# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 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
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#
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# GNU Affero General Public License for more details.
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"""
Module exports :class:`BaylessAbrahamson2018`
"""
import os
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import EAS
BA_COEFFS = os.path.join(os.path.dirname(__file__),
"bayless_abrahamson_2018.csv")
def _magnitude_scaling(C, ctx):
""" Compute the magnitude scaling term """
t1 = C['c1']
t2 = C['c2'] * (ctx.mag - 6.)
tmp = np.log(1.0 + np.exp(C['cn']*(C['cM']-ctx.mag)))
t3 = ((C['c2'] - C['c3']) / C['cn']) * tmp
return t1 + t2 + t3
def _path_scaling(C, ctx):
""" Compute path scaling term """
tmp = np.maximum(ctx.mag-C['chm'], 0.)
t1 = C['c4'] * np.log(ctx.rrup + C['c5'] * np.cosh(C['c6'] * tmp))
tmp = (ctx.rrup**2 + 50.**2)**0.5
t2 = (-0.5-C['c4'])*np.log(tmp)
t3 = C['c7'] * ctx.rrup
return t1 + t2 + t3
def _normal_fault_effect(C, ctx):
""" Compute the correction coefficient for the normal faulting """
idx = (ctx.rake > -150) & (ctx.rake < -30)
fnm = np.zeros_like(ctx.rake)
fnm[idx] = 1.0
return C['c10'] * fnm
def _ztor_scaling(C, ctx):
""" Compute top of rupture term """
return C['c9'] * np.minimum(ctx.ztor, 20.)
def _get_ln_ir_outcrop(self, ctx):
"""
Compute the natural logarithm of peak PGA at rock outcrop, Ir.
See eq.10e page 2092.
"""
# Set imt and cofficients. The value of frequency is consistent with
# the one used in the matlab script - line 156
im = EAS(5.0118725)
tc = self.COEFFS[im]
# Get mean
mean = (_magnitude_scaling(tc, ctx) +
_path_scaling(tc, ctx) +
_ztor_scaling(tc, ctx) +
_normal_fault_effect(tc, ctx))
return 1.238 + 0.846 * mean
def _linear_site_response(C, ctx):
""" Compute the site response term """
tmp = np.minimum(ctx.vs30, 1000.)
fsl = C['c8'] * np.log(tmp / 1000.)
return fsl
def _soil_depth_scaling(C, ctx):
""" Compute the soil depth scaling term """
# Set the c11 coefficient - See eq.13b at page 2093
c11 = np.ones_like(ctx.vs30) * C['c11a']
c11[(ctx.vs30 <= 300) & (ctx.vs30 > 200)] = C['c11b']
c11[(ctx.vs30 <= 500) & (ctx.vs30 > 300)] = C['c11c']
c11[(ctx.vs30 > 500)] = C['c11d']
# Compute the Z1ref parameter
tmp = (ctx.vs30**4 + 610**4) / (1360**4 + 610**4)
z1ref = 1/1000. * np.exp(-7.67/4*np.log(tmp))
# Return the fz1 parameter. The z1pt0 is converted from m (standard in OQ)
# to km as indicated in the paper
tmp = np.minimum(ctx.z1pt0/1000, np.ones_like(ctx.z1pt0)*2.0) + 0.01
return c11 * np.log(tmp / (z1ref + 0.01))
def _get_stddevs(C, ctx):
"""
Compute the standard deviations
"""
# Set components of std
tau = np.ones_like(ctx.mag) * C['s1']
phi_s2s = np.ones_like(ctx.mag) * C['s3']
phi_ss = np.ones_like(ctx.mag) * C['s5']
above = ctx.mag > 6
tau[above] = C['s2']
phi_s2s[above] = C['s4']
phi_ss[above] = C['s6']
below = (ctx.mag > 4) & (ctx.mag <= 6)
tau[below] = C['s1']+(C['s2']-C['s1'])/2.*(ctx.mag[below]-4)
phi_s2s[below] = C['s3']+(C['s4']-C['s3'])/2.*(ctx.mag[below]-4)
phi_ss[below] = C['s5']+(C['s6']-C['s5'])/2.*(ctx.mag[below]-4)
# Collect the requested stds
sigma = np.sqrt(tau**2+phi_s2s**2+phi_ss**2+C['c1a']**2)
phi = np.sqrt(phi_s2s**2+phi_ss**2)
sigma = np.ones_like(ctx.vs30) * sigma
tau = np.ones_like(ctx.vs30) * tau
phi = np.ones_like(ctx.vs30) * phi
return sigma, tau, phi
def _get_nl_site_response(C, ctx, imt, ln_ir_outcrop, freq_nl, coeff_nl):
"""
:param ln_ir_outcrop:
The peak ground acceleration (PGA [g]) at rock outcrop
:param freq_nl:
Frequencies for the coefficients f3, f4 and f5 used to compute the
non-linear term
:param coeff_nl:
A :class:`numpy.ndarray` instance of shape [# freq, 3] with the values
of the coefficients f3, f4 and f5 which are used to compute the
non-linear term
"""
vsref = 760.0
NSITES = len(ctx.vs30)
NFREQS = coeff_nl.shape[0]
# Updating the matrix with the coefficients. This has shape (number of
# frequencies) x (number of coeffs) x (number of sites)
coeff_nl = np.expand_dims(coeff_nl, 2)
coeff_nl = np.repeat(coeff_nl, NSITES, 2)
# Updating the matrix with Vs30 values. This has shape (number of
# frequencies) x (number of sites)
# vs30 = np.matlib.repmat(ctx.vs30, NFREQS, 1)
# ln_ir_outcrop = np.matlib.repmat(ln_ir_outcrop, NFREQS, 1)
vs30 = np.tile(ctx.vs30, (NFREQS, 1))
ln_ir_outcrop = np.tile(ln_ir_outcrop, (NFREQS, 1))
# Computing
t1 = np.exp(coeff_nl[:, 2] * (np.minimum(vs30, vsref)-360.))
t2 = np.exp(coeff_nl[:, 2] * (vsref-360.))
f2 = coeff_nl[:, 1] * (t1 - t2)
f3 = coeff_nl[:, 0]
fnl_0 = f2 * np.log((np.exp(ln_ir_outcrop) + f3) / f3)
idxs = np.argmin(fnl_0, axis=0)
# Applying correction as described at page 2093 in BA18
fnl = []
for i, j in enumerate(idxs):
fnl_0[j:, i] = min(fnl_0[:, i])
tmp = np.interp(imt.frequency, freq_nl, fnl_0[:, i])
fnl.append(tmp)
return np.array(fnl)
def _get_dimunition_factor(ctx, imt):
max_freq = 23.988321
kappa = np.exp(-0.4*np.log(ctx.vs30/760)-3.5)
D = np.exp(-np.pi * kappa * (imt.frequency - max_freq))
return D
def _get_mean_linear(C, ctx):
mean = (_magnitude_scaling(C, ctx) +
_path_scaling(C, ctx) +
_linear_site_response(C, ctx) +
_ztor_scaling(C, ctx) +
_normal_fault_effect(C, ctx) +
_soil_depth_scaling(C, ctx))
return mean
def _get_mean(self, C, ctx, imt):
if imt.frequency >= 24.:
im = EAS(23.988321)
C = self.COEFFS[im]
t1 = np.exp(_get_mean_linear(C, ctx))
mean = np.log(_get_dimunition_factor(ctx, imt) * t1)
else:
mean = _get_mean_linear(C, ctx)
return mean
[docs]class BaylessAbrahamson2018(GMPE):
"""
Implements the Bayless and Abrahamson (2018, 2019) model. References:
- Bayless, J., and N. A. Abrahamson (2018b). An empirical model for Fourier
amplitude spectra using the NGA-West2 database, PEER Rept. No. 2018/07,
Pacific Earthquake Engineering Research Center, University of California,
Berkeley, California.
- Bayless, J. and N.A. Abrahamson (2019). Summary of the BA18
Ground-Motion Model for Fourier Amplitude Spectra for Crustal Earthquakes
in California. Bull. Seism. Soc. Am., 109(5): 2088–2105
Disclaimer: The authors describe a smoothing technique that needs to be
applied to the non linear component of the site response. We did not
implement these smoothing functions in this initial versions since the
match with the values in the verification tables is good even without it.
"""
#: Supported tectonic region type is active shallow crust, see title!
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {EAS}
#: Supported intensity measure component
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL
#: Supported standard deviation types
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
}
#: Required site parameters
REQUIRES_SITES_PARAMETERS = {'vs30', 'z1pt0'}
#: Required rupture parameters
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'ztor'}
#: Required distance measures
REQUIRES_DISTANCES = {'rrup'}
[docs] def compute(self, ctx: np.recarray, imts, mean, sigma, tau, phi):
freq_nl, coeff_nl = self.COEFFS.get_coeffs(['f3', 'f4', 'f5'])
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
ln_ir_outcrop = _get_ln_ir_outcrop(self, ctx)
lin_component = _get_mean(self, C, ctx, imt)
nl_component = _get_nl_site_response(C, ctx, imt, ln_ir_outcrop,
freq_nl, coeff_nl)
mean[m] = (lin_component + nl_component)
sigma[m], tau[m], phi[m] = _get_stddevs(C, ctx)
with open(BA_COEFFS) as f:
COEFFS = CoeffsTable(table=f.read())
