# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2021 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:`CampbellBozorgnia2008`, and
:class:'CampbellBozorgnia2008Arbitrary'
"""
import numpy as np
from math import log, exp
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, PGD, CAV, SA
def _compute_basin_response_term(C, z2pt5):
"""
Returns the basin response term (equation 12, page 146)
"""
fsed = np.zeros_like(z2pt5, dtype=float)
idx = z2pt5 < 1.0
if np.any(idx):
fsed[idx] = C['c11'] * (z2pt5[idx] - 1.0)
idx = z2pt5 > 3.0
if np.any(idx):
fsed[idx] = (C['c12'] * C['k3'] * exp(-0.75)) *\
(1.0 - np.exp(-0.25 * (z2pt5[idx] - 3.0)))
return fsed
def _compute_distance_term(C, ctx):
"""
Returns the distance scaling factor (equation (3), page 145)
"""
return (C['c4'] + C['c5'] * ctx.mag) * \
np.log(np.sqrt(ctx.rrup ** 2. + C['c6'] ** 2.))
def _compute_hanging_wall_term(C, ctx):
"""
Returns the hanging wall scaling term, the product of the scaling
coefficient and four separate scaling terms for distance, magnitude,
rupture depth and dip (equations 6 - 10, page 146). Individual
scaling terms defined in separate functions
"""
return (C['c9'] *
_get_hanging_wall_distance_term(ctx) *
_get_hanging_wall_magnitude_term(ctx.mag) *
_get_hanging_wall_depth_term(ctx.ztor) *
_get_hanging_wall_dip_term(ctx.dip))
def _compute_imt1100(C, ctx, get_pga_site=False):
"""
Computes the PGA on reference (Vs30 = 1100 m/s) rock.
"""
# Calculates simple site response term assuming all sites 1100 m/s
fsite = (C['c10'] + (C['k2'] * C['n'])) * log(1100. / C['k1'])
# Calculates the PGA on rock
pga1100 = np.exp(_compute_magnitude_term(C, ctx.mag) +
_compute_distance_term(C, ctx) +
_compute_style_of_faulting_term(C, ctx) +
_compute_hanging_wall_term(C, ctx) +
_compute_basin_response_term(C, ctx.z2pt5) +
fsite)
# If PGA at the site is needed then remove factor for rock and
# re-calculate on correct site condition
if get_pga_site:
pga_site = np.exp(np.log(pga1100) - fsite)
fsite = _compute_shallow_site_response(C, ctx, pga1100)
pga_site = np.exp(np.log(pga_site) + fsite)
else:
pga_site = None
return pga1100, pga_site
def _compute_intra_event_alpha(C, vs30, pga1100):
"""
Returns the linearised functional relationship between fsite and
pga1100, determined from the partial derivative defined on equation 17
on page 148
"""
alpha = np.zeros_like(vs30, dtype=float)
idx = vs30 < C['k1']
if np.any(idx):
temp1 = (pga1100[idx] +
C['c'] * (vs30[idx] / C['k1']) ** C['n']) ** -1.
temp1 = temp1 - ((pga1100[idx] + C['c']) ** -1.)
alpha[idx] = C['k2'] * pga1100[idx] * temp1
return alpha
def _compute_intra_event_std(C, vs30, pga1100, sigma_pga):
"""
Returns the intra-event standard deviation at the site, as defined in
equation 15, page 147
"""
# Get intra-event standard deviation at the base of the site profile
sig_lnyb = np.sqrt(C['s_lny'] ** 2. - C['s_lnAF'] ** 2.)
sig_lnab = np.sqrt(sigma_pga ** 2. - C['s_lnAF'] ** 2.)
# Get linearised relationship between f_site and ln PGA
alpha = _compute_intra_event_alpha(C, vs30, pga1100)
return np.sqrt(
(sig_lnyb ** 2.) +
(C['s_lnAF'] ** 2.) +
((alpha ** 2.) * (sig_lnab ** 2.)) +
(2.0 * alpha * C['rho'] * sig_lnyb * sig_lnab))
def _compute_magnitude_term(C, mag):
"""
Returns the magnitude scaling factor (equation (2), page 144)
"""
fmag = C['c0'] + C['c1'] * mag
if mag <= 5.5:
return fmag
elif mag > 6.5:
return fmag + (C['c2'] * (mag - 5.5)) + (C['c3'] * (mag - 6.5))
else:
return fmag + (C['c2'] * (mag - 5.5))
def _compute_shallow_site_response(C, ctx, pga1100):
"""
Returns the shallow site response term (equation 11, page 146)
"""
stiff_factor = C['c10'] + (C['k2'] * C['n'])
# Initially default all sites to intermediate rock value
fsite = stiff_factor * np.log(ctx.vs30 / C['k1'])
# Check for soft soil ctx
idx = ctx.vs30 < C['k1']
if np.any(idx):
pga_scale = np.log(pga1100[idx] +
(C['c'] * ((ctx.vs30[idx] / C['k1']) **
C['n']))) - np.log(pga1100[idx] + C['c'])
fsite[idx] = C['c10'] * np.log(ctx.vs30[idx] / C['k1']) + \
(C['k2'] * pga_scale)
# Any very hard rock ctx are rendered to the constant amplification
# factor
idx = ctx.vs30 >= 1100.
if np.any(idx):
fsite[idx] = stiff_factor * log(1100. / C['k1'])
return fsite
def _compute_style_of_faulting_term(C, ctx):
"""
Returns the style of faulting factor, depending on the mechanism (rake)
and top of rupture depth (equations (4) and (5), pages 145 - 146)
"""
frv, fnm = _get_fault_type_dummy_variables(ctx.rake)
if frv > 0.:
# Top of rupture depth term only applies to reverse faults
if ctx.ztor < 1.:
ffltz = ctx.ztor
else:
ffltz = 1.
else:
ffltz = 0.
return (C['c7'] * frv * ffltz) + (C['c8'] * fnm)
def _get_fault_type_dummy_variables(rake):
"""
Returns the coefficients FRV and FNM, describing if the rupture is
reverse (FRV = 1.0, FNM = 0.0), normal (FRV = 0.0, FNM = 1.0) or
strike-slip/oblique-slip (FRV = 0.0, FNM = 0.0). Reverse faults are
classified as those with a rake in the range 30 to 150 degrees. Normal
faults are classified as having a rake in the range -150 to -30 degrees
:returns:
FRV, FNM
"""
if (rake > 30.0) and (rake < 150.):
return 1., 0.
elif (rake > -150.0) and (rake < -30.0):
return 0., 1.
else:
return 0., 0.
def _get_hanging_wall_depth_term(ztor):
"""
Returns the hanging wall depth scaling term (equation 9, page 146)
"""
if ztor >= 20.0:
return 0.
else:
return (20. - ztor) / 20.0
def _get_hanging_wall_dip_term(dip):
"""
Returns the hanging wall dip scaling term (equation 10, page 146)
"""
if dip > 70.0:
return (90.0 - dip) / 20.0
else:
return 1.0
def _get_hanging_wall_distance_term(ctx):
"""
Returns the hanging wall distance scaling term (equation 7, page 146)
"""
fhngr = np.ones_like(ctx.rjb, dtype=float)
idx = ctx.rjb > 0.
if ctx.ztor < 1.:
temp_rjb = np.sqrt(ctx.rjb[idx] ** 2. + 1.)
r_max = np.max(np.column_stack([ctx.rrup[idx], temp_rjb]),
axis=1)
fhngr[idx] = (r_max - ctx.rjb[idx]) / r_max
else:
fhngr[idx] = (ctx.rrup[idx] - ctx.rjb[idx]) / ctx.rrup[idx]
return fhngr
def _get_hanging_wall_magnitude_term(mag):
"""
Returns the hanging wall magnitude scaling term (equation 8, page 146)
"""
if mag <= 6.0:
return 0.
elif mag >= 6.5:
return 1.
else:
return 2. * (mag - 6.0)
def _get_stddevs(kind, C, ctx, pga1100, sigma_pga):
"""
Returns the standard deviations as described in the "ALEATORY
UNCERTAINTY MODEL" section of the paper. Equations 13 to 19, pages 147
to 151
"""
std_intra = _compute_intra_event_std(C, ctx.vs30, pga1100, sigma_pga)
std_inter = C['t_lny'] * np.ones_like(ctx.vs30)
return [_get_total_sigma(kind, C, std_intra, std_inter),
std_inter, std_intra]
def _get_total_sigma(kind, C, std_intra, std_inter):
"""
Returns the total sigma term as defined by equation 16, page 147
This method is defined here as the Campbell & Bozorgnia (2008) model
can also be applied to the "arbitrary" horizontal component
definition, in which case the total sigma is modified (see
equation 18, page 150).
"""
tot2 = std_intra ** 2. + std_inter ** 2.
if kind == 'arbitrary':
return np.sqrt(tot2 + C['c_lny'] ** 2.)
return np.sqrt(tot2)
[docs]class CampbellBozorgnia2008(GMPE):
"""
Implements GMPE developed by Kenneth W. Campbell and Yousef Bozorgnia,
published as "NGA Ground Motion Model for the Geometric Mean Horizontal
Component of PGA, PGV, PGD and 5 % Damped Linear Elastic Response Spectra
for Periods Ranging from 0.01 to 10s" (2008, Earthquake Spectra,
Volume 24, Number 1, pages 139 - 171).
This class implements the model for the Geometric Mean of the elastic
spectra.
Included in the coefficient set are the coefficients for the
Campbell & Bozorgnia (2010) GMPE for predicting Cumulative Absolute
Velocity (CAV), published as "A Ground Motion Prediction Equation for
the Horizontal Component of Cumulative Absolute Velocity (CSV) Based on
the PEER-NGA Strong Motion Database" (2010, Earthquake Spectra, Volume 26,
Number 3, 635 - 650).
"""
kind = "base"
#: Supported tectonic region type is active shallow crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration, peak
#: ground velocity, peak ground displacement and peak ground acceleration
#: Additional model for cumulative absolute velocity defined in
#: Campbell & Bozorgnia (2010)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, PGD, CAV, SA}
#: Supported intensity measure component is orientation-independent
#: average horizontal :attr:`~openquake.hazardlib.const.IMC.GMRotI50`
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GMRotI50
#: Supported standard deviation types are inter-event, intra-event
#: and total, see section "Aleatory Uncertainty Model", page 147.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameters are Vs30, Vs30 type (measured or inferred),
#: and depth (km) to the 2.5 km/s shear wave velocity layer (z2pt5)
REQUIRES_SITES_PARAMETERS = {'vs30', 'z2pt5'}
#: Required rupture parameters are magnitude, rake, dip, ztor
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'dip', 'ztor'}
#: Required distance measures are Rrup and Rjb.
REQUIRES_DISTANCES = {'rrup', 'rjb'}
[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()]
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
# compute median pga on rock (vs30=1100), needed for site response
# term calculation
# For spectral accelerations at periods between 0.0 and 0.25 s,
# Sa (T) cannot be less than PGA on soil, therefore if the IMT is
# in this period range it is necessary to calculate PGA on soil
get_pga_site = imt.period > 0.0 and imt.period < 0.25
pga1100, pga_site = _compute_imt1100(C_PGA, ctx, get_pga_site)
# Get the median ground motion
mean[m] = (_compute_magnitude_term(C, ctx.mag) +
_compute_distance_term(C, ctx) +
_compute_style_of_faulting_term(C, ctx) +
_compute_hanging_wall_term(C, ctx) +
_compute_shallow_site_response(C, ctx, pga1100) +
_compute_basin_response_term(C, ctx.z2pt5))
# If it is necessary to ensure that Sa(T) >= PGA
# (see previous comment)
if get_pga_site:
idx = mean[m] < np.log(pga_site)
mean[m, idx] = np.log(pga_site[idx])
sig[m], tau[m], phi[m] = _get_stddevs(
self.kind, C, ctx, pga1100, C_PGA['s_lny'])
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 k1 k2 k3 c n s_lny t_lny s_lnAF c_lny rho
cav -4.354 0.942 -0.178 -0.346 -1.309 0.087 7.24 0.111 -0.108 0.362 2.549 0.090 1.277 400 -2.690 1.000 1.88 1.18 0.371 0.196 0.300 0.089 0.735
pgd -5.270 1.600 -0.070 0.000 -2.000 0.17 4.00 0.000 0.000 0.000 -0.820 0.300 1.000 400 0.000 2.744 1.88 1.18 0.667 0.485 0.300 0.290 0.174
pgv 0.954 0.696 -0.309 -0.019 -2.016 0.17 4.00 0.245 0.000 0.358 1.694 0.092 1.000 400 -1.955 1.929 1.88 1.18 0.484 0.203 0.300 0.190 0.691
pga -1.715 0.500 -0.530 -0.262 -2.118 0.17 5.60 0.280 -0.120 0.490 1.058 0.040 0.610 865 -1.186 1.839 1.88 1.18 0.478 0.219 0.300 0.166 1.000
0.010 -1.715 0.500 -0.530 -0.262 -2.118 0.17 5.60 0.280 -0.120 0.490 1.058 0.040 0.610 865 -1.186 1.839 1.88 1.18 0.478 0.219 0.300 0.166 1.000
0.020 -1.680 0.500 -0.530 -0.262 -2.123 0.17 5.60 0.280 -0.120 0.490 1.102 0.040 0.610 865 -1.219 1.840 1.88 1.18 0.480 0.219 0.300 0.166 0.999
0.030 -1.552 0.500 -0.530 -0.262 -2.145 0.17 5.60 0.280 -0.120 0.490 1.174 0.040 0.610 908 -1.273 1.841 1.88 1.18 0.489 0.235 0.300 0.165 0.989
0.050 -1.209 0.500 -0.530 -0.267 -2.199 0.17 5.74 0.280 -0.120 0.490 1.272 0.040 0.610 1054 -1.346 1.843 1.88 1.18 0.510 0.258 0.300 0.162 0.963
0.075 -0.657 0.500 -0.530 -0.302 -2.277 0.17 7.09 0.280 -0.120 0.490 1.438 0.040 0.610 1086 -1.471 1.845 1.88 1.18 0.520 0.292 0.300 0.158 0.922
0.100 -0.314 0.500 -0.530 -0.324 -2.318 0.17 8.05 0.280 -0.099 0.490 1.604 0.040 0.610 1032 -1.624 1.847 1.88 1.18 0.531 0.286 0.300 0.170 0.898
0.150 -0.133 0.500 -0.530 -0.339 -2.309 0.17 8.79 0.280 -0.048 0.490 1.928 0.040 0.610 878 -1.931 1.852 1.88 1.18 0.532 0.280 0.300 0.180 0.890
0.200 -0.486 0.500 -0.446 -0.398 -2.220 0.17 7.60 0.280 -0.012 0.490 2.194 0.040 0.610 748 -2.188 1.856 1.88 1.18 0.534 0.249 0.300 0.186 0.871
0.250 -0.890 0.500 -0.362 -0.458 -2.146 0.17 6.58 0.280 0.000 0.490 2.351 0.040 0.700 654 -2.381 1.861 1.88 1.18 0.534 0.240 0.300 0.191 0.852
0.300 -1.171 0.500 -0.294 -0.511 -2.095 0.17 6.04 0.280 0.000 0.490 2.460 0.040 0.750 587 -2.518 1.865 1.88 1.18 0.544 0.215 0.300 0.198 0.831
0.400 -1.466 0.500 -0.186 -0.592 -2.066 0.17 5.30 0.280 0.000 0.490 2.587 0.040 0.850 503 -2.657 1.874 1.88 1.18 0.541 0.217 0.300 0.206 0.785
0.500 -2.569 0.656 -0.304 -0.536 -2.041 0.17 4.73 0.280 0.000 0.490 2.544 0.040 0.883 457 -2.669 1.883 1.88 1.18 0.550 0.214 0.300 0.208 0.735
0.750 -4.844 0.972 -0.578 -0.406 -2.000 0.17 4.00 0.280 0.000 0.490 2.133 0.077 1.000 410 -2.401 1.906 1.88 1.18 0.568 0.227 0.300 0.221 0.628
1.000 -6.406 1.196 -0.772 -0.314 -2.000 0.17 4.00 0.255 0.000 0.490 1.571 0.150 1.000 400 -1.955 1.929 1.88 1.18 0.568 0.255 0.300 0.225 0.534
1.500 -8.692 1.513 -1.046 -0.185 -2.000 0.17 4.00 0.161 0.000 0.490 0.406 0.253 1.000 400 -1.025 1.974 1.88 1.18 0.564 0.296 0.300 0.222 0.411
2.000 -9.701 1.600 -0.978 -0.236 -2.000 0.17 4.00 0.094 0.000 0.371 -0.456 0.300 1.000 400 -0.299 2.019 1.88 1.18 0.571 0.296 0.300 0.226 0.331
3.000 -10.556 1.600 -0.638 -0.491 -2.000 0.17 4.00 0.000 0.000 0.154 -0.820 0.300 1.000 400 0.000 2.110 1.88 1.18 0.558 0.326 0.300 0.229 0.289
4.000 -11.212 1.600 -0.316 -0.770 -2.000 0.17 4.00 0.000 0.000 0.000 -0.820 0.300 1.000 400 0.000 2.200 1.88 1.18 0.576 0.297 0.300 0.237 0.261
5.000 -11.684 1.600 -0.070 -0.986 -2.000 0.17 4.00 0.000 0.000 0.000 -0.820 0.300 1.000 400 0.000 2.291 1.88 1.18 0.601 0.359 0.300 0.237 0.200
7.500 -12.505 1.600 -0.070 -0.656 -2.000 0.17 4.00 0.000 0.000 0.000 -0.820 0.300 1.000 400 0.000 2.517 1.88 1.18 0.628 0.428 0.300 0.271 0.174
10.00 -13.087 1.600 -0.070 -0.422 -2.000 0.17 4.00 0.000 0.000 0.000 -0.820 0.300 1.000 400 0.000 2.744 1.88 1.18 0.667 0.485 0.300 0.290 0.174
""")
[docs]class CampbellBozorgnia2008Arbitrary(CampbellBozorgnia2008):
"""
Implements the Campbell & Bozorgnia (2008) GMPE as modified to represent
the arbitrary horizontal component of ground motion, instead of the
Rotationally Independent Geometric Mean (GMRotI) originally defined in
the paper.
"""
kind = "arbitrary"
#: Supported intensity measure component is arbitrary horizontal
#: :attr:`~openquake.hazardlib.const.IMC.HORIZONTAL`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL