# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2021 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:`AbrahamsonEtAl2015`
:class:`AbrahamsonEtAl2015SInter`
:class:`AbrahamsonEtAl2015SInterHigh`
:class:`AbrahamsonEtAl2015SInterLow`
:class:`AbrahamsonEtAl2015SSlab`
:class:`AbrahamsonEtAl2015SSlabHigh`
:class:`AbrahamsonEtAl2015SSlabLow`
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
# Period-Independent Coefficients (Table 2)
CONSTS = {
'n': 1.18,
'c': 1.88,
'theta3': 0.1,
'theta4': 0.9,
'theta5': 0.0,
'theta9': 0.4,
'c4': 10.0,
'C1': 7.8
}
C1 = 7.2 # for Montalva2017
# 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):
"""
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
def _compute_magterm(C1, theta1, theta4, theta5, theta13, dc1, mag):
"""
Computes the magnitude scaling term given by equation (2)
corrected by a local adjustment factor
"""
base = theta1 + theta4 * dc1
dmag = C1 + dc1
f_mag = np.where(mag > dmag,
theta5 * (mag - dmag) + theta13 * (10. - mag) ** 2.,
theta4 * (mag - dmag) + theta13 * (10. - mag) ** 2.)
return base + f_mag
# theta6_adj used in BCHydro
def _compute_disterm(trt, C1, theta2, theta14, theta3, ctx, c4, theta9,
theta6_adj, theta6, theta10):
if trt == const.TRT.SUBDUCTION_INTERFACE:
dists = ctx.rrup
assert theta10 == 0., theta10
elif trt == const.TRT.SUBDUCTION_INTRASLAB:
dists = ctx.rhypo
else:
raise NotImplementedError(trt)
return ((theta2 + theta14 + theta3 * (ctx.mag - C1)) * np.log(
dists + c4 * np.exp((ctx.mag - 6.) * theta9)) +
(theta6_adj + theta6) * dists) + theta10
def _compute_forearc_backarc_term(trt, faba_model, C, ctx):
if trt == const.TRT.SUBDUCTION_INTERFACE:
dists = ctx.rrup
a, b = C['theta15'], C['theta16']
min_dist = 100.
elif trt == const.TRT.SUBDUCTION_INTRASLAB:
dists = ctx.rhypo
a, b = C['theta7'], C['theta8']
min_dist = 85.
else:
raise NotImplementedError(trt)
if faba_model is None:
f_faba = np.zeros_like(dists)
# Term only applies to backarc ctx (F_FABA = 0. for forearc)
fixed_dists = dists[ctx.backarc]
fixed_dists[fixed_dists < min_dist] = min_dist
f_faba[ctx.backarc] = a + b * np.log(fixed_dists / 40.)
return f_faba
# in BCHydro subclasses
fixed_dists = np.copy(dists)
fixed_dists[fixed_dists < min_dist] = min_dist
f_faba = a + b * np.log(fixed_dists / 40.)
return f_faba * faba_model(-ctx.xvf)
def _compute_distance_term(kind, trt, theta6_adj, C, ctx):
"""
Computes the distance scaling term, as contained within equation (1)
"""
if kind.startswith("montalva"):
theta3 = C['theta3']
else:
theta3 = CONSTS['theta3']
if kind == "montalva17":
C1 = 7.2
else:
C1 = 7.8
if trt == const.TRT.SUBDUCTION_INTERFACE:
return _compute_disterm(
trt, C1, C['theta2'], 0., theta3, ctx, CONSTS['c4'],
CONSTS['theta9'], theta6_adj, C['theta6'], theta10=0.)
else: # sslab
return _compute_disterm(
trt, C1, C['theta2'], C['theta14'], theta3, ctx,
CONSTS['c4'], CONSTS['theta9'], theta6_adj, C['theta6'],
C["theta10"])
def _compute_focal_depth_term(trt, C, ctx):
"""
Computes the hypocentral depth scaling term - as indicated by
equation (3)
For interface events F_EVENT = 0.. so no depth scaling is returned.
For SSlab events computes the hypocentral depth scaling term as
indicated by equation (3)
"""
if trt == const.TRT.SUBDUCTION_INTERFACE:
return 0.
if ctx.hypo_depth > 120.0:
z_h = 120.0
else:
z_h = ctx.hypo_depth
return C['theta11'] * (z_h - 60.)
def _compute_magnitude_term(kind, C, dc1, mag):
"""
Computes the magnitude scaling term given by equation (2)
"""
if kind == "base":
return _compute_magterm(
CONSTS['C1'], C['theta1'], CONSTS['theta4'],
CONSTS['theta5'], C['theta13'], dc1, mag)
elif kind == "montalva16":
return _compute_magterm(
CONSTS['C1'], C['theta1'], C['theta4'],
C['theta5'], C['theta13'], dc1, mag)
elif kind == "montalva17":
return _compute_magterm(C1, C['theta1'], C['theta4'],
C['theta5'], 0., dc1, mag)
def _compute_pga_rock(kind, trt, theta6_adj, faba_model, C, dc1, ctx):
"""
Compute and return mean imt value for rock conditions
(vs30 = 1000 m/s)
"""
mean = (_compute_magnitude_term(kind, C, dc1, ctx.mag) +
_compute_distance_term(kind, trt, theta6_adj, C, ctx) +
_compute_focal_depth_term(trt, C, ctx) +
_compute_forearc_backarc_term(trt, faba_model, C, ctx))
# Apply linear site term
site_response = ((C['theta12'] + C['b'] * CONSTS['n']) *
np.log(1000. / C['vlin']))
return mean + site_response
def _compute_site_response_term(C, ctx, pga1000):
"""
Compute and return site response model term
This GMPE adopts the same site response scaling model of
Walling et al (2008) as implemented in the Abrahamson & Silva (2008)
GMPE. The functional form is retained here.
"""
vs_star = ctx.vs30.copy()
vs_star[vs_star > 1000.0] = 1000.
arg = vs_star / C["vlin"]
site_resp_term = C["theta12"] * np.log(arg)
# Get linear scaling term
idx = ctx.vs30 >= C["vlin"]
site_resp_term[idx] += (C["b"] * CONSTS["n"] * np.log(arg[idx]))
# Get nonlinear scaling term
idx = np.logical_not(idx)
site_resp_term[idx] += (
-C["b"] * np.log(pga1000[idx] + CONSTS["c"]) +
C["b"] * np.log(pga1000[idx] + CONSTS["c"] *
(arg[idx] ** CONSTS["n"])))
return site_resp_term
[docs]class AbrahamsonEtAl2015SInter(GMPE):
"""
Implements the Subduction GMPE developed by Norman Abrahamson, Nicholas
Gregor and Kofi Addo, otherwise known as the "BC Hydro" Model, published
as "BC Hydro Ground Motion Prediction Equations For Subduction Earthquakes
(2015, Earthquake Spectra, in press), for subduction interface events.
From observations of very large events it was found that the magnitude
scaling term can be adjusted as part of the epistemic uncertainty model.
The adjustment comes in the form of the parameter DeltaC1, which is
period dependent for interface events. To capture the epistemic uncertainty
in DeltaC1, three models are proposed: a 'central', 'upper' and 'lower'
model. The current class implements the 'central' model, whilst additional
classes will implement the 'upper' and 'lower' alternatives.
"""
#: Supported tectonic region type is subduction interface
DEFINED_FOR_TECTONIC_REGION_TYPE = trt = const.TRT.SUBDUCTION_INTERFACE
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is the geometric mean component
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types are inter-event, intra-event
#: and total, see table 3, pages 12 - 13
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Site amplification is dependent upon Vs30
#: For the Abrahamson et al (2013) GMPE a new term is introduced to
#: determine whether a site is on the forearc with respect to the
#: subduction interface, or on the backarc. This boolean is a vector
#: containing True for a backarc site or False for a forearc or
#: unknown site.
REQUIRES_SITES_PARAMETERS = {'vs30', 'backarc'}
#: Required rupture parameters are magnitude for the interface model
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is closest distance to rupture, for
#: interface events
REQUIRES_DISTANCES = {'rrup'}
#: Reference soil conditions (bottom of page 29)
DEFINED_FOR_REFERENCE_VELOCITY = 1000
delta_c1 = None
kind = "base"
FABA_ALL_MODELS = {} # overridden in BCHydro
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.ergodic = kwargs.get('ergodic', True)
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")
if 'xvf' in self.REQUIRES_SITES_PARAMETERS: # BCHydro subclasses
self.faba_model = self.FABA_ALL_MODELS[faba_type](**kwargs)
else:
self.faba_model = None
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
C_PGA = self.COEFFS[PGA()]
dc1_pga = self.delta_c1 or self.COEFFS_MAG_SCALE[PGA()]["dc1"]
# compute median pga on rock (vs30=1000), needed for site response
# term calculation
pga1000 = np.exp(_compute_pga_rock(
self.kind, self.trt, self.theta6_adj, self.faba_model,
C_PGA, dc1_pga, ctx))
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
dc1 = self.delta_c1 or self.COEFFS_MAG_SCALE[imt]["dc1"]
mean[m] = (
_compute_magnitude_term(
self.kind, C, dc1, ctx.mag) +
_compute_distance_term(
self.kind, self.trt, self.theta6_adj, C, ctx) +
_compute_focal_depth_term(
self.trt, C, ctx) +
_compute_forearc_backarc_term(
self.trt, self.faba_model, C, ctx) +
_compute_site_response_term(
C, ctx, pga1000))
if self.sigma_mu_epsilon:
sigma_mu = get_stress_factor(
imt, self.DEFINED_FOR_TECTONIC_REGION_TYPE ==
const.TRT.SUBDUCTION_INTRASLAB)
mean[m] += sigma_mu * self.sigma_mu_epsilon
sig[m] = C["sigma"] if self.ergodic else C["sigma_ss"]
tau[m] = C['tau']
phi[m] = C["phi"] if self.ergodic else np.sqrt(
C["sigma_ss"] ** 2. - C["tau"] ** 2.)
# Period-dependent coefficients (Table 3)
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 -0.0012 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 -0.0012 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 -0.0012 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 -0.0012 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 -0.0012 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 -0.0014 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 -0.0018 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 -0.0023 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 -0.0027 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 -0.0035 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 -0.0044 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 -0.0050 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 -0.0058 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 -0.0062 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 -0.0064 -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 -0.0064 -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 -0.0064 -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 -0.0064 -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 -0.0064 -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 -0.0064 -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 -0.0064 -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 -0.0064 -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 -0.0064 -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
""")
COEFFS_MAG_SCALE = CoeffsTable(sa_damping=5, table="""
IMT dc1
pga 0.2
0.02 0.2
0.30 0.2
0.50 0.1
1.00 0.0
2.00 -0.1
3.00 -0.2
10.0 -0.2
""")
[docs]class AbrahamsonEtAl2015SInterHigh(AbrahamsonEtAl2015SInter):
"""
Defines the Abrahamson et al. (2013) scaling relation assuming the upper
values of the magnitude scaling for large slab earthquakes, as defined in
table 4
"""
COEFFS_MAG_SCALE = CoeffsTable(sa_damping=5, table="""
IMT dc1
pga 0.4
0.02 0.4
0.30 0.4
0.50 0.3
1.00 0.2
2.00 0.1
3.00 0.0
10.0 0.0
""")
[docs]class AbrahamsonEtAl2015SInterLow(AbrahamsonEtAl2015SInter):
"""
Defines the Abrahamson et al. (2013) scaling relation assuming the lower
values of the magnitude scaling for large slab earthquakes, as defined in
table 4
"""
COEFFS_MAG_SCALE = CoeffsTable(sa_damping=5, table="""
IMT dc1
pga 0.0
0.02 0.0
0.30 0.0
0.50 -0.1
1.00 -0.2
2.00 -0.3
3.00 -0.4
10.0 -0.4
""")
[docs]class AbrahamsonEtAl2015SSlab(AbrahamsonEtAl2015SInter):
"""
Implements the Subduction GMPE developed by Norman Abrahamson, Nicholas
Gregor and Kofi Addo, otherwise known as the "BC Hydro" Model, published
as "BC Hydro Ground Motion Prediction Equations For Subduction Earthquakes
(2013, Earthquake Spectra, in press).
This implements only the inslab GMPE. For inslab events the source is
considered to be a point source located at the hypocentre. Therefore
the hypocentral distance metric is used in place of the rupture distance,
and the hypocentral depth is used to scale the ground motion by depth
"""
#: Supported tectonic region type is subduction in-slab
DEFINED_FOR_TECTONIC_REGION_TYPE = trt = const.TRT.SUBDUCTION_INTRASLAB
#: Required distance measure is hypocentral for in-slab events
REQUIRES_DISTANCES = {'rhypo'}
#: In-slab events require constraint of hypocentral depth and magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'}
delta_c1 = -0.3
[docs]class AbrahamsonEtAl2015SSlabHigh(AbrahamsonEtAl2015SSlab):
"""
Defines the Abrahamson et al. (2013) scaling relation assuming the upper
values of the magnitude scaling for large slab earthquakes, as defined in
table 8
"""
delta_c1 = -0.1
[docs]class AbrahamsonEtAl2015SSlabLow(AbrahamsonEtAl2015SSlab):
"""
Defines the Abrahamson et al. (2013) scaling relation assuming the lower
values of the magnitude scaling for large slab earthquakes, as defined in
table 8
"""
delta_c1 = -0.5