# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2022 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports :class:`KothaEtAl2020`,
:class:`KothaEtAl2020Site`,
:class:`KothaEtAl2020Slope`,
:class:`KothaEtAl2020ESHM20`,
:class:`KothaEtAl2020ESHM20SlopeGeology`
"""
import numpy as np
from scipy.constants import g
from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
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)
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
""")
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")
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")
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[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_term(kind, c3, c3_epsilon, C, ctx, rjb, imt):
"""
Returns the distance attenuation factor
"""
h = _get_h(C, ctx.hypo_depth)
rval = np.sqrt(rjb ** 2. + h ** 2.)
rref_val = np.sqrt(CONSTANTS["Rref"] ** 2. + h ** 2.)
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_sigma_mu_adjustment(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 = 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 == "base": # no site amplification
ampl = 0.
elif kind == "site":
# 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 == "ESHM20":
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 == "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)
else:
tau = C["tau_event_0"]
phi = C["phi_0"]
if ergodic:
if kind == 'ESHM20':
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"]
phi = np.sqrt(phi ** 2. + phi_s2s ** 2.)
elif kind == 'site':
phi = np.sqrt(phi ** 2.0 + C["phi_s2s_vs30"] ** 2.)
elif kind == 'slope':
phi = np.sqrt(phi ** 2. + C["phi_s2s_slope"] ** 2.)
elif kind == 'geology':
phi = np.sqrt(phi ** 2. + phi_s2s ** 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 == 'ESHM20':
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 == '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
mean[m] = (get_magnitude_scaling(C, ctx.mag) +
get_distance_term(self.kind, self.c3, self.c3_epsilon,
C, ctx, ctx.rjb, imt) +
get_site_amplification(self.kind, extra, C, ctx, imt))
# GMPE originally in cm/s/s - convert to g
if imt.string.startswith(('PGA', 'SA')):
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.sigma_mu_epsilon:
# epistemic uncertainty factor (sigma_mu) multiplied by
# the number of standard deviations
sigma_mu = get_sigma_mu_adjustment(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 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
""")