# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2018 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/>.
import numpy as np
from scipy.special import erf
from openquake.hazardlib.gsim.base import CoeffsTable
from openquake.hazardlib.gsim.abrahamson_2015 import (
AbrahamsonEtAl2015SInter, AbrahamsonEtAl2015SInterLow,
AbrahamsonEtAl2015SInterHigh, AbrahamsonEtAl2015SSlab,
AbrahamsonEtAl2015SSlabLow, AbrahamsonEtAl2015SSlabHigh)
# Total epistemic uncertainty factors from Abrahamson et al. (2018)
BCHYDRO_SIGMA_MU = CoeffsTable(sa_damping=5, table="""
imt SIGMA_MU_SINTER SIGMA_MU_SSLAB
pga 0.3 0.50
0.010 0.3 0.50
0.020 0.3 0.50
0.030 0.3 0.50
0.050 0.3 0.50
0.075 0.3 0.50
0.100 0.3 0.50
0.150 0.3 0.50
0.200 0.3 0.50
0.250 0.3 0.46
0.300 0.3 0.42
0.400 0.3 0.38
0.500 0.3 0.34
0.600 0.3 0.30
0.750 0.3 0.30
1.000 0.3 0.30
1.500 0.3 0.30
2.000 0.3 0.30
2.500 0.3 0.30
3.000 0.3 0.30
4.000 0.3 0.30
5.000 0.3 0.30
6.000 0.3 0.30
7.500 0.3 0.30
10.00 0.3 0.30
""")
[docs]def get_stress_factor(imt, slab=False):
"""
Returns the stress adjustment factor for the BC Hydro GMPE according to
Abrahamson et al. (2018)
"""
if slab:
sigma_mu = BCHYDRO_SIGMA_MU[imt]["SIGMA_MU_SSLAB"]
else:
sigma_mu = BCHYDRO_SIGMA_MU[imt]["SIGMA_MU_SINTER"]
return sigma_mu / 1.65
[docs]class FABATaperStep(object):
"""
General class for a tapering function, in this case
a step function such that the backarc scaling term takes 0 for
forearc sites (negative backarc distance), and 1 for backarc sites
(positive backarc distance)
"""
def __init__(self, **kwargs):
"""
Instantiates the class with any required arguments controlling the
shape of the taper (none in the case of the current step taper). As
the range of possible parameters take different meanings and default
values in the subclasses of the function an indefinite set of inputs
(**kwargs) is used rather than an explicit parameter list. The
definition of parameters used within each subclass can be found in the
respective subclass documentation strings.
"""
pass
def __call__(self, x):
"""
:param numpy.ndarray x:
Independent variable.
Returns
-------
:param numpy.ndarray y:
Backarc scaling term
"""
y = np.zeros(x.shape)
y[x > 0.0] = 1.
return y
[docs]class FABATaperSFunc(FABATaperStep):
"""
Implements tapering of x according to a S-function
(Named such because of its S-like shape.)
:param float a:
'ceiling', where the function begins falling from 1.
:param float b:
'floor', where the function reaches zero.
"""
def __init__(self, **kwargs):
super().__init__()
self.a = kwargs.get("a", 0.0)
self.b = kwargs.get("b", 0.0)
# a must be less than or equal to b
assert self.a <= self.b
def __call__(self, x):
"""
Returns
-------
:param numpy.ndarray y:
Backarc scaling term
"""
y = np.ones(x.shape)
idx = x <= self.a
y[idx] = 0
idx = np.logical_and(self.a <= x, x <= (self.a + self.b) / 2.)
y[idx] = 2. * ((x[idx] - self.a) / (self.b - self.a)) ** 2.
idx = np.logical_and((self.a + self.b) / 2. <= x, x <= self.b)
y[idx] = 1 - 2. * ((x[idx] - self.b) / (self.b - self.a)) ** 2.
return y
[docs]class FABATaperLinear(FABATaperStep):
"""
Implements a tapering of x according to a linear function
with a fixed distance and a midpoint (y = 0.5) at x = 0
:param float width:
Distance (km) across which x tapers to 0
"""
def __init__(self, **kwargs):
super().__init__()
self.width = kwargs.get("width", 1.0)
# width must be greater than 0
assert self.width > 0.0
def __call__(self, x):
"""
Returns
-------
:param numpy.ndarray y:
Backarc scaling term
"""
upper = self.width / 2.
lower = -self.width / 2.
y = (x - lower) / (upper - lower)
y[x > upper] = 1.
y[x < lower] = 0.
return y
[docs]class FABATaperSigmoid(FABATaperStep):
"""
Implements tapering of x according to a sigmoid function
(Note that this only tends to 1, 0 it does not reach it)
:param float c: Bandwidth in km of the sigmoid function
"""
def __init__(self, **kwargs):
super().__init__()
self.c = kwargs.get("c", 1.0)
# sigmoid function bandwidth must be greater than zero
assert self.c > 0.
def __call__(self, x):
"""
Returns
-------
:param numpy.ndarray y:
Backarc scaling term
"""
return 1. / (1. + np.exp(-(1. / self.c) * x))
# Get Gaussian cdf of a standard normal distribution
phix = lambda x: 0.5 * (1.0 + erf(x / np.sqrt(2.)))
[docs]class FABATaperGaussian(FABATaperStep):
"""
Implements tapering of x according to a truncated Gaussian function
:param float sigma:
Bandwidth of function (according to a Gaussian standard deviation)
:param float a:
Initiation point of tapering (km)
:param float b:
Termination point of tapering (km)
"""
def __init__(self, **kwargs):
super().__init__()
self.sigma = kwargs.get("sigma", 1.0)
a = kwargs.get("a", -np.inf)
b = kwargs.get("b", np.inf)
# Gaussian sigma must be positive non-zero and upper bound must be
# greater than or equal to the lower bound
assert self.sigma > 0
assert b >= a
self.phi_a = phix(a / self.sigma)
self.phi_diff = phix(b / self.sigma) - self.phi_a
def __call__(self, x):
"""
Returns
-------
:param numpy.ndarray y:
Backarc scaling term
"""
y = (phix(x / self.sigma) - self.phi_a) / self.phi_diff
y[y < 0.] = 0.
y[y > 1.] = 1.
return y
FABA_ALL_MODELS = {
"Step": FABATaperStep,
"Linear": FABATaperLinear,
"SFunc": FABATaperSFunc,
"Sigmoid": FABATaperSigmoid,
"Gaussian": FABATaperGaussian
}
[docs]class BCHydroESHM20SInter(AbrahamsonEtAl2015SInter):
"""
ESHM20 adjustment of the BC Hydro GMPE for subduction interface events with
theta6 calibrated to Mediterranean data.
Introduces several configurable parameters:
:param float theta6_adjustment:
The amount to increase or decrease the theta6 - should be +0.0015 (for
slower attenuation) and -0.0015 (for faster attenuation)
:param float sigma_mu_epsilon:
The number of standard deviations above or below the mean to apply the
statistical uncertainty sigma_mu term.
:param faba_model:
Choice of model for the forearc/backarc tapering function, choice of
{"Step", "Linear", "SFunc", "Sigmoid", "Gaussian"}
Depending on the choice of taper model, additional parameters may be passed
"""
experimental = True
# Requires Vs30 and distance to the volcanic front
REQUIRES_SITES_PARAMETERS = set(('vs30', 'xvf'))
def __init__(self, **kwargs):
super().__init__(ergodic=kwargs.get("ergodic", True), **kwargs)
self.theta6_adj = kwargs.get("theta6_adjustment", 0.0)
self.sigma_mu_epsilon = kwargs.get("sigma_mu_epsilon", 0.0)
faba_type = kwargs.get("faba_taper_model", "Step")
self.faba_model = FABA_ALL_MODELS[faba_type](**kwargs)
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
Returns mean and stddevs applying the statistical uncertainty if
needed
"""
mean, stddevs = super().get_mean_and_stddevs(sites, rup, dists, imt,
stddev_types)
if self.sigma_mu_epsilon:
sigma_mu = get_stress_factor(imt, slab=False)
return mean + (sigma_mu * self.sigma_mu_epsilon), stddevs
else:
return mean, stddevs
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1)
"""
return (C['theta2'] + self.CONSTS['theta3'] * (mag - 7.8)) *\
np.log(dists.rrup + self.CONSTS['c4'] * np.exp((mag - 6.) *
self.CONSTS['theta9'])) +\
((self.theta6_adj + C['theta6']) * dists.rrup)
def _compute_forearc_backarc_term(self, C, sites, dists):
"""
Computes the forearc/backarc scaling term given by equation (4)
"""
max_dist = np.copy(dists.rrup)
max_dist[max_dist < 100.0] = 100.0
f_faba = C['theta15'] + (C['theta16'] * np.log(max_dist / 40.0))
return f_faba * self.faba_model(-sites.xvf)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt vlin b theta1 theta2 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma sigma_ss
pga 865.1000 -1.1860 4.2203 -1.3500 -0.00721467 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0200 865.1000 -1.1860 4.2203 -1.3500 -0.00719296 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0500 1053.5000 -1.3460 4.5371 -1.4000 -0.00712619 1.2536 -1.6500 3.3700 0.0130 1.2880 -0.0138 -0.4000 1.1030 -1.1800 0.6000 0.4300 0.7400 0.6000
0.0750 1085.7000 -1.4710 5.0733 -1.4500 -0.00701600 1.4175 -1.8000 3.3700 0.0130 1.4830 -0.0142 -0.4000 1.2732 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1000 1032.5000 -1.6240 5.2892 -1.4500 -0.00687258 1.3997 -1.8000 3.3300 0.0130 1.6130 -0.0145 -0.4000 1.3042 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1500 877.6000 -1.9310 5.4563 -1.4500 -0.00671633 1.3582 -1.6900 3.2500 0.0130 1.8820 -0.0153 -0.4000 1.2600 -1.3000 0.6000 0.4300 0.7400 0.6000
0.2000 748.2000 -2.1880 5.2684 -1.4000 -0.00657867 1.1648 -1.4900 3.0300 0.0129 2.0760 -0.0162 -0.3500 1.2230 -1.2500 0.6000 0.4300 0.7400 0.6000
0.2500 654.3000 -2.3810 5.0594 -1.3500 -0.00648602 0.9940 -1.3000 2.8000 0.0129 2.2480 -0.0172 -0.3100 1.1600 -1.1700 0.6000 0.4300 0.7400 0.6000
0.3000 587.1000 -2.5180 4.7945 -1.2800 -0.00643709 0.8821 -1.1800 2.5900 0.0128 2.3480 -0.0183 -0.2800 1.0500 -1.0600 0.6000 0.4300 0.7400 0.6000
0.4000 503.0000 -2.6570 4.4644 -1.1800 -0.00639138 0.7046 -0.9800 2.2000 0.0127 2.4270 -0.0206 -0.2300 0.8000 -0.7800 0.6000 0.4300 0.7400 0.6000
0.5000 456.6000 -2.6690 4.0181 -1.0800 -0.00629147 0.5799 -0.8200 1.9200 0.0125 2.3990 -0.0231 -0.1900 0.6620 -0.6200 0.6000 0.4300 0.7400 0.6000
0.6000 430.3000 -2.5990 3.6055 -0.9900 -0.00609857 0.5021 -0.7000 1.7000 0.0124 2.2730 -0.0256 -0.1600 0.5800 -0.5000 0.6000 0.4300 0.7400 0.6000
0.7500 410.5000 -2.4010 3.2174 -0.9100 -0.00581454 0.3687 -0.5400 1.4200 0.0120 1.9930 -0.0296 -0.1200 0.4800 -0.3400 0.6000 0.4300 0.7400 0.6000
1.0000 400.0000 -1.9550 2.7981 -0.8500 -0.00548905 0.1746 -0.3400 1.1000 0.0114 1.4700 -0.0363 -0.0700 0.3300 -0.1400 0.6000 0.4300 0.7400 0.6000
1.5000 400.0000 -1.0250 2.0123 -0.7700 -0.00520499 -0.0820 -0.0500 0.7000 0.0100 0.4080 -0.0493 0.0000 0.3100 0.0000 0.6000 0.4300 0.7400 0.6000
2.0000 400.0000 -0.2990 1.4128 -0.7100 -0.00505022 -0.2821 0.1200 0.7000 0.0085 -0.4010 -0.0610 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
2.5000 400.0000 0.0000 0.9976 -0.6700 -0.00507967 -0.4108 0.2500 0.7000 0.0069 -0.7230 -0.0711 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
3.0000 400.0000 0.0000 0.6443 -0.6400 -0.00529221 -0.4466 0.3000 0.7000 0.0054 -0.6730 -0.0798 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
4.0000 400.0000 0.0000 0.0657 -0.5800 -0.00564790 -0.4344 0.3000 0.7000 0.0027 -0.6270 -0.0935 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
5.0000 400.0000 0.0000 -0.4624 -0.5400 -0.00607621 -0.4368 0.3000 0.7000 0.0005 -0.5960 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
6.0000 400.0000 0.0000 -0.9809 -0.5000 -0.00647922 -0.4586 0.3000 0.7000 -0.0013 -0.5660 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
7.5000 400.0000 0.0000 -1.6017 -0.4600 -0.00676355 -0.4433 0.3000 0.7000 -0.0033 -0.5280 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
10.0000 400.0000 0.0000 -2.2937 -0.4000 -0.00686566 -0.4828 0.3000 0.7000 -0.0060 -0.5040 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
""")
[docs]class BCHydroESHM20SInterLow(AbrahamsonEtAl2015SInterLow):
"""
ESHM20 Adjustment of the BC Hydro GMPE for subduction interface events
with theta6 calibrated to Mediterranean data, for the low magnitude
scaling branch.
"""
experimental = True
# Requires Vs30 and distance to the volcanic front
REQUIRES_SITES_PARAMETERS = set(('vs30', 'xvf'))
def __init__(self, **kwargs):
super().__init__(ergodic=kwargs.get("ergodic", True), **kwargs)
self.theta6_adj = kwargs.get("theta6_adjustment", 0.0)
self.sigma_mu_epsilon = kwargs.get("sigma_mu_epsilon", 0.0)
faba_type = kwargs.get("faba_taper_model", "Step")
self.faba_model = FABA_ALL_MODELS[faba_type](**kwargs)
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
Returns mean and stddevs applying the statistical uncertainty if
needed
"""
mean, stddevs = super().get_mean_and_stddevs(sites, rup, dists, imt,
stddev_types)
if self.sigma_mu_epsilon:
sigma_mu = get_stress_factor(imt, slab=False)
return mean + (sigma_mu * self.sigma_mu_epsilon), stddevs
else:
return mean, stddevs
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1)
"""
return (C['theta2'] + self.CONSTS['theta3'] * (mag - 7.8)) *\
np.log(dists.rrup + self.CONSTS['c4'] * np.exp((mag - 6.) *
self.CONSTS['theta9'])) +\
((self.theta6_adj + C['theta6']) * dists.rrup)
def _compute_forearc_backarc_term(self, C, sites, dists):
"""
Computes the forearc/backarc scaling term given by equation (4)
"""
max_dist = np.copy(dists.rrup)
max_dist[max_dist < 100.0] = 100.0
f_faba = C['theta15'] + (C['theta16'] * np.log(max_dist / 40.0))
return f_faba * self.faba_model(-sites.xvf)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt vlin b theta1 theta2 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma sigma_ss
pga 865.1000 -1.1860 4.2203 -1.3500 -0.00721467 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0200 865.1000 -1.1860 4.2203 -1.3500 -0.00719296 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0500 1053.5000 -1.3460 4.5371 -1.4000 -0.00712619 1.2536 -1.6500 3.3700 0.0130 1.2880 -0.0138 -0.4000 1.1030 -1.1800 0.6000 0.4300 0.7400 0.6000
0.0750 1085.7000 -1.4710 5.0733 -1.4500 -0.00701600 1.4175 -1.8000 3.3700 0.0130 1.4830 -0.0142 -0.4000 1.2732 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1000 1032.5000 -1.6240 5.2892 -1.4500 -0.00687258 1.3997 -1.8000 3.3300 0.0130 1.6130 -0.0145 -0.4000 1.3042 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1500 877.6000 -1.9310 5.4563 -1.4500 -0.00671633 1.3582 -1.6900 3.2500 0.0130 1.8820 -0.0153 -0.4000 1.2600 -1.3000 0.6000 0.4300 0.7400 0.6000
0.2000 748.2000 -2.1880 5.2684 -1.4000 -0.00657867 1.1648 -1.4900 3.0300 0.0129 2.0760 -0.0162 -0.3500 1.2230 -1.2500 0.6000 0.4300 0.7400 0.6000
0.2500 654.3000 -2.3810 5.0594 -1.3500 -0.00648602 0.9940 -1.3000 2.8000 0.0129 2.2480 -0.0172 -0.3100 1.1600 -1.1700 0.6000 0.4300 0.7400 0.6000
0.3000 587.1000 -2.5180 4.7945 -1.2800 -0.00643709 0.8821 -1.1800 2.5900 0.0128 2.3480 -0.0183 -0.2800 1.0500 -1.0600 0.6000 0.4300 0.7400 0.6000
0.4000 503.0000 -2.6570 4.4644 -1.1800 -0.00639138 0.7046 -0.9800 2.2000 0.0127 2.4270 -0.0206 -0.2300 0.8000 -0.7800 0.6000 0.4300 0.7400 0.6000
0.5000 456.6000 -2.6690 4.0181 -1.0800 -0.00629147 0.5799 -0.8200 1.9200 0.0125 2.3990 -0.0231 -0.1900 0.6620 -0.6200 0.6000 0.4300 0.7400 0.6000
0.6000 430.3000 -2.5990 3.6055 -0.9900 -0.00609857 0.5021 -0.7000 1.7000 0.0124 2.2730 -0.0256 -0.1600 0.5800 -0.5000 0.6000 0.4300 0.7400 0.6000
0.7500 410.5000 -2.4010 3.2174 -0.9100 -0.00581454 0.3687 -0.5400 1.4200 0.0120 1.9930 -0.0296 -0.1200 0.4800 -0.3400 0.6000 0.4300 0.7400 0.6000
1.0000 400.0000 -1.9550 2.7981 -0.8500 -0.00548905 0.1746 -0.3400 1.1000 0.0114 1.4700 -0.0363 -0.0700 0.3300 -0.1400 0.6000 0.4300 0.7400 0.6000
1.5000 400.0000 -1.0250 2.0123 -0.7700 -0.00520499 -0.0820 -0.0500 0.7000 0.0100 0.4080 -0.0493 0.0000 0.3100 0.0000 0.6000 0.4300 0.7400 0.6000
2.0000 400.0000 -0.2990 1.4128 -0.7100 -0.00505022 -0.2821 0.1200 0.7000 0.0085 -0.4010 -0.0610 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
2.5000 400.0000 0.0000 0.9976 -0.6700 -0.00507967 -0.4108 0.2500 0.7000 0.0069 -0.7230 -0.0711 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
3.0000 400.0000 0.0000 0.6443 -0.6400 -0.00529221 -0.4466 0.3000 0.7000 0.0054 -0.6730 -0.0798 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
4.0000 400.0000 0.0000 0.0657 -0.5800 -0.00564790 -0.4344 0.3000 0.7000 0.0027 -0.6270 -0.0935 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
5.0000 400.0000 0.0000 -0.4624 -0.5400 -0.00607621 -0.4368 0.3000 0.7000 0.0005 -0.5960 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
6.0000 400.0000 0.0000 -0.9809 -0.5000 -0.00647922 -0.4586 0.3000 0.7000 -0.0013 -0.5660 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
7.5000 400.0000 0.0000 -1.6017 -0.4600 -0.00676355 -0.4433 0.3000 0.7000 -0.0033 -0.5280 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
10.0000 400.0000 0.0000 -2.2937 -0.4000 -0.00686566 -0.4828 0.3000 0.7000 -0.0060 -0.5040 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
""")
[docs]class BCHydroESHM20SInterHigh(AbrahamsonEtAl2015SInterHigh):
"""
ESHM20 adjustment of the BC Hydro GMPE for subduction interface events
with theta6 calibrated to Mediterranean data, for the high
magnitude scaling branch.
"""
experimental = True
# Requires Vs30 and distance to the volcanic front
REQUIRES_SITES_PARAMETERS = set(('vs30', 'xvf'))
def __init__(self, **kwargs):
super().__init__(ergodic=kwargs.get("ergodic", True), **kwargs)
self.theta6_adj = kwargs.get("theta6_adjustment", 0.0)
self.sigma_mu_epsilon = kwargs.get("sigma_mu_epsilon", 0.0)
faba_type = kwargs.get("faba_taper_model", "Step")
self.faba_model = FABA_ALL_MODELS[faba_type](**kwargs)
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
Returns mean and stddevs applying the statistical uncertainty if
needed
"""
mean, stddevs = super().get_mean_and_stddevs(sites, rup, dists, imt,
stddev_types)
if self.sigma_mu_epsilon:
sigma_mu = get_stress_factor(imt, slab=False)
return mean + (sigma_mu * self.sigma_mu_epsilon), stddevs
else:
return mean, stddevs
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1)
"""
return (C['theta2'] + self.CONSTS['theta3'] * (mag - 7.8)) *\
np.log(dists.rrup + self.CONSTS['c4'] * np.exp((mag - 6.) *
self.CONSTS['theta9'])) +\
((self.theta6_adj + C['theta6']) * dists.rrup)
def _compute_forearc_backarc_term(self, C, sites, dists):
"""
Computes the forearc/backarc scaling term given by equation (4)
"""
max_dist = np.copy(dists.rrup)
max_dist[max_dist < 100.0] = 100.0
f_faba = C['theta15'] + (C['theta16'] * np.log(max_dist / 40.0))
return f_faba * self.faba_model(-sites.xvf)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt vlin b theta1 theta2 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma sigma_ss
pga 865.1000 -1.1860 4.2203 -1.3500 -0.00721467 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0200 865.1000 -1.1860 4.2203 -1.3500 -0.00719296 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0500 1053.5000 -1.3460 4.5371 -1.4000 -0.00712619 1.2536 -1.6500 3.3700 0.0130 1.2880 -0.0138 -0.4000 1.1030 -1.1800 0.6000 0.4300 0.7400 0.6000
0.0750 1085.7000 -1.4710 5.0733 -1.4500 -0.00701600 1.4175 -1.8000 3.3700 0.0130 1.4830 -0.0142 -0.4000 1.2732 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1000 1032.5000 -1.6240 5.2892 -1.4500 -0.00687258 1.3997 -1.8000 3.3300 0.0130 1.6130 -0.0145 -0.4000 1.3042 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1500 877.6000 -1.9310 5.4563 -1.4500 -0.00671633 1.3582 -1.6900 3.2500 0.0130 1.8820 -0.0153 -0.4000 1.2600 -1.3000 0.6000 0.4300 0.7400 0.6000
0.2000 748.2000 -2.1880 5.2684 -1.4000 -0.00657867 1.1648 -1.4900 3.0300 0.0129 2.0760 -0.0162 -0.3500 1.2230 -1.2500 0.6000 0.4300 0.7400 0.6000
0.2500 654.3000 -2.3810 5.0594 -1.3500 -0.00648602 0.9940 -1.3000 2.8000 0.0129 2.2480 -0.0172 -0.3100 1.1600 -1.1700 0.6000 0.4300 0.7400 0.6000
0.3000 587.1000 -2.5180 4.7945 -1.2800 -0.00643709 0.8821 -1.1800 2.5900 0.0128 2.3480 -0.0183 -0.2800 1.0500 -1.0600 0.6000 0.4300 0.7400 0.6000
0.4000 503.0000 -2.6570 4.4644 -1.1800 -0.00639138 0.7046 -0.9800 2.2000 0.0127 2.4270 -0.0206 -0.2300 0.8000 -0.7800 0.6000 0.4300 0.7400 0.6000
0.5000 456.6000 -2.6690 4.0181 -1.0800 -0.00629147 0.5799 -0.8200 1.9200 0.0125 2.3990 -0.0231 -0.1900 0.6620 -0.6200 0.6000 0.4300 0.7400 0.6000
0.6000 430.3000 -2.5990 3.6055 -0.9900 -0.00609857 0.5021 -0.7000 1.7000 0.0124 2.2730 -0.0256 -0.1600 0.5800 -0.5000 0.6000 0.4300 0.7400 0.6000
0.7500 410.5000 -2.4010 3.2174 -0.9100 -0.00581454 0.3687 -0.5400 1.4200 0.0120 1.9930 -0.0296 -0.1200 0.4800 -0.3400 0.6000 0.4300 0.7400 0.6000
1.0000 400.0000 -1.9550 2.7981 -0.8500 -0.00548905 0.1746 -0.3400 1.1000 0.0114 1.4700 -0.0363 -0.0700 0.3300 -0.1400 0.6000 0.4300 0.7400 0.6000
1.5000 400.0000 -1.0250 2.0123 -0.7700 -0.00520499 -0.0820 -0.0500 0.7000 0.0100 0.4080 -0.0493 0.0000 0.3100 0.0000 0.6000 0.4300 0.7400 0.6000
2.0000 400.0000 -0.2990 1.4128 -0.7100 -0.00505022 -0.2821 0.1200 0.7000 0.0085 -0.4010 -0.0610 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
2.5000 400.0000 0.0000 0.9976 -0.6700 -0.00507967 -0.4108 0.2500 0.7000 0.0069 -0.7230 -0.0711 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
3.0000 400.0000 0.0000 0.6443 -0.6400 -0.00529221 -0.4466 0.3000 0.7000 0.0054 -0.6730 -0.0798 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
4.0000 400.0000 0.0000 0.0657 -0.5800 -0.00564790 -0.4344 0.3000 0.7000 0.0027 -0.6270 -0.0935 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
5.0000 400.0000 0.0000 -0.4624 -0.5400 -0.00607621 -0.4368 0.3000 0.7000 0.0005 -0.5960 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
6.0000 400.0000 0.0000 -0.9809 -0.5000 -0.00647922 -0.4586 0.3000 0.7000 -0.0013 -0.5660 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
7.5000 400.0000 0.0000 -1.6017 -0.4600 -0.00676355 -0.4433 0.3000 0.7000 -0.0033 -0.5280 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
10.0000 400.0000 0.0000 -2.2937 -0.4000 -0.00686566 -0.4828 0.3000 0.7000 -0.0060 -0.5040 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
""")
[docs]class BCHydroESHM20SSlab(AbrahamsonEtAl2015SSlab):
"""
ESHM20 adjustment of the BC Hydro GMPE for subduction in-slab events with
theta6 calibrated to Mediterranean data.
Introduces two configurable parameters:
a6_adjustment - the amount to increase or decrease the theta6 (should be
+0.0015 (for slower attenuation) and -0.0015 (for faster attenuation)
sigma_mu_epsilon - number of standard deviations above or below the mean
to apply the statistical uncertainty sigma_mu term.
"""
experimental = True
# Requires Vs30 and distance to the volcanic front
REQUIRES_SITES_PARAMETERS = set(('vs30', 'xvf'))
def __init__(self, **kwargs):
super().__init__(ergodic=kwargs.get("ergodic", True), **kwargs)
self.theta6_adj = kwargs.get("theta6_adjustment", 0.0)
self.sigma_mu_epsilon = kwargs.get("sigma_mu_epsilon", 0.0)
faba_type = kwargs.get("faba_taper_model", "Step")
self.faba_model = FABA_ALL_MODELS[faba_type](**kwargs)
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
Returns mean and stddevs applying the statistical uncertainty if
needed
"""
mean, stddevs = super().get_mean_and_stddevs(sites, rup, dists, imt,
stddev_types)
if self.sigma_mu_epsilon:
sigma_mu = get_stress_factor(imt, slab=True)
return mean + (sigma_mu * self.sigma_mu_epsilon), stddevs
else:
return mean, stddevs
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1)
"""
return ((C['theta2'] + C['theta14'] + self.CONSTS['theta3'] *
(mag - 7.8)) * np.log(dists.rhypo + self.CONSTS['c4'] *
np.exp((mag - 6.) * self.CONSTS['theta9'])) +
((self.theta6_adj + C['theta6']) * dists.rhypo)) + C["theta10"]
def _compute_forearc_backarc_term(self, C, sites, dists):
"""
Computes the forearc/backarc scaling term given by equation (4).
"""
max_dist = np.copy(dists.rhypo)
max_dist[max_dist < 85.0] = 85.0
f_faba = C['theta7'] + (C['theta8'] * np.log(max_dist / 40.0))
return f_faba * self.faba_model(-sites.xvf)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt vlin b theta1 theta2 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma sigma_ss
pga 865.1000 -1.1860 4.2203 -1.3500 -0.00278801 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0200 865.1000 -1.1860 4.2203 -1.3500 -0.00275821 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0500 1053.5000 -1.3460 4.5371 -1.4000 -0.00268517 1.2536 -1.6500 3.3700 0.0130 1.2880 -0.0138 -0.4000 1.1030 -1.1800 0.6000 0.4300 0.7400 0.6000
0.0750 1085.7000 -1.4710 5.0733 -1.4500 -0.00261360 1.4175 -1.8000 3.3700 0.0130 1.4830 -0.0142 -0.4000 1.2732 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1000 1032.5000 -1.6240 5.2892 -1.4500 -0.00259240 1.3997 -1.8000 3.3300 0.0130 1.6130 -0.0145 -0.4000 1.3042 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1500 877.6000 -1.9310 5.4563 -1.4500 -0.00264688 1.3582 -1.6900 3.2500 0.0130 1.8820 -0.0153 -0.4000 1.2600 -1.3000 0.6000 0.4300 0.7400 0.6000
0.2000 748.2000 -2.1880 5.2684 -1.4000 -0.00277703 1.1648 -1.4900 3.0300 0.0129 2.0760 -0.0162 -0.3500 1.2230 -1.2500 0.6000 0.4300 0.7400 0.6000
0.2500 654.3000 -2.3810 5.0594 -1.3500 -0.00296427 0.9940 -1.3000 2.8000 0.0129 2.2480 -0.0172 -0.3100 1.1600 -1.1700 0.6000 0.4300 0.7400 0.6000
0.3000 587.1000 -2.5180 4.7945 -1.2800 -0.00318216 0.8821 -1.1800 2.5900 0.0128 2.3480 -0.0183 -0.2800 1.0500 -1.0600 0.6000 0.4300 0.7400 0.6000
0.4000 503.0000 -2.6570 4.4644 -1.1800 -0.00340820 0.7046 -0.9800 2.2000 0.0127 2.4270 -0.0206 -0.2300 0.8000 -0.7800 0.6000 0.4300 0.7400 0.6000
0.5000 456.6000 -2.6690 4.0181 -1.0800 -0.00363798 0.5799 -0.8200 1.9200 0.0125 2.3990 -0.0231 -0.1900 0.6620 -0.6200 0.6000 0.4300 0.7400 0.6000
0.6000 430.3000 -2.5990 3.6055 -0.9900 -0.00388267 0.5021 -0.7000 1.7000 0.0124 2.2730 -0.0256 -0.1600 0.5800 -0.5000 0.6000 0.4300 0.7400 0.6000
0.7500 410.5000 -2.4010 3.2174 -0.9100 -0.00415403 0.3687 -0.5400 1.4200 0.0120 1.9930 -0.0296 -0.1200 0.4800 -0.3400 0.6000 0.4300 0.7400 0.6000
1.0000 400.0000 -1.9550 2.7981 -0.8500 -0.00445479 0.1746 -0.3400 1.1000 0.0114 1.4700 -0.0363 -0.0700 0.3300 -0.1400 0.6000 0.4300 0.7400 0.6000
1.5000 400.0000 -1.0250 2.0123 -0.7700 -0.00478084 -0.0820 -0.0500 0.7000 0.0100 0.4080 -0.0493 0.0000 0.3100 0.0000 0.6000 0.4300 0.7400 0.6000
2.0000 400.0000 -0.2990 1.4128 -0.7100 -0.00513159 -0.2821 0.1200 0.7000 0.0085 -0.4010 -0.0610 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
2.5000 400.0000 0.0000 0.9976 -0.6700 -0.00550694 -0.4108 0.2500 0.7000 0.0069 -0.7230 -0.0711 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
3.0000 400.0000 0.0000 0.6443 -0.6400 -0.00590809 -0.4466 0.3000 0.7000 0.0054 -0.6730 -0.0798 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
4.0000 400.0000 0.0000 0.0657 -0.5800 -0.00634283 -0.4344 0.3000 0.7000 0.0027 -0.6270 -0.0935 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
5.0000 400.0000 0.0000 -0.4624 -0.5400 -0.00680074 -0.4368 0.3000 0.7000 0.0005 -0.5960 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
6.0000 400.0000 0.0000 -0.9809 -0.5000 -0.00722208 -0.4586 0.3000 0.7000 -0.0013 -0.5660 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
7.5000 400.0000 0.0000 -1.6017 -0.4600 -0.00752097 -0.4433 0.3000 0.7000 -0.0033 -0.5280 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
10.0000 400.0000 0.0000 -2.2937 -0.4000 -0.00762908 -0.4828 0.3000 0.7000 -0.0060 -0.5040 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
""")
[docs]class BCHydroESHM20SSlabLow(AbrahamsonEtAl2015SSlabLow):
"""
ESHM20 adjustment of the BC Hydro GMPE for subduction in-slab events
with theta6 calibrated to Mediterranean data, for the low magnitude
scaling branch.
"""
experimental = True
# Requires Vs30 and distance to the volcanic front
REQUIRES_SITES_PARAMETERS = set(('vs30', 'xvf'))
def __init__(self, **kwargs):
super().__init__(ergodic=kwargs.get("ergodic", True), **kwargs)
self.theta6_adj = kwargs.get("theta6_adjustment", 0.0)
self.sigma_mu_epsilon = kwargs.get("sigma_mu_epsilon", 0.0)
faba_type = kwargs.get("faba_taper_model", "Step")
self.faba_model = FABA_ALL_MODELS[faba_type](**kwargs)
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
Returns mean and stddevs applying the statistical uncertainty if
needed
"""
mean, stddevs = super().get_mean_and_stddevs(sites, rup, dists, imt,
stddev_types)
if self.sigma_mu_epsilon:
sigma_mu = get_stress_factor(imt, slab=True)
return mean + (sigma_mu * self.sigma_mu_epsilon), stddevs
else:
return mean, stddevs
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1)
"""
return ((C['theta2'] + C['theta14'] + self.CONSTS['theta3'] *
(mag - 7.8)) * np.log(dists.rhypo + self.CONSTS['c4'] *
np.exp((mag - 6.) * self.CONSTS['theta9'])) +
((self.theta6_adj + C['theta6']) * dists.rhypo)) + C["theta10"]
def _compute_forearc_backarc_term(self, C, sites, dists):
"""
Computes the forearc/backarc scaling term given by equation (4).
"""
max_dist = np.copy(dists.rhypo)
max_dist[max_dist < 85.0] = 85.0
f_faba = C['theta7'] + (C['theta8'] * np.log(max_dist / 40.0))
return f_faba * self.faba_model(-sites.xvf)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt vlin b theta1 theta2 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma sigma_ss
pga 865.1000 -1.1860 4.2203 -1.3500 -0.00278801 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0200 865.1000 -1.1860 4.2203 -1.3500 -0.00275821 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0500 1053.5000 -1.3460 4.5371 -1.4000 -0.00268517 1.2536 -1.6500 3.3700 0.0130 1.2880 -0.0138 -0.4000 1.1030 -1.1800 0.6000 0.4300 0.7400 0.6000
0.0750 1085.7000 -1.4710 5.0733 -1.4500 -0.00261360 1.4175 -1.8000 3.3700 0.0130 1.4830 -0.0142 -0.4000 1.2732 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1000 1032.5000 -1.6240 5.2892 -1.4500 -0.00259240 1.3997 -1.8000 3.3300 0.0130 1.6130 -0.0145 -0.4000 1.3042 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1500 877.6000 -1.9310 5.4563 -1.4500 -0.00264688 1.3582 -1.6900 3.2500 0.0130 1.8820 -0.0153 -0.4000 1.2600 -1.3000 0.6000 0.4300 0.7400 0.6000
0.2000 748.2000 -2.1880 5.2684 -1.4000 -0.00277703 1.1648 -1.4900 3.0300 0.0129 2.0760 -0.0162 -0.3500 1.2230 -1.2500 0.6000 0.4300 0.7400 0.6000
0.2500 654.3000 -2.3810 5.0594 -1.3500 -0.00296427 0.9940 -1.3000 2.8000 0.0129 2.2480 -0.0172 -0.3100 1.1600 -1.1700 0.6000 0.4300 0.7400 0.6000
0.3000 587.1000 -2.5180 4.7945 -1.2800 -0.00318216 0.8821 -1.1800 2.5900 0.0128 2.3480 -0.0183 -0.2800 1.0500 -1.0600 0.6000 0.4300 0.7400 0.6000
0.4000 503.0000 -2.6570 4.4644 -1.1800 -0.00340820 0.7046 -0.9800 2.2000 0.0127 2.4270 -0.0206 -0.2300 0.8000 -0.7800 0.6000 0.4300 0.7400 0.6000
0.5000 456.6000 -2.6690 4.0181 -1.0800 -0.00363798 0.5799 -0.8200 1.9200 0.0125 2.3990 -0.0231 -0.1900 0.6620 -0.6200 0.6000 0.4300 0.7400 0.6000
0.6000 430.3000 -2.5990 3.6055 -0.9900 -0.00388267 0.5021 -0.7000 1.7000 0.0124 2.2730 -0.0256 -0.1600 0.5800 -0.5000 0.6000 0.4300 0.7400 0.6000
0.7500 410.5000 -2.4010 3.2174 -0.9100 -0.00415403 0.3687 -0.5400 1.4200 0.0120 1.9930 -0.0296 -0.1200 0.4800 -0.3400 0.6000 0.4300 0.7400 0.6000
1.0000 400.0000 -1.9550 2.7981 -0.8500 -0.00445479 0.1746 -0.3400 1.1000 0.0114 1.4700 -0.0363 -0.0700 0.3300 -0.1400 0.6000 0.4300 0.7400 0.6000
1.5000 400.0000 -1.0250 2.0123 -0.7700 -0.00478084 -0.0820 -0.0500 0.7000 0.0100 0.4080 -0.0493 0.0000 0.3100 0.0000 0.6000 0.4300 0.7400 0.6000
2.0000 400.0000 -0.2990 1.4128 -0.7100 -0.00513159 -0.2821 0.1200 0.7000 0.0085 -0.4010 -0.0610 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
2.5000 400.0000 0.0000 0.9976 -0.6700 -0.00550694 -0.4108 0.2500 0.7000 0.0069 -0.7230 -0.0711 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
3.0000 400.0000 0.0000 0.6443 -0.6400 -0.00590809 -0.4466 0.3000 0.7000 0.0054 -0.6730 -0.0798 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
4.0000 400.0000 0.0000 0.0657 -0.5800 -0.00634283 -0.4344 0.3000 0.7000 0.0027 -0.6270 -0.0935 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
5.0000 400.0000 0.0000 -0.4624 -0.5400 -0.00680074 -0.4368 0.3000 0.7000 0.0005 -0.5960 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
6.0000 400.0000 0.0000 -0.9809 -0.5000 -0.00722208 -0.4586 0.3000 0.7000 -0.0013 -0.5660 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
7.5000 400.0000 0.0000 -1.6017 -0.4600 -0.00752097 -0.4433 0.3000 0.7000 -0.0033 -0.5280 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
10.0000 400.0000 0.0000 -2.2937 -0.4000 -0.00762908 -0.4828 0.3000 0.7000 -0.0060 -0.5040 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
""")
[docs]class BCHydroESHM20SSlabHigh(AbrahamsonEtAl2015SSlabHigh):
"""
ESHM20 adjustment of the BC Hydro GMPE for subduction interface events
with theta6 calibrated to Mediterranean data, for the high magnitude
scaling branch.
"""
experimental = True
# Requires Vs30 and distance to the volcanic front
REQUIRES_SITES_PARAMETERS = set(('vs30', 'xvf'))
def __init__(self, **kwargs):
super().__init__(ergodic=kwargs.get("ergodic", True), **kwargs)
self.theta6_adj = kwargs.get("theta6_adjustment", 0.0)
self.sigma_mu_epsilon = kwargs.get("sigma_mu_epsilon", 0.0)
faba_type = kwargs.get("faba_taper_model", "Step")
self.faba_model = FABA_ALL_MODELS[faba_type](**kwargs)
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
Returns mean and stddevs applying the statistical uncertainty if
needed
"""
mean, stddevs = super().get_mean_and_stddevs(sites, rup, dists, imt,
stddev_types)
if self.sigma_mu_epsilon:
sigma_mu = get_stress_factor(imt, slab=True)
return mean + (sigma_mu * self.sigma_mu_epsilon), stddevs
else:
return mean, stddevs
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1)
"""
return ((C['theta2'] + C['theta14'] + self.CONSTS['theta3'] *
(mag - 7.8)) * np.log(dists.rhypo + self.CONSTS['c4'] *
np.exp((mag - 6.) * self.CONSTS['theta9'])) +
((self.theta6_adj + C['theta6']) * dists.rhypo)) + C["theta10"]
def _compute_forearc_backarc_term(self, C, sites, dists):
"""
Computes the forearc/backarc scaling term given by equation (4).
"""
max_dist = np.copy(dists.rhypo)
max_dist[max_dist < 85.0] = 85.0
f_faba = C['theta7'] + (C['theta8'] * np.log(max_dist / 40.0))
return f_faba * self.faba_model(-sites.xvf)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt vlin b theta1 theta2 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma sigma_ss
pga 865.1000 -1.1860 4.2203 -1.3500 -0.00278801 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0200 865.1000 -1.1860 4.2203 -1.3500 -0.00275821 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000
0.0500 1053.5000 -1.3460 4.5371 -1.4000 -0.00268517 1.2536 -1.6500 3.3700 0.0130 1.2880 -0.0138 -0.4000 1.1030 -1.1800 0.6000 0.4300 0.7400 0.6000
0.0750 1085.7000 -1.4710 5.0733 -1.4500 -0.00261360 1.4175 -1.8000 3.3700 0.0130 1.4830 -0.0142 -0.4000 1.2732 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1000 1032.5000 -1.6240 5.2892 -1.4500 -0.00259240 1.3997 -1.8000 3.3300 0.0130 1.6130 -0.0145 -0.4000 1.3042 -1.3600 0.6000 0.4300 0.7400 0.6000
0.1500 877.6000 -1.9310 5.4563 -1.4500 -0.00264688 1.3582 -1.6900 3.2500 0.0130 1.8820 -0.0153 -0.4000 1.2600 -1.3000 0.6000 0.4300 0.7400 0.6000
0.2000 748.2000 -2.1880 5.2684 -1.4000 -0.00277703 1.1648 -1.4900 3.0300 0.0129 2.0760 -0.0162 -0.3500 1.2230 -1.2500 0.6000 0.4300 0.7400 0.6000
0.2500 654.3000 -2.3810 5.0594 -1.3500 -0.00296427 0.9940 -1.3000 2.8000 0.0129 2.2480 -0.0172 -0.3100 1.1600 -1.1700 0.6000 0.4300 0.7400 0.6000
0.3000 587.1000 -2.5180 4.7945 -1.2800 -0.00318216 0.8821 -1.1800 2.5900 0.0128 2.3480 -0.0183 -0.2800 1.0500 -1.0600 0.6000 0.4300 0.7400 0.6000
0.4000 503.0000 -2.6570 4.4644 -1.1800 -0.00340820 0.7046 -0.9800 2.2000 0.0127 2.4270 -0.0206 -0.2300 0.8000 -0.7800 0.6000 0.4300 0.7400 0.6000
0.5000 456.6000 -2.6690 4.0181 -1.0800 -0.00363798 0.5799 -0.8200 1.9200 0.0125 2.3990 -0.0231 -0.1900 0.6620 -0.6200 0.6000 0.4300 0.7400 0.6000
0.6000 430.3000 -2.5990 3.6055 -0.9900 -0.00388267 0.5021 -0.7000 1.7000 0.0124 2.2730 -0.0256 -0.1600 0.5800 -0.5000 0.6000 0.4300 0.7400 0.6000
0.7500 410.5000 -2.4010 3.2174 -0.9100 -0.00415403 0.3687 -0.5400 1.4200 0.0120 1.9930 -0.0296 -0.1200 0.4800 -0.3400 0.6000 0.4300 0.7400 0.6000
1.0000 400.0000 -1.9550 2.7981 -0.8500 -0.00445479 0.1746 -0.3400 1.1000 0.0114 1.4700 -0.0363 -0.0700 0.3300 -0.1400 0.6000 0.4300 0.7400 0.6000
1.5000 400.0000 -1.0250 2.0123 -0.7700 -0.00478084 -0.0820 -0.0500 0.7000 0.0100 0.4080 -0.0493 0.0000 0.3100 0.0000 0.6000 0.4300 0.7400 0.6000
2.0000 400.0000 -0.2990 1.4128 -0.7100 -0.00513159 -0.2821 0.1200 0.7000 0.0085 -0.4010 -0.0610 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
2.5000 400.0000 0.0000 0.9976 -0.6700 -0.00550694 -0.4108 0.2500 0.7000 0.0069 -0.7230 -0.0711 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
3.0000 400.0000 0.0000 0.6443 -0.6400 -0.00590809 -0.4466 0.3000 0.7000 0.0054 -0.6730 -0.0798 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
4.0000 400.0000 0.0000 0.0657 -0.5800 -0.00634283 -0.4344 0.3000 0.7000 0.0027 -0.6270 -0.0935 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
5.0000 400.0000 0.0000 -0.4624 -0.5400 -0.00680074 -0.4368 0.3000 0.7000 0.0005 -0.5960 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
6.0000 400.0000 0.0000 -0.9809 -0.5000 -0.00722208 -0.4586 0.3000 0.7000 -0.0013 -0.5660 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
7.5000 400.0000 0.0000 -1.6017 -0.4600 -0.00752097 -0.4433 0.3000 0.7000 -0.0033 -0.5280 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
10.0000 400.0000 0.0000 -2.2937 -0.4000 -0.00762908 -0.4828 0.3000 0.7000 -0.0060 -0.5040 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000
""")