0.441761487685862 0.355279206886721 0.467151252053241 -0.222196028066344 -0.558848724731566 -0.1330148640403130 0.389712940326169 -0.0267105106085816 -0.1098813702713090 -0.01742373265620930 0.506725958082485
0.010 3.94038760011295 2.06441772899445 0.305294151898347 0.444352974827805 -1.50006146971318 0.2816120431678390 -0.608869451197394 0.253797652143759 0.607030265833062 0.441635449735044 0.356047209347534 0.467206938011971 -0.221989239810027 -0.558181442039516 -0.1330144520414310 0.391254585814764 -0.0266572723455345 -0.1097145490975510 -0.01741863169765470 0.506706245975056
0.025 3.97499686979384 2.04519749120013 0.308841647142436 0.439374383710060 -1.54376149680542 0.2830031280602480 -0.573207556417252 0.252734624432000 0.610030865927204 0.437676505154608 0.368398604288111 0.468698397037258 -0.218745638720123 -0.546810177342948 -0.1315295091425130 0.395303566681041 -0.0254040142855204 -0.1072422064249640 -0.01765069385301560 0.506705856554187
0.040 4.08702279605872 1.99149766561616 0.319673428428720 0.418531185104657 -1.63671359040283 0.2984823762486280 -0.535139204130152 0.244894143623498 0.626413180170373 0.429637401735540 0.412921240156940 0.473730661220076 -0.206923687805771 -0.525141264234585 -0.1368798835282360 0.415116874033842 -0.0222919270649348 -0.1024278275345350 -0.01847074311083690 0.515812197849121
0.050 4.18397570399970 1.96912968528742 0.328982074841989 0.389853296189063 -1.66358950776148 0.3121928913488560 -0.555191107011420 0.260330694464557 0.638967955474841 0.433639923327438 0.444324049044753 0.479898166019243 -0.205629239209508 -0.514739138349666 -0.1368385040078350 0.422549340781658 -0.0209153599570857 -0.0989203779863760 -0.01851248498790100 0.526875631632610
0.070 4.38176649786342 1.92450788134500 0.321182873495225 0.379581373255289 -1.64352914575492 0.3138101953091510 -0.641089475725666 0.286976037026550 0.661064599433347 0.444338223383705 0.470938801038256 0.487060899687138 -0.209348356311787 -0.506896476331228 -0.1456117952510990 0.443318525820235 -0.0188838682625869 -0.0951010574545904 -0.01880576764531640 0.553542604942032
0.100 4.60722959404894 1.90125096928647 0.298805051330753 0.393002352641809 -1.54339428982169 0.2849395739776680 -0.744270750619733 0.321927482439715 0.663309669119995 0.458382304191096 0.478737965504940 0.496152397155402 -0.193509476649993 -0.521463491048192 -0.1824674441457950 0.437214022468042 -0.0165212272103937 -0.0871969707343552 -0.01674749313351450 0.537128822815826
0.150 4.78583314367062 1.92620172077838 0.249893333649662 0.435396192976506 -1.38136438628699 0.2254113422224680 -0.815688997995934 0.322145126407981 0.655406109737959 0.459702777214781 0.414046169030935 0.497805936702476 -0.215418461095753 -0.579757224642522 -0.2016525247813580 0.457311836251173 -0.0153013615272199 -0.0898557092287409 -0.01820533201066010 0.548306674706135
0.200 4.81847463780069 1.97006598187863 0.218722883323200 0.469713318293785 -1.30697558633587 0.1826533194804230 -0.773372802995208 0.301795870071949 0.643585009231006 0.464006126996261 0.321975745683642 0.494075956910651 -0.232802520913539 -0.646162914187111 -0.2102452066359760 0.449595599604904 -0.0185432743074803 -0.1091715402153590 -0.02203326475372750 0.542391858770537
0.250 4.75134747347049 2.01097445156370 0.195062831156806 0.532210412551561 -1.26259484078950 0.1551575007473110 -0.722012122448262 0.274998157533509 0.623240061418664 0.457687642192569 0.293329526713994 0.488950837091220 -0.238646255489286 -0.649028548718928 -0.1965317433344580 0.449701754122993 -0.0268512786854638 -0.1177223461809770 -0.01990310375762760 0.514759188358396
0.300 4.65252285968525 2.09278551802016 0.194929941231544 0.557034893811231 -1.24071282395616 0.1370008066985060 -0.660466290850886 0.260774631679394 0.609748615552919 0.457514283978959 0.266836791529257 0.482157450259502 -0.246093988657936 -0.645741652187205 -0.1720972685448300 0.429850112026890 -0.0356644839782008 -0.1265719157414280 -0.01728437065375890 0.490014753971745
0.350 4.53350897671045 2.14179725762371 0.189511462582876 0.609892595327716 -1.21514531872583 0.1247122464559250 -0.618593385936676 0.254261888951322 0.609506191611413 0.450960093750492 0.231614185359720 0.480254056040507 -0.254026518879524 -0.648402249765170 -0.1446513637358710 0.397602725132059 -0.0423519589829896 -0.1401638874897640 -0.01672203482354180 0.483807852643816
0.400 4.44193244811952 2.22862498827440 0.200305171692326 0.614767001033243 -1.18897228839914 0.1156387616270450 -0.591574546068960 0.243643375298288 0.615477199296824 0.441122908694716 0.240825814626397 0.475193646646757 -0.263328502132230 -0.653476851717702 -0.1186474533289450 0.439991306965322 -0.0452239204802930 -0.1514100096093150 -0.01778303668068960 0.500388492016146
0.450 4.33697728548038 2.29103572171716 0.209573442606565 0.634252522127606 -1.18013993982454 0.1100834686500940 -0.555234498707119 0.245883260391068 0.619384591074073 0.436294164198843 0.249245758570064 0.469672671050266 -0.264631841951527 -0.638852650094042 -0.0836039291412020 0.424224393510765 -0.0543649832422398 -0.1588148016645050 -0.01500762961938830 0.492980996451707
0.500 4.23507897753587 2.35399193121686 0.218088423514177 0.658541873692286 -1.17726165949601 0.1026978146186720 -0.519413341065942 0.238559829231160 0.624993564560933 0.428500398327627 0.243778652813106 0.463165027132890 -0.269124654561252 -0.626175743644433 -0.0537720540773490 0.423230860170143 -0.0610661425543540 -0.1647334612739770 -0.01304441434577370 0.495138633047097
0.600 4.02306439391925 2.42753387249929 0.218787915039312 0.754615594874153 -1.16678688970027 0.0940582863096094 -0.454043559543982 0.216855298090451 0.635090711921061 0.426296731581312 0.246117069779268 0.451206692163190 -0.269626118151597 -0.582682427052082 0.0203225530214242 0.475220856944347 -0.0680919086636438 -0.1730542985615550 -0.00960057312582767 0.510149252547482
0.700 3.83201580121827 2.51268432884949 0.225024841305000 0.765438564882833 -1.16236278470164 0.0865917976706938 -0.397781532595396 0.215716276719833 0.633635835573626 0.425379430268476 0.246750734502549 0.446704739768374 -0.272441022824943 -0.558163103244591 0.0652728074463838 0.446489639181972 -0.0742129950461250 -0.1739452472381870 -0.00549504377749866 0.502939558871623
0.750 3.74614211993052 2.55840246083607 0.231604957273506 0.793480645885641 -1.15333203234665 0.0824927940948198 -0.376630503031279 0.209593410875067 0.637877956868669 0.428563811859323 0.245166749142241 0.444311331912854 -0.268471953245116 -0.546146873703377 0.0840210504832594 0.451727019248850 -0.0742883211225450 -0.1757280229442730 -0.00571924409424620 0.513908669690317
0.800 3.65168809980226 2.59467404437385 0.237334498546207 0.828241777740572 -1.14645090256437 0.0837439530041729 -0.363246464853852 0.192106714053294 0.638753820813416 0.433880652259324 0.240072953116796 0.439300059540554 -0.268043587730749 -0.528310722806634 0.1053131905955920 0.476641301777151 -0.0733362133528447 -0.1769632805164950 -0.00623439334393725 0.516534123477592
0.900 3.51228638217709 2.68810225072750 0.251716558693382 0.845561170244942 -1.13599614124436 0.0834018259445213 -0.333908265367165 0.177456610405390 0.640328521929993 0.438913972406961 0.247662698012904 0.433043490235851 -0.270747888599204 -0.498749188701101 0.1514549282913290 0.492678009609922 -0.0705690120386147 -0.1842212802961380 -0.00948523310240806 0.508758129697782
1.000 3.36982044793917 2.74249776483975 0.256784133033388 0.896648260528882 -1.12443352348542 0.0854384622609198 -0.317465939881623 0.171997778367260 0.638429444564638 0.444086895369946 0.238111905941701 0.426703815544157 -0.268682366673877 -0.472355589159814 0.1912725393732170 0.486349823748500 -0.0730202296385978 -0.1861995093276410 -0.00833302021378029 0.499129039268700
1.200 3.10224418952824 2.82683484364226 0.262683442221073 0.982921357727718 -1.12116148624672 0.0973231293288241 -0.275616235541070 0.160445653296358 0.640086303643832 0.446121165446841 0.226825215617356 0.416539877732589 -0.263517582328224 -0.465411813875967 0.2014565230611100 0.460802894674431 -0.0761329216007339 -0.1923688484322410 -0.00790676960410267 0.494333782654409
1.400 2.84933745949861 2.89911332547612 0.272065572034688 1.040000637056720 -1.12848926976065 0.1002887249133400 -0.234977212668109 0.150949141990859 0.649359928046388 0.457011583377380 0.231922092201736 0.409641113489270 -0.253077954003716 -0.450716220871832 0.1900019177957120 0.520330220947425 -0.0777847149574368 -0.1977821544457880 -0.00694977055552574 0.521824672837616
1.600 2.63503429015231 2.98365736561984 0.289670716036571 1.073002118658300 -1.14064711059980 0.1100788214866130 -0.198050139347725 0.148738498099927 0.650540540696659 0.462781403376806 0.223897549097876 0.404985162254916 -0.246009048662975 -0.427498542497053 0.2013164560891230 0.498576704112864 -0.0808481108779988 -0.1956817304755080 -0.00420478503206788 0.520676267977361
1.800 2.43032254290751 3.06358840071518 0.316828766785138 1.109809835991900 -1.15419967841818 0.1131278831612640 -0.167123738873435 0.156141593013035 0.656949311785981 0.468432106332010 0.205207971335941 0.399057812399511 -0.259365145858505 -0.436165813138372 0.2103523943478280 0.494419960120798 -0.0866501788741884 -0.1968633287340960 0.00084917955133917 0.521315249011902
2.000 2.24716354703519 3.11067747935049 0.326774527695550 1.132479221218060 -1.16620971948721 0.1162990300931710 -0.140731664063789 0.155054491423268 0.647763389017009 0.476577198889343 0.196850466599025 0.396502973620567 -0.255846430844076 -0.425096032934296 0.2073318834508050 0.484354097558551 -0.0881098607385541 -0.1980665849538590 0.00178776027496752 0.509385313956226
2.500 1.83108464781202 3.23289020747997 0.374214285707986 1.226390493979360 -1.17531326311999 0.1395412164588280 -0.120745041347963 0.176744551716694 0.629481669044830 0.479859874942997 0.190867925368865 0.393288023064441 -0.257425360830402 -0.394240493031487 0.2135940556445740 0.460612029226665 -0.0842255772225518 -0.1909303606402940 0.00128428761198652 0.505686965707424
3.000 1.58259215964414 3.44640772476285 0.454951810817816 1.313954219909490 -1.15664484431459 0.1494902905791280 -0.149050671035371 0.174876785480317 0.616446588503561 0.488309107285476 0.220914253465451 0.390859427279163 -0.251876760182310 -0.364653376508969 0.2122004191615380 0.407986805228384 -0.0784780440908414 -0.1844510105227600 -0.00047381737627311 0.485603444879608
3.500 1.32153652077149 3.56445182133655 0.518610571029448 1.394984393379380 -1.16368470057735 0.1543445278711660 -0.142873831246493 0.193619214137258 0.600202108018105 0.479187019962682 0.237281350236338 0.388102875218375 -0.242628051593659 -0.322323015714785 0.2138248326399060 0.396737062193148 -0.0787732613082041 -0.1718918693565610 0.00223831455352896 0.479608514060425
4.000 1.10607064193676 3.64336885536264 0.555331865800278 1.418144933323620 -1.17757508691221 0.1730832048262120 -0.142053716741244 0.193571789393738 0.593046407283143 0.482524831704549 0.233827536969510 0.386956009422453 -0.239634395956042 -0.294311486158724 0.2268951652965890 0.396113359026388 -0.0764209712209348 -0.1648847320168560 0.00295327439998048 0.475041314185757
4.500 1.05987610378773 3.82152567982841 0.666476453600402 1.430548279466630 -1.17323633891422 0.1936210609543320 -0.156076448842833 0.152553585766189 0.581331910387036 0.456765160173852 0.196697785051230 0.372827866334900 -0.246998133746262 -0.241579092689847 0.2474533712720740 0.397717123177902 -0.0668746312766319 -0.1735273164380950 -0.00530669973001712 0.473200567096548
5.000 0.82373381739570 3.84747968562771 0.684665144355361 1.496536314224210 -1.20969230916539 0.2213041109459350 -0.126052481240424 0.137919529808920 0.558954997903623 0.464229101930025 0.195572800413952 0.377458812369736 -0.234334071379258 -0.208962718979667 0.2332755435126690 0.338344656676906 -0.0617201190392144 -0.1636990315777190 -0.00649134386415973 0.450949884766277
6.000 0.50685354955206 3.80040950285788 0.700805222359295 1.625591116375650 -1.22440411739130 0.2292764533844400 -0.113766839623945 0.141669390606605 0.538973145096788 0.439059204276786 0.190680023411634 0.384862538848542 -0.205342867591920 -0.166350345553781 0.2189842473229210 0.338688052762081 -0.0568786587375636 -0.1519590377762100 -0.00580039515645921 0.439827391985479
7.000 0.19675504234642 3.78431011962409 0.716569352050671 1.696310364814470 -1.28517895409644 0.2596896867469380 -0.070585399916418 0.146488759166368 0.523331606096182 0.434396029381517 0.208231539543981 0.385850838707000 -0.204046508080049 -0.155173106999605 0.2164856914333770 0.339211265835413 -0.0541313319257671 -0.1393109833551150 -0.00443019667996698 0.432359150492787
8.000 -0.08979569600589 3.74815514351616 0.726493405776986 1.695347146909250 -1.32882937608962 0.2849197966362740 -0.051296439369391 0.150981191615944 0.508537123776905 0.429104860654150 0.216201318346277 0.387633769846605 -0.193908824182191 -0.148759113452472 0.2094261301289650 0.337650861518699 -0.0507933301386227 -0.1365792860813190 -0.00532310915144333 0.411101516213337
""")
[docs]class KothaEtAl2020regional(KothaEtAl2020):
"""
Adaptation of the Kotha et al. (2020) GMPE using
the source and site specific adjustments.
"""
experimental = True
#: Required rupture parameters are magnitude, hypocentral location
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_lat', 'hypo_lon', 'hypo_depth'}
#: Required site parameter are vs30, lat and lon of the site
REQUIRES_SITES_PARAMETERS = {'vs30', 'lat', 'lon'}
kind = "regional"
def __init__(self, delta_l2l_epsilon=0.0, delta_c3_epsilon=0.0,
ergodic=True, c3=None, dl2l=None, **kwargs):
"""
Instantiate setting the dl2l and c3 terms.
"""
super().__init__(delta_l2l_epsilon=delta_l2l_epsilon,
delta_c3_epsilon=delta_c3_epsilon,
ergodic=ergodic, **kwargs)
self.delta_l2l_epsilon = delta_l2l_epsilon
self.delta_c3_epsilon = delta_c3_epsilon
self.ergodic = ergodic
attenuation_file = os.path.join(DATA_FOLDER, 'kotha_attenuation_regions.geojson')
self.att = list(fiona.open(attenuation_file))
tectonic_file = os.path.join(DATA_FOLDER, 'kotha_tectonic_regions.geojson')
self.tec = list(fiona.open(tectonic_file))
[docs]class KothaEtAl2020Site(KothaEtAl2020):
"""
Preliminary adaptation of the Kotha et al. (2020) GMPE using
a polynomial site amplification function dependent on Vs30 (m/s)
"""
#: Required site parameter is not set
REQUIRES_SITES_PARAMETERS = {"vs30"}
kind = "site"
[docs]class KothaEtAl2020Slope(KothaEtAl2020):
"""
Preliminary adaptation of the Kotha et al. (2020) GMPE using
a polynomial site amplification function dependent on slope (m/m)
"""
#: Required site parameter is not set
REQUIRES_SITES_PARAMETERS = {"slope"}
kind = "slope"
# Defines the c3 distribution (expected and variance [tau]) for each of the
# residual attenuation regions shown in Weatherill et al. (2020)
C3_REGIONS = CoeffsTable(sa_damping=5, table="""\
imt region_1 tau_region_1 region_2 tau_region_2 region_3 tau_region_3 region_4 tau_region_4 region_5 tau_region_5
pga -0.45763990 0.12162060 -0.67064060 0.07538030 -0.94171710 0.10869170 -0.58146760 0.06361280 -0.06978450 0.11077130
0.010 -0.45625230 0.12146360 -0.67063220 0.07654980 -0.93989760 0.10676080 -0.58019070 0.06459080 -0.09103080 0.12710680
0.025 -0.42309710 0.11756810 -0.63522410 0.07630320 -0.90689690 0.11038900 -0.54050790 0.07589760 -0.12747550 0.16806130
0.040 -0.39097280 0.11707830 -0.59696790 0.07228980 -0.85504400 0.12076280 -0.50717210 0.07771300 -0.14249730 0.18893460
0.050 -0.39513900 0.11826330 -0.61908410 0.07248790 -0.89234840 0.12109140 -0.53160100 0.07993880 -0.13942630 0.18369880
0.070 -0.45957040 0.10764180 -0.71040880 0.09406360 -1.00552160 0.13724410 -0.63070410 0.10958830 -0.13291470 0.17896380
0.100 -0.52099420 0.13029080 -0.82289280 0.09869630 -1.15422780 0.13169510 -0.75266100 0.11450560 -0.08288840 0.11615220
0.150 -0.59200740 0.12319070 -0.89972030 0.08844380 -1.24255770 0.16734440 -0.82179530 0.08966500 -0.21028500 0.16064740
0.200 -0.57153280 0.13489290 -0.84916880 0.07358340 -1.19208340 0.15783590 -0.76891860 0.05839290 -0.21648230 0.17399630
0.250 -0.55014010 0.14351500 -0.78444460 0.07522180 -1.10829210 0.17141070 -0.70329730 0.06207950 -0.18984460 0.18522660
0.300 -0.50509870 0.14583000 -0.71748520 0.07218780 -1.02348990 0.16273460 -0.63133950 0.06122670 -0.13991660 0.19909820
0.350 -0.48056150 0.14950310 -0.67675880 0.06622260 -0.95401710 0.14718070 -0.57059020 0.09801470 -0.11083090 0.20642470
0.400 -0.46882610 0.15182940 -0.64969270 0.06447500 -0.90303360 0.15704530 -0.53491330 0.11598100 -0.09551250 0.21549390
0.450 -0.44202290 0.15440110 -0.60495950 0.06457860 -0.86315180 0.14679390 -0.49352160 0.13364080 -0.10089570 0.20926840
0.500 -0.42273000 0.14456970 -0.56473220 0.07014270 -0.81550440 0.13322880 -0.45404570 0.14251830 -0.07437870 0.20839480
0.600 -0.37260270 0.11837610 -0.49811720 0.07395310 -0.70844270 0.13133940 -0.39191570 0.13619340 -0.04463750 0.18552380
0.700 -0.32647710 0.11447010 -0.44770750 0.07916100 -0.64266210 0.11883890 -0.32374040 0.14591360 -0.00538170 0.16207570
0.750 -0.31212810 0.10504110 -0.42376660 0.07993050 -0.61865170 0.11495330 -0.30231640 0.14234970 -0.00657300 0.15210100
0.800 -0.30885360 0.09543160 -0.40634850 0.07581030 -0.58033210 0.09944790 -0.28537540 0.12282200 -0.01381650 0.15335160
0.900 -0.29346380 0.09175490 -0.37405220 0.07021550 -0.53477520 0.09812570 -0.24896750 0.10985930 -0.02411190 0.17978300
1.000 -0.28336210 0.09792990 -0.35762020 0.07145350 -0.50242310 0.10013390 -0.23100550 0.10572390 -0.01772240 0.17872480
1.200 -0.25305440 0.08181450 -0.31606630 0.08745020 -0.43732660 0.09978290 -0.18635810 0.09066140 0.01266630 0.16111360
1.400 -0.22429860 0.08927280 -0.27056900 0.09790690 -0.37099700 0.08939350 -0.14771960 0.06408710 0.01575050 0.17588430
1.600 -0.20453730 0.08994080 -0.23500030 0.09531560 -0.32625390 0.14451300 -0.09812040 0.06719240 0.06392270 0.14553870
1.800 -0.18202610 0.09563320 -0.21138570 0.09154740 -0.29356600 0.13625630 -0.05090820 0.06169050 0.14456010 0.09006530
2.000 -0.16424010 0.09879570 -0.18541590 0.09221880 -0.26361980 0.14820630 -0.01584600 0.03570300 0.13974470 0.11070380
2.500 -0.15855170 0.13226060 -0.17398540 0.11824340 -0.23076620 0.12647370 0.02472620 0.05698800 0.19515140 0.09070650
3.000 -0.19290470 0.12142990 -0.20313660 0.11317040 -0.23228890 0.07428720 -0.00302590 0.08495680 0.14726330 0.16269230
3.500 -0.20613910 0.14784030 -0.19631370 0.12839930 -0.21001250 0.06708210 0.01380630 0.11764140 0.14993210 0.11916760
4.000 -0.21595710 0.16486300 -0.20044260 0.12168210 -0.19922260 0.09732930 0.00398580 0.12362070 0.19772940 0.08648060
4.500 -0.22996680 0.14376190 -0.18437470 0.13098060 -0.18127450 0.09355350 -0.03302300 0.12887510 -0.01661270 0.20710350
5.000 -0.19078450 0.12716500 -0.17112740 0.15092340 -0.13823220 0.09430520 -0.02007680 0.12041280 -0.00218690 0.20707570
6.000 -0.18627470 0.12265290 -0.15729310 0.15258570 -0.12751980 0.07698390 -0.02685550 0.12260700 -0.00063180 0.19921860
7.000 -0.13330430 0.13230600 -0.10941040 0.16592930 -0.09001300 0.08303110 -0.00013490 0.12385470 0.05526720 0.19002620
8.000 -0.11027270 0.14320590 -0.07803880 0.16456320 -0.06784910 0.06704120 0.01757900 0.12861430 0.06941030 0.18559830
""")
# Heteroskedastic values for single-station phi from measured and smoothed
# distributions of event- and site- orrected within-event residuals
HETERO_PHI0 = CoeffsTable(sa_damping=5, table="""\
imt a b
pgv 0.44654 0.38340
pga 0.46719 0.36079
0.010 0.46725 0.36104
0.025 0.46874 0.36515
0.040 0.47377 0.37658
0.050 0.47995 0.38890
0.070 0.48709 0.39474
0.100 0.49618 0.39219
0.150 0.49784 0.37381
0.200 0.49409 0.34159
0.250 0.48895 0.34269
0.300 0.48217 0.33936
0.350 0.48025 0.33843
0.400 0.47515 0.34693
0.450 0.46967 0.34665
0.500 0.46318 0.34085
0.600 0.45123 0.33823
0.700 0.44672 0.35944
0.750 0.44428 0.35283
0.800 0.43930 0.34529
0.900 0.43301 0.34187
1.000 0.42666 0.34207
1.200 0.41647 0.35920
1.400 0.40957 0.37407
1.600 0.40494 0.38140
1.800 0.39905 0.36336
2.000 0.39648 0.35648
2.500 0.39329 0.36285
3.000 0.39085 0.36192
3.500 0.38808 0.38585
4.000 0.38696 0.38696
4.500 0.37283 0.37283
5.000 0.37743 0.37743
6.000 0.38494 0.38494
7.000 0.38589 0.38589
8.000 0.38768 0.38768
""")
[docs]def get_tau(imt, mag):
"""
Heteroskedastic Tau model adopts the "global" model from Al Atik (2015)
"""
tau_model = TAU_SETUP["global"]
tau = get_tau_at_quantile(tau_model["MEAN"], tau_model["STD"], None)
return TAU_EXECUTION["global"](imt, mag, tau)
[docs]def get_phi_ss(imt, mag):
"""
Returns the single station phi (or it's variance) for a given magnitude
and intensity measure type according to equation 5.14 of Al Atik (2015)
with coefficients calibrated on the ESM data set and Kotha et al. (2020)
GMPE
"""
C = HETERO_PHI0[imt]
phi = C["a"] + (mag - 5.0) * ((C["b"] - C["a"]) / 1.5)
phi[mag <= 5.0] = C["a"]
phi[mag > 6.5] = C["b"]
return phi
[docs]class KothaEtAl2020ESHM20(KothaEtAl2020):
"""
Adaptation of the Kotha et al. (2020) GMPE for application to the
2020 European Seismic Hazard Model, as described in Weatherill et al.
(2020)
Weatherill, G., Kotha, S. R. and Cotton, F. (2020) "A regionally-adaptable
'scaled-backbone' ground motion logic tree for shallow seismicity in
Europe: application to the 2020 European seismic hazard model". Bulletin
of Earthquake Engineering, 18:5087 - 5117
There are three key adaptations of the original Kotha et al. (2020) GMM:
1) The use of the residual attenuation regions, which represent the five
main sub-regions of Europe with similar attenuation characteristics. The
assignment to a particular group is now a site-dependent property,
requiring the definition of the "eshm20_region", an integer value between
0 and 5 indicating the residual attenuation region to which the site
belongs (1 - 5) or else the default values (0). For each region an expected
c3 and variance, tau_c3, are defined from which the resulting c3 is taken
as a multiple of the number of standard deviations of tau_c3.
2) The site amplification is defined using a two-segment piecewise linear
linear function. This form of the GMPE defines the site in terms of a
measured or inferred Vs30, with the total aleatory variability adjusted
accordingly.
3) A magnitude-dependent heteroskedastic aleatroy uncertainty model is
used for the region-corrected between-event residuals and the site-
corrected within event residuals. The former taken from the "global" tau
model of Al Atik (2015), while the later is adapted from the "global" phi0
model of Al Atik (2015) adapted to the distribution of site-corrected
within-event residuals determined by the original regression of Kotha et
al. (2020).
Al Atik, L. (2015) NGA-East: Ground-Motion Standard Deviation Models for
Central and Eastern North America, PEER Technical Report, No 2015/07
"""
#: Required site parameters are vs30, vs30measured and the eshm20_region
REQUIRES_SITES_PARAMETERS = set(("region", "vs30", "vs30measured"))
kind = "ESHM20"
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt e1 b1 b2 b3 c1 c2 c3 tau_c3 phi_s2s tau_event_0 tau_l2l phi_0 d0_obs d1_obs phi_s2s_obs d0_inf d1_inf phi_s2s_inf
pgv 1.11912161648479 2.55771078860152 0.353267224391297 0.879839839344054 -1.41931258132547 0.2706807258213520 -0.304426142175370 0.178233997535235 0.560627759977840 0.422935885699239 0.258560350227890 0.446525247049620 3.30975201 -0.53326451 0.36257068 2.78401517 -0.43790954 0.42677529
pga 3.93782347219377 2.06573167101440 0.304988012209292 0.444773874960317 -1.49787542346412 0.2812414746313380 -0.609876182476899 0.253818777234181 0.606771946180224 0.441761487685862 0.355279206886721 0.467151252053241 2.65261454 -0.43301831 0.38806156 1.88258216 -0.29656277 0.51606938
0.010 3.94038760011295 2.06441772899445 0.305294151898347 0.444352974827805 -1.50006146971318 0.2816120431678390 -0.608869451197394 0.253797652143759 0.607030265833062 0.441635449735044 0.356047209347534 0.467206938011971 2.56961762 -0.41981270 0.40044760 1.82057082 -0.28687880 0.51867018
0.025 3.97499686979384 2.04519749120013 0.308841647142436 0.439374383710060 -1.54376149680542 0.2830031280602480 -0.573207556417252 0.252734624432000 0.610030865927204 0.437676505154608 0.368398604288111 0.468698397037258 2.52820436 -0.41328371 0.40623719 1.79206766 -0.28244435 0.52160624
0.040 4.08702279605872 1.99149766561616 0.319673428428720 0.418531185104657 -1.63671359040283 0.2984823762486280 -0.535139204130152 0.244894143623498 0.626413180170373 0.429637401735540 0.412921240156940 0.473730661220076 2.42784360 -0.39762162 0.41977221 1.72300482 -0.27169228 0.53093819
0.050 4.18397570399970 1.96912968528742 0.328982074841989 0.389853296189063 -1.66358950776148 0.3121928913488560 -0.555191107011420 0.260330694464557 0.638967955474841 0.433639923327438 0.444324049044753 0.479898166019243 2.30956730 -0.37937894 0.43465421 1.64224336 -0.25906654 0.54404664
0.070 4.38176649786342 1.92450788134500 0.321182873495225 0.379581373255289 -1.64352914575492 0.3138101953091510 -0.641089475725666 0.286976037026550 0.661064599433347 0.444338223383705 0.470938801038256 0.487060899687138 2.21859665 -0.36551691 0.44921838 1.56920377 -0.24754055 0.55532276
0.100 4.60722959404894 1.90125096928647 0.298805051330753 0.393002352641809 -1.54339428982169 0.2849395739776680 -0.744270750619733 0.321927482439715 0.663309669119995 0.458382304191096 0.478737965504940 0.496152397155402 2.22143266 -0.36624939 0.46432610 1.53915732 -0.24268225 0.56118134
0.150 4.78583314367062 1.92620172077838 0.249893333649662 0.435396192976506 -1.38136438628699 0.2254113422224680 -0.815688997995934 0.322145126407981 0.655406109737959 0.459702777214781 0.414046169030935 0.497805936702476 2.35118737 -0.38662423 0.47703588 1.59963888 -0.25206957 0.55911690
0.200 4.81847463780069 1.97006598187863 0.218722883323200 0.469713318293785 -1.30697558633587 0.1826533194804230 -0.773372802995208 0.301795870071949 0.643585009231006 0.464006126996261 0.321975745683642 0.494075956910651 2.55240529 -0.41806691 0.48025344 1.75423282 -0.27634242 0.54824186
0.250 4.75134747347049 2.01097445156370 0.195062831156806 0.532210412551561 -1.26259484078950 0.1551575007473110 -0.722012122448262 0.274998157533509 0.623240061418664 0.457687642192569 0.293329526713994 0.488950837091220 2.74904047 -0.44882046 0.46891833 1.96527860 -0.30954933 0.53109975
0.300 4.65252285968525 2.09278551802016 0.194929941231544 0.557034893811231 -1.24071282395616 0.1370008066985060 -0.660466290850886 0.260774631679394 0.609748615552919 0.457514283978959 0.266836791529257 0.482157450259502 2.93212957 -0.47759683 0.44983953 2.19913556 -0.34634476 0.51454301
0.350 4.53350897671045 2.14179725762371 0.189511462582876 0.609892595327716 -1.21514531872583 0.1247122464559250 -0.618593385936676 0.254261888951322 0.609506191611413 0.450960093750492 0.231614185359720 0.480254056040507 3.12993498 -0.50873128 0.43569377 2.44212272 -0.38459154 0.50459028
0.400 4.44193244811952 2.22862498827440 0.200305171692326 0.614767001033243 -1.18897228839914 0.1156387616270450 -0.591574546068960 0.243643375298288 0.615477199296824 0.441122908694716 0.240825814626397 0.475193646646757 3.33033435 -0.54013326 0.43045602 2.67707249 -0.42163058 0.50107926
0.450 4.33697728548038 2.29103572171716 0.209573442606565 0.634252522127606 -1.18013993982454 0.1100834686500940 -0.555234498707119 0.245883260391068 0.619384591074073 0.436294164198843 0.249245758570064 0.469672671050266 3.50290267 -0.56696060 0.43223316 2.88578405 -0.45456492 0.50146998
0.500 4.23507897753587 2.35399193121686 0.218088423514177 0.658541873692286 -1.17726165949601 0.1026978146186720 -0.519413341065942 0.238559829231160 0.624993564560933 0.428500398327627 0.243778652813106 0.463165027132890 3.65227902 -0.58990263 0.43887979 3.06576841 -0.48290522 0.50314566
0.600 4.02306439391925 2.42753387249929 0.218787915039312 0.754615594874153 -1.16678688970027 0.0940582863096094 -0.454043559543982 0.216855298090451 0.635090711921061 0.426296731581312 0.246117069779268 0.451206692163190 3.78937389 -0.61070144 0.44724118 3.20894580 -0.50535303 0.50313816
0.700 3.83201580121827 2.51268432884949 0.225024841305000 0.765438564882833 -1.16236278470164 0.0865917976706938 -0.397781532595396 0.215716276719833 0.633635835573626 0.425379430268476 0.246750734502549 0.446704739768374 3.90172707 -0.62754331 0.45268279 3.29999705 -0.51955858 0.50200072
0.750 3.74614211993052 2.55840246083607 0.231604957273506 0.793480645885641 -1.15333203234665 0.0824927940948198 -0.376630503031279 0.209593410875067 0.637877956868669 0.428563811859323 0.245166749142241 0.444311331912854 3.97560847 -0.63847685 0.45583313 3.34616641 -0.52673049 0.50236259
0.800 3.65168809980226 2.59467404437385 0.237334498546207 0.828241777740572 -1.14645090256437 0.0837439530041729 -0.363246464853852 0.192106714053294 0.638753820813416 0.433880652259324 0.240072953116796 0.439300059540554 4.01969394 -0.64478309 0.46384687 3.37966751 -0.53196741 0.50266660
0.900 3.51228638217709 2.68810225072750 0.251716558693382 0.845561170244942 -1.13599614124436 0.0834018259445213 -0.333908265367165 0.177456610405390 0.640328521929993 0.438913972406961 0.247662698012904 0.433043490235851 4.05410191 -0.64939631 0.47448247 3.42678904 -0.53940883 0.49912472
1.000 3.36982044793917 2.74249776483975 0.256784133033388 0.896648260528882 -1.12443352348542 0.0854384622609198 -0.317465939881623 0.171997778367260 0.638429444564638 0.444086895369946 0.238111905941701 0.426703815544157 4.07365692 -0.65153510 0.48134887 3.49473194 -0.55015995 0.49404787
1.200 3.10224418952824 2.82683484364226 0.262683442221073 0.982921357727718 -1.12116148624672 0.0973231293288241 -0.275616235541070 0.160445653296358 0.640086303643832 0.446121165446841 0.226825215617356 0.416539877732589 4.05048971 -0.64704214 0.48708350 3.57270165 -0.56244631 0.49375397
1.400 2.84933745949861 2.89911332547612 0.272065572034688 1.040000637056720 -1.12848926976065 0.1002887249133400 -0.234977212668109 0.150949141990859 0.649359928046388 0.457011583377380 0.231922092201736 0.409641113489270 3.99349305 -0.63756820 0.49596280 3.64615783 -0.57391983 0.49885402
1.600 2.63503429015231 2.98365736561984 0.289670716036571 1.073002118658300 -1.14064711059980 0.1100788214866130 -0.198050139347725 0.148738498099927 0.650540540696659 0.462781403376806 0.223897549097876 0.404985162254916 3.94048869 -0.62914699 0.50237219 3.70614492 -0.58319956 0.50427003
1.800 2.43032254290751 3.06358840071518 0.316828766785138 1.109809835991900 -1.15419967841818 0.1131278831612640 -0.167123738873435 0.156141593013035 0.656949311785981 0.468432106332010 0.205207971335941 0.399057812399511 3.90126474 -0.62332928 0.49599967 3.73733460 -0.58797931 0.50406486
2.000 2.24716354703519 3.11067747935049 0.326774527695550 1.132479221218060 -1.16620971948721 0.1162990300931710 -0.140731664063789 0.155054491423268 0.647763389017009 0.476577198889343 0.196850466599025 0.396502973620567 3.84084468 -0.61459972 0.47661567 3.71781492 -0.58487198 0.49679447
2.500 1.83108464781202 3.23289020747997 0.374214285707986 1.226390493979360 -1.17531326311999 0.1395412164588280 -0.120745041347963 0.176744551716694 0.629481669044830 0.479859874942997 0.190867925368865 0.393288023064441 3.71684077 -0.59605682 0.44991701 3.63149526 -0.57133201 0.48588889
3.000 1.58259215964414 3.44640772476285 0.454951810817816 1.313954219909490 -1.15664484431459 0.1494902905791280 -0.149050671035371 0.174876785480317 0.616446588503561 0.488309107285476 0.220914253465451 0.390859427279163 3.54176439 -0.56936072 0.42220113 3.49013277 -0.54916732 0.47625314
3.500 1.32153652077149 3.56445182133655 0.518610571029448 1.394984393379380 -1.16368470057735 0.1543445278711660 -0.142873831246493 0.193619214137258 0.600202108018105 0.479187019962682 0.237281350236338 0.388102875218375 3.34546112 -0.53906501 0.39951709 3.34520093 -0.52645323 0.47012445
4.000 1.10607064193676 3.64336885536264 0.555331865800278 1.418144933323620 -1.17757508691221 0.1730832048262120 -0.142053716741244 0.193571789393738 0.593046407283143 0.482524831704549 0.233827536969510 0.386956009422453 3.13392178 -0.50620694 0.38303088 3.23169516 -0.50870031 0.46555128
4.500 1.05987610378773 3.82152567982841 0.666476453600402 1.430548279466630 -1.17323633891422 0.1936210609543320 -0.156076448842833 0.152553585766189 0.581331910387036 0.456765160173852 0.196697785051230 0.372827866334900 2.90740942 -0.47082887 0.36840706 3.13020974 -0.49278809 0.46035806
5.000 0.82373381739570 3.84747968562771 0.684665144355361 1.496536314224210 -1.20969230916539 0.2213041109459350 -0.126052481240424 0.137919529808920 0.558954997903623 0.464229101930025 0.195572800413952 0.377458812369736 2.68344324 -0.43562070 0.35254196 2.99932475 -0.47213713 0.45347349
6.000 0.50685354955206 3.80040950285788 0.700805222359295 1.625591116375650 -1.22440411739130 0.2292764533844400 -0.113766839623945 0.141669390606605 0.538973145096788 0.439059204276786 0.190680023411634 0.384862538848542 2.50354874 -0.40714992 0.33854229 2.83412987 -0.44598168 0.44328149
7.000 0.19675504234642 3.78431011962409 0.716569352050671 1.696310364814470 -1.28517895409644 0.2596896867469380 -0.070585399916418 0.146488759166368 0.523331606096182 0.434396029381517 0.208231539543981 0.385850838707000 2.39499327 -0.38989994 0.33074643 2.69365804 -0.42370171 0.43214765
8.000 -0.08979569600589 3.74815514351616 0.726493405776986 1.695347146909250 -1.32882937608962 0.2849197966362740 -0.051296439369391 0.150981191615944 0.508537123776905 0.429104860654150 0.216201318346277 0.387633769846605 2.35979253 -0.38432385 0.32874669 2.64017872 -0.41521615 0.42722298
""")
[docs]class KothaEtAl2020ESHM20SlopeGeology(KothaEtAl2020ESHM20):
"""
Adaptation of the ESHM20-implemented Kotha et al. (2020) model for use when
defining site amplification based on with slope and geology rather than
inferred/measured Vs30.
"""
kind = "geology"
#: Required site parameter is not set
REQUIRES_SITES_PARAMETERS = {"region", "slope", "geology"}
#: Geological Units
GEOLOGICAL_UNITS = [b"CENOZOIC", b"HOLOCENE", b"JURASSIC-TRIASSIC",
b"CRETACEOUS", b"PALEOZOIC", b"PLEISTOCENE",
b"PRECAMBRIAN", b"UNKNOWN"]
COEFFS_FIXED = CoeffsTable(sa_damping=5, table="""\
imt V1 V2 phi_s2s
pgv -0.32011591 -0.10821634 0.43790400
pga -0.21384649 -0.07866419 0.50748976
0.0100 -0.21204938 -0.07786954 0.50767629
0.0250 -0.21022718 -0.07807579 0.51225982
0.0400 -0.20136301 -0.07541908 0.52670786
0.0500 -0.18838689 -0.07108179 0.54493364
0.0700 -0.17184538 -0.06571920 0.55944471
0.1000 -0.16163003 -0.06208429 0.56625853
0.1500 -0.16374630 -0.06294572 0.56162087
0.2000 -0.18251959 -0.06818065 0.54476261
0.2500 -0.21409731 -0.07647401 0.52514338
0.3000 -0.24386901 -0.08391627 0.50768598
0.3500 -0.27400911 -0.09230534 0.49756674
0.4000 -0.30308465 -0.09970264 0.49551267
0.4500 -0.33071023 -0.10723760 0.49886138
0.5000 -0.35922788 -0.11481966 0.50191789
0.6000 -0.38424135 -0.12166326 0.50383885
0.7000 -0.39238013 -0.12282731 0.50457268
0.7500 -0.39666705 -0.12348753 0.50522559
0.8000 -0.39392763 -0.12143042 0.50479578
0.9000 -0.39358294 -0.12038202 0.50477401
1.0000 -0.40028453 -0.12131011 0.50481908
1.2000 -0.40988732 -0.12295578 0.50573308
1.4000 -0.41409963 -0.12225306 0.50983436
1.6000 -0.42464935 -0.12508523 0.51411562
1.8000 -0.42930176 -0.12713783 0.51401210
2.0000 -0.42551341 -0.12617452 0.50714903
2.5000 -0.41410716 -0.12316018 0.49538482
3.0000 -0.39322101 -0.11745721 0.48285566
3.5000 -0.37377357 -0.11156417 0.47392688
4.0000 -0.35892700 -0.10678276 0.46498100
4.5000 -0.34593942 -0.10289679 0.45244339
5.0000 -0.32936086 -0.09799475 0.43779077
6.0000 -0.31083191 -0.09367866 0.41948366
7.0000 -0.29038396 -0.08769334 0.40349430
8.0000 -0.26798948 -0.07870836 0.39340689
""")
COEFFS_RANDOM_INT = CoeffsTable(sa_damping=5, table="""\
imt PRECAMBRIAN PALEOZOIC JURASSIC-TRIASSIC CRETACEOUS CENOZOIC PLEISTOCENE HOLOCENE UNKNOWN
pgv 0.00750400 -0.00515204 -0.06153554 -0.07234031 0.00736992 0.07121264 0.09269472 -0.03724508
pga 0.04246887 -0.04689335 -0.12550972 -0.09220607 -0.12856371 0.17767008 0.03348558 0.14349446
0.0100 0.04467747 -0.04719901 -0.12081014 -0.09275987 -0.12809141 0.17716640 0.03412759 0.13726836
0.0250 0.03889165 -0.03778649 -0.12589811 -0.09016890 -0.13626584 0.17014868 0.02134094 0.16217912
0.0400 0.03635013 -0.03184964 -0.12934774 -0.08599260 -0.14795654 0.16674580 0.00796619 0.18513009
0.0500 0.03822106 -0.02889265 -0.13253481 -0.08320332 -0.15923731 0.16673471 -0.00399086 0.20306016
0.0700 0.04842870 -0.02905574 -0.14094162 -0.08691977 -0.16757093 0.17089787 -0.01750887 0.22231487
0.1000 0.06479680 -0.02666152 -0.14538543 -0.09881407 -0.15653309 0.17427644 -0.00898158 0.19655244
0.1500 0.07592359 -0.03449021 -0.15017012 -0.11171407 -0.15175902 0.18843894 0.00585402 0.17659703
0.2000 0.06707266 -0.03684141 -0.13591923 -0.10829435 -0.12956987 0.18685906 0.02395110 0.13564373
0.2500 0.04549958 -0.03952544 -0.11954550 -0.09789634 -0.09538165 0.18260210 0.04789909 0.08864124
0.3000 0.02309429 -0.04882340 -0.11020150 -0.08252276 -0.07858957 0.18895661 0.04729437 0.08229878
0.3500 -0.00088865 -0.06080297 -0.11913566 -0.08032219 -0.04845977 0.19164678 0.08244406 0.05906910
0.4000 -0.01394235 -0.06808797 -0.12746882 -0.07669384 -0.02102129 0.19645651 0.10471131 0.03662866
0.4500 -0.01906609 -0.07042464 -0.12110002 -0.07169866 -0.00983259 0.18151311 0.11431121 0.02414359
0.5000 -0.03318464 -0.06324744 -0.09788143 -0.06556113 0.01225172 0.15414730 0.12243590 -0.00543195
0.6000 -0.05314149 -0.06436228 -0.08251682 -0.06918568 0.03294078 0.14637439 0.13892579 -0.02912185
0.7000 -0.06083543 -0.06057868 -0.07101886 -0.06961153 0.03534846 0.13592405 0.12293154 -0.01958169
0.7500 -0.07740521 -0.06314197 -0.07585198 -0.08188938 0.04827896 0.13735651 0.15060589 -0.03505339
0.8000 -0.08428220 -0.06419910 -0.07628445 -0.08388821 0.04721248 0.14534687 0.14702926 -0.02542895
0.9000 -0.08850823 -0.06219820 -0.07133046 -0.08391446 0.04406568 0.14264248 0.14560420 -0.02087862
1.0000 -0.08695550 -0.05738604 -0.06232390 -0.07771771 0.03851214 0.13291669 0.13551423 -0.01697581
1.2000 -0.08279930 -0.05351583 -0.05407772 -0.06869238 0.03347951 0.12221589 0.12328935 -0.01431109
1.4000 -0.05949173 -0.03635251 -0.03538338 -0.04669483 0.02212916 0.08304733 0.08247065 -0.00669157
1.6000 -0.06113887 -0.03333011 -0.03515454 -0.04035535 0.01985126 0.07993816 0.07719776 -0.00437551
1.8000 -0.05820670 -0.02944153 -0.03437685 -0.03687461 0.01776400 0.07504155 0.07187361 -0.00344321
2.0000 -0.05511928 -0.03048829 -0.03394715 -0.03445489 0.01725827 0.07299828 0.06981133 -0.00381850
2.5000 -0.05529251 -0.03317679 -0.03524865 -0.03775773 0.01589549 0.07794768 0.07737765 -0.00519144
3.0000 -0.04578721 -0.02599141 -0.02744938 -0.03513471 0.01117042 0.06571772 0.06714184 -0.00465567
3.5000 -0.03981912 -0.02964418 -0.03012732 -0.03891412 0.00837912 0.06854646 0.07457700 -0.00526904
4.0000 -0.04195342 -0.03422243 -0.03649884 -0.04116601 0.00956496 0.07505321 0.08162242 -0.00456870
4.5000 -0.04206465 -0.04256136 -0.04317528 -0.04860474 0.01084912 0.08895943 0.09449063 -0.00778319
5.0000 -0.04307842 -0.05127801 -0.05181793 -0.06233230 0.01139912 0.11137228 0.11654077 -0.01560194
6.0000 -0.05288405 -0.06153656 -0.06086908 -0.08447680 0.01226796 0.14461811 0.15121486 -0.02571369
7.0000 -0.05313788 -0.05972963 -0.05698048 -0.08639775 0.01139303 0.14354253 0.15094746 -0.02675383
8.0000 -0.03321449 -0.03672124 -0.03072781 -0.04927415 0.00752873 0.07812242 0.08445355 -0.01061799
""")
COEFFS_RANDOM_GRAD = CoeffsTable(sa_damping=5, table="""\
imt PRECAMBRIAN PALEOZOIC JURASSIC-TRIASSIC CRETACEOUS CENOZOIC PLEISTOCENE HOLOCENE UNKNOWN
pgv -0.00151889 0.00104283 0.01245549 0.01464249 -0.00149176 -0.01441424 -0.01876246 0.00753883
pga 0.01074547 -0.01778485 -0.02616742 -0.02035435 -0.04046745 0.04524993 -0.00317088 0.05341858
0.0100 0.01110581 -0.01817585 -0.02362103 -0.01978543 -0.04021423 0.04414265 -0.00393577 0.05210902
0.0250 0.01054942 -0.01375128 -0.03204231 -0.02329083 -0.04298207 0.04740963 -0.00096118 0.05596879
0.0400 0.01063103 -0.01076982 -0.03745690 -0.02482504 -0.04632847 0.04969505 -0.00047448 0.05991117
0.0500 0.01167666 -0.00905529 -0.04064013 -0.02545862 -0.04918531 0.05122655 -0.00149106 0.06298322
0.0700 0.01522096 -0.00866859 -0.04456948 -0.02765443 -0.05138391 0.05364480 -0.00391298 0.06719302
0.1000 0.01898016 -0.00727708 -0.04378241 -0.02975827 -0.04595861 0.05216548 -0.00146284 0.05692836
0.1500 0.02078272 -0.01041484 -0.04151626 -0.03076920 -0.04242245 0.05227380 0.00117824 0.05081748
0.2000 0.01679209 -0.01251480 -0.03159881 -0.02500107 -0.03540564 0.04583389 0.00087255 0.04165261
0.2500 0.01047086 -0.01254293 -0.01977080 -0.01652711 -0.02642314 0.03637504 -0.00140843 0.03164479
0.3000 0.00492601 -0.01305137 -0.00935782 -0.00502304 -0.02551784 0.02973268 -0.01268061 0.03384470
0.3500 0.00068207 -0.01138237 -0.00760508 -0.00115452 -0.01955133 0.02442332 -0.01202183 0.03011394
0.4000 -0.00007763 -0.00826703 -0.00615682 0.00128058 -0.01483467 0.02048270 -0.01209326 0.02192539
0.4500 0.00259298 -0.00548582 -0.00129611 0.00457027 -0.01408782 0.01079136 -0.01568248 0.01890988
0.5000 0.00454355 0.00005525 0.00659854 0.00875027 -0.00980836 -0.00351454 -0.01917515 0.01134711
0.6000 0.00604685 0.00440535 0.01064001 0.00948379 -0.00612234 -0.01236742 -0.01943292 0.00551060
0.7000 0.01095305 0.00931412 0.01504193 0.01493469 -0.00924357 -0.02220648 -0.02871351 0.00826076
0.7500 0.01369981 0.01235745 0.01395140 0.01427521 -0.00674976 -0.02722199 -0.02425577 0.00311240
0.8000 0.01694348 0.01219280 0.01497930 0.01689579 -0.00946095 -0.02828030 -0.02848641 0.00440800
0.9000 0.01892074 0.01405716 0.01640228 0.01933592 -0.01002078 -0.03204632 -0.03297697 0.00504239
1.0000 0.02512104 0.01688438 0.01837402 0.02268965 -0.01141742 -0.03884472 -0.03943641 0.00505860
1.2000 0.03327967 0.01980375 0.01991772 0.02534680 -0.01264104 -0.04622581 -0.04560074 0.00437189
1.4000 0.04722160 0.02594108 0.02737100 0.03392452 -0.01676537 -0.06227400 -0.06074314 0.00371247
1.6000 0.05194873 0.02697120 0.02973620 0.03495830 -0.01732309 -0.06667116 -0.06444819 0.00317279
1.8000 0.05328046 0.02727815 0.03128253 0.03528866 -0.01722153 -0.06854742 -0.06616442 0.00307244
2.0000 0.05210980 0.02951740 0.03229472 0.03437065 -0.01640282 -0.06939661 -0.06746935 0.00295572
2.5000 0.04758107 0.02930987 0.03042051 0.03195468 -0.01450440 -0.06586126 -0.06512613 0.00334992
3.0000 0.04481012 0.02796003 0.02876396 0.03433113 -0.01191492 -0.06543141 -0.06637460 0.00371933
3.5000 0.03960965 0.02549857 0.02640242 0.03376046 -0.00933018 -0.06073490 -0.06386255 0.00364497
4.0000 0.03061486 0.02435131 0.02643817 0.03285260 -0.00685464 -0.05646726 -0.06036334 0.00381148
4.5000 0.02253163 0.02199085 0.02451190 0.02935520 -0.00551367 -0.04940159 -0.05254284 0.00387614
5.0000 0.01675139 0.01898142 0.02123988 0.02293046 -0.00517242 -0.04022363 -0.04159239 0.00326963
6.0000 0.00884584 0.01248789 0.01338540 0.01433546 -0.00328602 -0.02576612 -0.02615088 0.00321300
7.0000 0.00754320 0.01081496 0.00952506 0.01292858 -0.00247815 -0.02210686 -0.02284293 0.00365737
8.0000 0.01794388 0.01906271 0.01478150 0.02515701 -0.00401437 -0.03950798 -0.04270189 0.00480742
""")
# Add aliases for the ESHM20 selection - shallow crustal sources
eshm20_crust_lines = '''\
ESHM20ShallowCrustVLowStressFastAtten -2.85697 -1.732051
ESHM20ShallowCrustVLowStressMidAtten -2.85697 0.000000
ESHM20ShallowCrustVLowStressSlowAtten -2.85697 1.732051
ESHM20ShallowCrustLowStressFastAtten -1.35563 -1.732051
ESHM20ShallowCrustLowStressMidAtten -1.35563 0.000000
ESHM20ShallowCrustLowStressSlowAtten -1.35563 1.732051
ESHM20ShallowCrustMidStressFastAtten 0.00000 -1.732051
ESHM20ShallowCrustMidStressMidAtten 0.00000 0.000000
ESHM20ShallowCrustMidStressSlowAtten 0.00000 1.732051
ESHM20ShallowCrustHighStressFastAtten 1.35563 -1.732051
ESHM20ShallowCrustHighStressMidAtten 1.35563 0.000000
ESHM20ShallowCrustHighStressSlowAtten 1.35563 1.732051
ESHM20ShallowCrustVHighStressFastAtten 2.85697 -1.732051
ESHM20ShallowCrustVHighStressMidAtten 2.85697 0.000000
ESHM20ShallowCrustVHighStressSlowAtten 2.85697 1.732051'''.splitlines()
for line_shallow in eshm20_crust_lines:
alias, sig_mu_eps, c3_eps = line_shallow.split()
add_alias(alias, KothaEtAl2020ESHM20,
sigma_mu_epsilon=float(sig_mu_eps),
c3_epsilon=float(c3_eps))
# Add aliases for the ESHM20 Iceland ground motion model
# dl2l values
ICELAND_dL2L = {
"IMTs": ['PGA', 'SA(0.01)', 'SA(0.025)', 'SA(0.04)', 'SA(0.05)',
'SA(0.07)', 'SA(0.1)', 'SA(0.15)', 'SA(0.2)', 'SA(0.25)',
'SA(0.3)', 'SA(0.35)', 'SA(0.4)', 'SA(0.45)', 'SA(0.5)',
'SA(0.6)', 'SA(0.7)', 'SA(0.75)', 'SA(0.8)', 'SA(0.9)', 'SA(1.0)',
'SA(1.2)', 'SA(1.4)', 'SA(1.6)', 'SA(1.8)', 'SA(2.0)', 'SA(2.5)',
'SA(3.0)', 'SA(3.5)', 'SA(4.0)', 'SA(4.5)', 'SA(5.0)', 'SA(6.0)',
'SA(7.0)', 'SA(8.0)'],
"VLow": [-1.320714, -1.334702, -1.411144, -1.593190, -1.732470, -1.846624,
-1.869080, -1.666701, -1.370120, -1.239216, -1.107578, -0.953322,
-0.919893, -0.888578, -0.819694, -0.763689, -0.703255, -0.641188,
-0.592629, -0.560762, -0.453129, -0.320960, -0.235436, -0.159245,
-0.011255, 0.114595, 0.268825, 0.214030, 0.061128, -0.066012,
-0.016226, 0.005109, 0.144121, 0.125620, -0.081479],
"Low": [-0.787319, -0.800154, -0.858052, -0.973254, -1.065389, -1.139585,
-1.150332, -1.045077, -0.886725, -0.798828, -0.706965, -0.605590,
-0.558332, -0.514375, -0.453700, -0.394184, -0.332799, -0.273109,
-0.232198, -0.188936, -0.095642, 0.019582, 0.112757, 0.176902,
0.296832, 0.410135, 0.555383, 0.545697, 0.417368, 0.285042,
0.279085, 0.298731, 0.430396, 0.438246, 0.243113],
"Mid": [-0.305692, -0.317486, -0.358640, -0.413486, -0.463050, -0.501166,
-0.501340, -0.483784, -0.450245, -0.401182, -0.345233, -0.291607,
-0.231861, -0.176490, -0.123226, -0.060540, 0.001704, 0.059246,
0.093252, 0.146803, 0.227150, 0.327073, 0.427158, 0.480424,
0.575018, 0.676991, 0.814129, 0.845175, 0.739034, 0.602026,
0.545734, 0.563855, 0.688888, 0.720531, 0.536202],
"High": [0.175935, 0.165182, 0.140772, 0.146282, 0.139289, 0.137253,
0.147652, 0.077509, -0.013765, -0.003536, 0.016499, 0.022376,
0.094610, 0.161395, 0.207248, 0.273104, 0.336207, 0.391601,
0.418702, 0.482542, 0.549942, 0.634564, 0.741559, 0.783946,
0.853204, 0.943847, 1.072875, 1.144653, 1.060700, 0.919010,
0.812383, 0.828979, 0.947380, 1.002816, 0.829291],
"VHigh": [0.709330, 0.699730, 0.693864, 0.766218, 0.806370, 0.844292,
0.866400, 0.699133, 0.469630, 0.436852, 0.417112, 0.370108,
0.456171, 0.535598, 0.573242, 0.642609, 0.706663, 0.759680,
0.779133, 0.854368, 0.907429, 0.975106, 1.089752, 1.120093,
1.161291, 1.239387, 1.359433, 1.476320, 1.416940, 1.270064,
1.107694, 1.122601, 1.233655, 1.315442, 1.153883],
}
# Build the set of aliases
for stress in list(ICELAND_dL2L)[1:]:
dl2l = dict(list(zip(ICELAND_dL2L["IMTs"], ICELAND_dL2L[stress])))
for c3_key, c3_eps in zip(["Fast", "Mid", "Slow"],
[-1.732051, 0.0, 1.732051]):
alias = "ESHM20Iceland{:s}Stress{:s}Atten".format(stress, c3_key)
add_alias(alias, KothaEtAl2020ESHM20, dl2l=dl2l, c3_epsilon=c3_eps)
C3_REGIONS_AVGSA = CoeffsTable(sa_damping=5, table="""\
imt region_1 tau_region_1 region_2 tau_region_2 region_3 tau_region_3 region_4 tau_region_4 region_5 tau_region_5
AvgSA(0.050) -0.4656716000 0.1180142000 -0.7133721000 0.0946938000 -0.9685200000 0.1338548000 -0.5888355000 0.1820359000 -0.1240944000 0.1570220000
AvgSA(0.100) -0.5310625000 0.1309543000 -0.8190398000 0.1062527000 -1.1068865000 0.1375049000 -0.7067665000 0.1882153000 -0.1469747000 0.1360697000
AvgSA(0.150) -0.5581186000 0.1317465000 -0.8442356000 0.1110502000 -1.1565822000 0.1337646000 -0.7421298000 0.1763761000 -0.1974244000 0.1813739000
AvgSA(0.200) -0.5529085000 0.1327567000 -0.8229416000 0.1162142000 -1.1460833000 0.1362717000 -0.7302299000 0.1698309000 -0.1933789000 0.1984123000
AvgSA(0.250) -0.5372297000 0.1328342000 -0.7929952000 0.1156845000 -1.1136433000 0.1366984000 -0.7016690000 0.1682029000 -0.1857899000 0.2149315000
AvgSA(0.300) -0.5254234000 0.1334462000 -0.7654788000 0.1150564000 -1.0814921000 0.1377804000 -0.6748147000 0.1734933000 -0.1752417000 0.2206030000
AvgSA(0.400) -0.4898486000 0.1312907000 -0.7025190000 0.1123262000 -1.0049232000 0.1345776000 -0.6052932000 0.1785973000 -0.1397568000 0.2171827000
AvgSA(0.500) -0.4563844000 0.1284697000 -0.6492117000 0.1073397000 -0.9333463000 0.1320078000 -0.5430056000 0.1839070000 -0.1067728000 0.2055740000
AvgSA(0.600) -0.4252573000 0.1246073000 -0.6008299000 0.1033843000 -0.8654133000 0.1245591000 -0.4767390000 0.1872128000 -0.0830896000 0.1956748000
AvgSA(0.700) -0.4001896000 0.1204433000 -0.5650228000 0.0985488000 -0.8101765000 0.1193220000 -0.4274777000 0.1901049000 -0.0532689000 0.1719868000
AvgSA(0.800) -0.3825042000 0.1120253000 -0.5299286000 0.0981232000 -0.7604156000 0.1162526000 -0.3847776000 0.1938995000 -0.0476572000 0.1797690000
AvgSA(0.900) -0.3608326000 0.1070064000 -0.4965110000 0.0951311000 -0.7121393000 0.1103616000 -0.3488966000 0.1921782000 -0.0319083000 0.1744172000
AvgSA(1.000) -0.3445518000 0.1019015000 -0.4680719000 0.0933419000 -0.6699090000 0.1067803000 -0.3119548000 0.1899378000 -0.0231772000 0.1709575000
AvgSA(1.250) -0.3085981000 0.0942465000 -0.4043969000 0.0921493000 -0.5814821000 0.1020569000 -0.2430170000 0.1879356000 0.0096703000 0.1518318000
AvgSA(1.500) -0.2769769000 0.0909386000 -0.3528436000 0.0920438000 -0.5123643000 0.0996129000 -0.1845231000 0.1803464000 0.0388261000 0.1430487000
AvgSA(1.750) -0.2575783000 0.0904296000 -0.3244613000 0.0952487000 -0.4561763000 0.0864028000 -0.1453873000 0.1738825000 0.0564608000 0.1302481000
AvgSA(2.000) -0.2463514000 0.0909783000 -0.3030979000 0.0949550000 -0.4213413000 0.0836152000 -0.1120286000 0.1733245000 0.0705411000 0.1301361000
AvgSA(2.500) -0.2395616000 0.1008508000 -0.2822054000 0.0973938000 -0.3730267000 0.0823939000 -0.0721809000 0.1728203000 0.1038858000 0.1195501000
AvgSA(3.000) -0.2503677000 0.1049288000 -0.2777608000 0.0968775000 -0.3381454000 0.0639946000 -0.0809930000 0.1658070000 0.1030135000 0.1401671000
AvgSA(3.500) -0.2298273000 0.1105661000 -0.2450972000 0.0987783000 -0.2853042000 0.0523550000 -0.0565065000 0.1612552000 0.1442919000 0.0838447000
AvgSA(4.000) -0.2181743000 0.1188117000 -0.2285558000 0.1063640000 -0.2579791000 0.0561007000 -0.0374827000 0.1651242000 0.1518847000 0.0902318000
AvgSA(4.500) -0.2189357000 0.0947278000 -0.2256616000 0.1216485000 -0.2320831000 0.0557586000 -0.0572455000 0.1370899000 -0.0290722000 0.1395083000
AvgSA(5.000) -0.2069729000 0.0981588000 -0.2110292000 0.1268101000 -0.2118488000 0.0593289000 -0.0379903000 0.1392759000 -0.0114503000 0.1387377000
""")
# Coefficients for components of variability for AvgSa based on the indirect
# variability approach and the ESHM20-based cross-correlation model
COEFFS_AVGSA_TAU_PHI = CoeffsTable(sa_damping=5, table="""\
imt tau1 tau2 tau3 tau4 phi0_a phi0_b phi_s2s_obs phi_s2s_inf
AvgSA(0.050) 0.450265228 0.425534126 0.385047171 0.349550065 0.469793727 0.373637252 0.422827263 0.533408863
AvgSA(0.100) 0.443613368 0.419285824 0.379383631 0.344424617 0.469327412 0.368595315 0.441139506 0.539238447
AvgSA(0.150) 0.437547947 0.413317059 0.374115591 0.339638982 0.463561498 0.350760067 0.446779972 0.532620604
AvgSA(0.200) 0.433537996 0.409666567 0.370677538 0.336554639 0.456535303 0.338264036 0.443403456 0.521297604
AvgSA(0.250) 0.430914023 0.407242752 0.368479157 0.334545957 0.450475499 0.330248213 0.436886715 0.510932860
AvgSA(0.300) 0.429339157 0.405793790 0.367079555 0.333355308 0.445321228 0.326114255 0.431313565 0.503221482
AvgSA(0.400) 0.426838581 0.403389369 0.364995154 0.331386762 0.433932123 0.317686930 0.426627088 0.493039840
AvgSA(0.500) 0.426838581 0.403389369 0.364995154 0.331386762 0.427499912 0.318111364 0.426920015 0.488374099
AvgSA(0.600) 0.426838581 0.403389369 0.364995154 0.331386762 0.421075089 0.315927942 0.430202863 0.484867766
AvgSA(0.700) 0.426838581 0.403389369 0.364995154 0.331386762 0.415377483 0.315623688 0.433889171 0.481497235
AvgSA(0.800) 0.426838581 0.403389369 0.364995154 0.331386762 0.409761405 0.316458809 0.437527308 0.478941984
AvgSA(0.900) 0.426838581 0.403389369 0.364995154 0.331386762 0.404749602 0.318527404 0.441076619 0.477263647
AvgSA(1.000) 0.426838581 0.403389369 0.364995154 0.331386762 0.400538795 0.319660717 0.444733966 0.476613844
AvgSA(1.250) 0.426838581 0.403389369 0.364995154 0.331386762 0.391173979 0.323422526 0.449968173 0.475330279
AvgSA(1.500) 0.426838581 0.403389369 0.364995154 0.331386762 0.384207569 0.324736699 0.448480052 0.472810059
AvgSA(1.750) 0.426838581 0.403389369 0.364995154 0.331386762 0.378940921 0.324776768 0.444166577 0.469909402
AvgSA(2.000) 0.426838581 0.403389369 0.364995154 0.331386762 0.375055253 0.327256765 0.438096814 0.466775537
AvgSA(2.500) 0.426838581 0.403389369 0.364995154 0.331386762 0.368731863 0.331137495 0.425405874 0.461923495
AvgSA(3.000) 0.426838581 0.403389369 0.364995154 0.331386762 0.362799048 0.333181208 0.412446255 0.456919212
AvgSA(3.500) 0.426838581 0.403389369 0.364995154 0.331386762 0.359200676 0.337125666 0.399372262 0.452070311
AvgSA(4.000) 0.426838581 0.403389369 0.364995154 0.331386762 0.357004460 0.337999154 0.388331894 0.447539253
AvgSA(4.500) 0.426838581 0.403389369 0.364995154 0.331386762 0.355726550 0.340391710 0.379435900 0.442846515
AvgSA(5.000) 0.426838581 0.403389369 0.364995154 0.331386762 0.354587686 0.340853193 0.371880106 0.438313782
""")
[docs]def get_heteroskedastic_tau_phi0_avgsa(imt, mag):
"""Returns the heteroskedastic between-event and single-station within-
event variability for AvgSa
"""
C = COEFFS_AVGSA_TAU_PHI[imt]
tau = np.full_like(mag, C["tau1"])
tau[mag > 6.5] = C["tau4"]
idx = (mag > 5.5) & (mag <= 6.5)
tau[idx] = ITPL(mag[idx], C["tau4"], C["tau3"], 5.5, 1.0)
idx = (mag > 5.0) & (mag <= 5.5)
tau[idx] = ITPL(mag[idx], C["tau3"], C["tau2"], 5.0, 0.5)
idx = (mag > 4.5) & (mag <= 5.0)
tau[idx] = ITPL(mag[idx], C["tau2"], C["tau1"], 4.5, 0.5)
phi0 = C["phi0_a"] + (mag - 5.0) * ((C["phi0_b"] - C["phi0_a"]) / 1.5)
phi0[mag <= 5.0] = C["phi0_a"]
phi0[mag > 6.5] = C["phi0_b"]
return tau, phi0
