# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2016 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`
"""
from __future__ import division
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[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 = const.TRT.SUBDUCTION_INTERFACE
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
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 = set([
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 = set(('vs30', 'backarc'))
#: Required rupture parameters are magnitude for the interface model
REQUIRES_RUPTURE_PARAMETERS = set(('mag',))
#: Required distance measure is closest distance to rupture, for
#: interface events
REQUIRES_DISTANCES = set(('rrup',))
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
# extract dictionaries of coefficients specific to required
# intensity measure type and for PGA
C = self.COEFFS[imt]
dc1 = self._get_delta_c1(imt)
C_PGA = self.COEFFS[PGA()]
dc1_pga = self._get_delta_c1(PGA())
# compute median pga on rock (vs30=1000), needed for site response
# term calculation
pga1000 = np.exp(
self._compute_pga_rock(C_PGA, dc1_pga, sites, rup, dists))
mean = (self._compute_magnitude_term(C, dc1, rup.mag) +
self._compute_distance_term(C, rup.mag, dists) +
self._compute_focal_depth_term(C, rup) +
self._compute_forearc_backarc_term(C, sites, dists) +
self._compute_site_response_term(C, sites, pga1000))
stddevs = self._get_stddevs(C, stddev_types, len(sites.vs30))
return mean, stddevs
def _get_delta_c1(self, imt):
"""
Returns the magnitude scaling parameter deltaC1 for capturing scaling
for large events.
"""
return self.COEFFS_MAG_SCALE[imt]["dc1"]
def _compute_pga_rock(self, C, dc1, sites, rup, dists):
"""
Compute and return mean imt value for rock conditions
(vs30 = 1000 m/s)
"""
mean = (self._compute_magnitude_term(C, dc1, rup.mag) +
self._compute_distance_term(C, rup.mag, dists) +
self._compute_focal_depth_term(C, rup) +
self._compute_forearc_backarc_term(C, sites, dists))
# Apply linear site term
site_response = ((C['theta12'] + C['b'] * self.CONSTS['n']) *
np.log(1000. / C['vlin']))
return mean + site_response
def _compute_magnitude_term(self, C, dc1, mag):
"""
Computes the magnitude scaling term given by equation (2)
"""
base = C['theta1'] + (self.CONSTS['theta4'] * dc1)
dmag = self.CONSTS["C1"] + dc1
if mag > dmag:
f_mag = (self.CONSTS['theta5'] * (mag - dmag)) +\
C['theta13'] * ((10. - mag) ** 2.)
else:
f_mag = (self.CONSTS['theta4'] * (mag - dmag)) +\
C['theta13'] * ((10. - mag) ** 2.)
return base + f_mag
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'])) + (C['theta6'] * dists.rrup)
def _compute_focal_depth_term(self, C, rup):
"""
Computes the hypocentral depth scaling term - as indicated by
equation (3)
For interface events F_EVENT = 0.. so no depth scaling is returned
"""
return 0.
def _compute_forearc_backarc_term(self, C, sites, dists):
"""
Computes the forearc/backarc scaling term given by equation (4)
"""
f_faba = np.zeros_like(dists.rrup)
# Term only applies to backarc sites (F_FABA = 0. for forearc)
max_dist = dists.rrup[sites.backarc]
max_dist[max_dist < 100.0] = 100.0
f_faba[sites.backarc] = C['theta15'] + \
(C['theta16'] * np.log(max_dist / 40.0))
return f_faba
def _compute_site_response_term(self, C, sites, 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 = sites.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 = sites.vs30 >= C["vlin"]
site_resp_term[idx] += (C["b"] * self.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] + self.CONSTS["c"]) +
C["b"] * np.log(pga1000[idx] + self.CONSTS["c"] *
(arg[idx] ** self.CONSTS["n"])))
return site_resp_term
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return standard deviations as defined in Table 3
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(C['sigma'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['tau'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(C['phi'] + np.zeros(num_sites))
return stddevs
# 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
""")
CONSTS = {
# Period-Independent Coefficients (Table 2)
'n': 1.18,
'c': 1.88,
'theta3': 0.1,
'theta4': 0.9,
'theta5': 0.0,
'theta9': 0.4,
'c4': 10.0,
'C1': 7.8
}
[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 = const.TRT.SUBDUCTION_INTRASLAB
#: Required distance measure is hypocentral for in-slab events
REQUIRES_DISTANCES = set(('rhypo',))
#: In-slab events require constraint of hypocentral depth and magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth'))
def _get_delta_c1(self, imt):
"""
Returns the magnitude scaling parameter deltaC1 which is fixed at -0.3
for the central branch of the in-slab model
"""
return -0.3
def _compute_focal_depth_term(self, C, rup):
"""
Computes the hypocentral depth scaling term - as indicated by
equation (3)
"""
if rup.hypo_depth > 120.0:
z_h = 120.0
else:
z_h = rup.hypo_depth
return C['theta11'] * (z_h - 60.)
def _compute_distance_term(self, C, mag, dists):
"""
Computes the distance scaling term, as contained within equation (1b)
"""
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'])) +
(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).
"""
f_faba = np.zeros_like(dists.rhypo)
# Term only applies to backarc sites (F_FABA = 0. for forearc)
max_dist = dists.rhypo[sites.backarc]
max_dist[max_dist < 85.0] = 85.0
f_faba[sites.backarc] = C['theta7'] +\
(C['theta8'] * np.log(max_dist / 40.0))
return f_faba
[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
"""
def _get_delta_c1(self, imt):
"""
Returns them agnitude scaling parameter deltaC1 which is fixed at -0.1
for the upper branch of the in-slab model
"""
return -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
"""
def _get_delta_c1(self, imt):
"""
Returns them agnitude scaling parameter deltaC1 which is fixed at -0.5
for the lower branch of the in-slab model
"""
return -0.5