# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2021 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:`BooreAtkinson2008`,
:class:`AtkinsonBoore2006`,
:class:`AtkinsonBoore2006Modified2011`.
:class:`AtkinsonBoore2006SGS`.
"""
import numpy as np
from scipy.constants import g
from math import log10
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable, add_alias
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
from openquake.hazardlib.gsim.utils import (
mblg_to_mw_atkinson_boore_87, mblg_to_mw_johnston_96, clip_mean)
#: IMT-independent coefficients. std_total is the total standard deviation,
#: see Table 6, pag 2192 and Table 9, pag 2202. R0, R1, R2 are coefficients
#: required for mean calculation - see equation (5) pag 2191. v1, v2, Vref
#: are coefficients required for soil response calculation, see table 8,
#: p. 2201
# the std is converted from base 10 to base e
std_total = np.log(10 ** 0.30),
R0 = 10.0
R1 = 70.0
R2 = 140.0
# v1 = 180.0
# v2 = 300.0
# Vref = 760.0
def _clip_distances(rrup):
"""
Return array of distances with values clipped to 1. See end of
paragraph 'Methodology and Model Parameters', p. 2182. The equations
have a singularity for distance = 0, so that's why distances are
clipped to 1.
"""
rrup = rrup.copy()
rrup[rrup < 1] = 1
return rrup
def _compute_distance_scaling(ctx, C):
"""
Compute distance-scaling term, equations (3) and (4), pag 107.
"""
Mref = 4.5
Rref = 1.0
R = np.sqrt(ctx.rjb ** 2 + C['h'] ** 2)
return (C['c1'] + C['c2'] * (ctx.mag - Mref)) * np.log(R / Rref) + \
C['c3'] * (R - Rref)
def _compute_f0_factor(rrup):
"""
Compute and return factor f0 - see equation (5), 6th term, p. 2191.
"""
f0 = np.log10(R0 / rrup)
f0[f0 < 0] = 0.0
return f0
def _compute_f1_factor(rrup):
"""
Compute and return factor f1 - see equation (5), 4th term, p. 2191
"""
f1 = np.log10(rrup)
logR1 = np.log10(R1)
f1[f1 > logR1] = logR1
return f1
def _compute_f2_factor(rrup):
"""
Compute and return factor f2, see equation (5), 5th term, pag 2191
"""
f2 = np.log10(rrup / R2)
f2[f2 < 0] = 0.0
return f2
def _compute_magnitude_scaling(ctx, C):
"""
Compute magnitude-scaling term, equations (5a) and (5b), pag 107.
"""
return _compute_ms(ctx, C)
def _compute_mean(C, f0, f1, f2, SC, mag, rrup, idxs, mean,
scale_fac):
"""
Compute mean value (for a set of indexes) without site amplification
terms. This is equation (5), p. 2191, without S term.
"""
mean[idxs] = (C['c1'] +
C['c2'] * mag +
C['c3'] * (mag ** 2) +
(C['c4'] + C['c5'] * mag) * f1[idxs] +
(C['c6'] + C['c7'] * mag) * f2[idxs] +
(C['c8'] + C['c9'] * mag) * f0[idxs] +
C['c10'] * rrup[idxs] +
_compute_stress_drop_adjustment(SC, mag, scale_fac))
def _compute_ms(ctx, C):
U, SS, NS, RS = _get_fault_type_dummy_variables(ctx)
if ctx.mag <= C['Mh']:
return C['e1'] * U + C['e2'] * SS + C['e3'] * NS + C['e4'] * RS + \
C['e5'] * (ctx.mag - C['Mh']) + \
C['e6'] * (ctx.mag - C['Mh']) ** 2
else:
return C['e1'] * U + C['e2'] * SS + C['e3'] * NS + C['e4'] * RS + \
C['e7'] * (ctx.mag - C['Mh'])
def _compute_non_linear_slope(vs30, C):
"""
Compute non-linear slope factor,
equations (13a) to (13d), pag 108-109.
"""
V1 = 180.0
V2 = 300.0
Vref = 760.0
# equation (13d), values are zero for vs30 >= Vref = 760.0
bnl = np.zeros(vs30.shape)
# equation (13a)
bnl[vs30 <= V1] = C['b1']
# equation (13b)
idx = np.where((vs30 > V1) & (vs30 <= V2))
bnl[idx] = (C['b1'] - C['b2']) * \
np.log(vs30[idx] / V2) / np.log(V1 / V2) + C['b2']
# equation (13c)
idx = np.where((vs30 > V2) & (vs30 < Vref))
bnl[idx] = C['b2'] * np.log(vs30[idx] / Vref) / np.log(V2 / Vref)
return bnl
def _compute_non_linear_term(pga4nl, bnl):
"""
Compute non-linear term,
equation (8a) to (8c), pag 108.
"""
fnl = np.zeros(pga4nl.shape)
if len(bnl) < len(fnl): # single site case, fix shape
bnl = np.repeat(bnl, len(fnl))
a1 = 0.03
a2 = 0.09
pga_low = 0.06
# equation (8a)
idx = pga4nl <= a1
fnl[idx] = bnl[idx] * np.log(pga_low / 0.1)
# equation (8b)
idx = np.where((pga4nl > a1) & (pga4nl <= a2))
delta_x = np.log(a2 / a1)
delta_y = bnl[idx] * np.log(a2 / pga_low)
c = (3 * delta_y - bnl[idx] * delta_x) / delta_x ** 2
d = -(2 * delta_y - bnl[idx] * delta_x) / delta_x ** 3
fnl[idx] = bnl[idx] * np.log(pga_low / 0.1) +\
c * (np.log(pga4nl[idx] / a1) ** 2) + \
d * (np.log(pga4nl[idx] / a1) ** 3)
# equation (8c)
idx = pga4nl > a2
fnl[idx] = np.squeeze(bnl[idx]) * np.log(pga4nl[idx] / 0.1)
return fnl
def _compute_soil_amplification(C, vs30, pga_bc, mean):
"""
Compute soil amplification, that is S term in equation (5), p. 2191,
and add to mean values for non hard rock sites.
"""
# convert from base e (as defined in BA2008) to base 10 (as used in
# AB2006)
sal = np.log10(np.exp(_get_site_amplification_linear(vs30, C)))
sanl = np.log10(np.exp(
_get_site_amplification_non_linear(vs30, pga_bc, C)))
idxs = vs30 < 2000.0
mean[idxs] = mean[idxs] + sal[idxs] + sanl[idxs]
def _compute_stress_drop_adjustment(SC, mag, scale_fac):
"""
Compute equation (6) p. 2200
"""
return scale_fac * np.minimum(
SC['delta'] + 0.05,
0.05 + SC['delta'] * (
np.maximum(mag - SC['M1'], 0) / (SC['Mh'] - SC['M1'])))
def _convert_magnitude(mag_eq, mag):
"""
Convert magnitude from Mblg to Mw using various equations
equation
"""
if mag_eq == 'Mblg87':
return mblg_to_mw_atkinson_boore_87(mag)
elif mag_eq == 'Mblg96':
return mblg_to_mw_johnston_96(mag)
elif mag_eq == 'Mw':
return mag
def _extract_coeffs(self, imt):
"""
Extract dictionaries of coefficients specific to required
intensity measure type.
"""
C_HR = self.COEFFS_HARD_ROCK[imt]
C_BC = self.COEFFS_BC[imt]
C_SR = self.COEFFS_SOIL_RESPONSE[imt]
SC = self.COEFFS_STRESS[imt]
return C_HR, C_BC, C_SR, SC
def _get_fault_type_dummy_variables(ctx):
"""
Get fault type dummy variables, see Table 2, pag 107.
Fault type (Strike-slip, Normal, Thrust/reverse) is
derived from rake angle.
Rakes angles within 30 of horizontal are strike-slip,
angles from 30 to 150 are reverse, and angles from
-30 to -150 are normal. See paragraph 'Predictor Variables'
pag 103.
Note that the 'Unspecified' case is not considered,
because rake is always given.
"""
U, SS, NS, RS = 0, 0, 0, 0
if ctx.rake == 'undefined':
U = 1
elif np.abs(ctx.rake) <= 30.0 or (180.0 - np.abs(ctx.rake)) <= 30.0:
# strike-slip
SS = 1
elif ctx.rake > 30.0 and ctx.rake < 150.0:
# reverse
RS = 1
else:
# normal
NS = 1
return U, SS, NS, RS
def _get_mean(self, vs30, mag, rrup, imt, scale_fac):
"""
Compute and return mean
"""
C_HR, C_BC, C_SR, SC = _extract_coeffs(self, imt)
rrup = _clip_distances(rrup)
f0 = _compute_f0_factor(rrup)
f1 = _compute_f1_factor(rrup)
f2 = _compute_f2_factor(rrup)
pga_bc = _get_pga_bc(
self.COEFFS_BC[PGA()], f0, f1, f2, SC, mag, rrup, vs30, scale_fac)
# compute mean values for hard-rock sites (vs30 >= 2000),
# and non-hard-rock sites (vs30 < 2000) and add soil amplification
# term
mean = np.zeros_like(vs30)
_compute_mean(C_HR, f0, f1, f2, SC, mag, rrup,
vs30 >= 2000.0, mean, scale_fac)
_compute_mean(C_BC, f0, f1, f2, SC, mag, rrup,
vs30 < 2000.0, mean, scale_fac)
_compute_soil_amplification(C_SR, vs30, pga_bc, mean)
# convert from base 10 to base e
if imt == PGV():
mean = np.log(10 ** mean)
else:
# convert from cm/s**2 to g
mean = np.log((10 ** mean) * 1e-2 / g)
return mean
def _get_pga_bc(C_pga_bc, f0, f1, f2, SC, mag, rrup, vs30, scale_fac):
"""
Compute and return PGA on BC boundary
"""
pga_bc = np.zeros_like(vs30)
_compute_mean(C_pga_bc, f0, f1, f2, SC, mag,
rrup, vs30 < 2000.0, pga_bc, scale_fac)
return (10 ** pga_bc) * 1e-2 / g
def _get_pga_on_rock(C_pga, ctx):
"""
Compute and return PGA on rock conditions (that is vs30 = 760.0 m/s).
This is needed to compute non-linear site amplification term
"""
# Median PGA in g for Vref = 760.0, without site amplification,
# that is equation (1) pag 106, without the third and fourth terms
# Mref and Rref values are given in the caption to table 6, pag 119
# Note that in the original paper, the caption reads:
# "Distance-scaling coefficients (Mref=4.5 and Rref=1.0 km for all
# periods, except Rref=5.0 km for pga4nl)". However this is a mistake
# as reported in http://www.daveboore.com/pubs_online.php:
# ERRATUM: 27 August 2008. Tom Blake pointed out that the caption to
# Table 6 should read "Distance-scaling coefficients (Mref=4.5 and
# Rref=1.0 km for all periods)".
pga4nl = np.exp(_compute_magnitude_scaling(ctx, C_pga) +
_compute_distance_scaling(ctx, C_pga))
return pga4nl
def _get_site_amplification_linear(vs30, C):
"""
Compute site amplification linear term,
equation (7), pag 107.
"""
return C['blin'] * np.log(vs30 / 760.0)
def _get_site_amplification_non_linear(vs30, pga4nl, C):
"""
Compute site amplification non-linear term,
equations (8a) to (13d), pag 108-109.
"""
# non linear slope
bnl = _compute_non_linear_slope(vs30, C)
# compute the actual non-linear term
return _compute_non_linear_term(pga4nl, bnl)
[docs]def set_sig(kind, C, sig, tau, phi):
"""
Set standard deviations as defined in table 8, pag 121.
"""
if kind == 'hawaii':
# Using a frequency independent value of sigma as recommended
# in the caption of Table 2 of Atkinson (2010)
sig[:] = 0.26 / np.log10(np.e)
elif kind == '2006':
sig[:] = std_total
else:
sig[:] = C['std']
tau[:] = C['tau']
phi[:] = C['sigma']
def _get_stress_drop_scaling_factor(magnitude):
"""
Returns the magnitude dependent stress drop scaling factor defined in
equation 6 (page 1128) of Atkinson & Boore (2011)
"""
stress_drop = 10.0 ** (3.45 - 0.2 * magnitude)
cap = 10.0 ** (3.45 - 0.2 * 5.0)
if stress_drop > cap:
stress_drop = cap
return log10(stress_drop / 140.0) / log10(2.0)
[docs]class AtkinsonBoore2006(GMPE):
"""
Implements GMPE developed by Gail M. Atkinson and David M. Boore and
published as "Earthquake Ground-Motion Prediction Equations for Eastern
North America" (2006, Bulletin of the Seismological Society of America,
Volume 96, No. 6, pages 2181-2205). This class implements only the
equations for stress parameter of 140 bars. The correction described in
'Adjustment of Equations to Consider Alternative Stress Parameters',
p. 2198, is not implemented.
This class uses the same soil amplification function as the
BooreAtkinson2008. Note that in the paper, the reported soil
amplification function is the one used in a preliminary version of the
Boore and Atkinson 2008 GMPE, while the one that should be used is the
one described in the final paper. See comment in:
http://www.daveboore.com/pubs_online/ab06_gmpes_programs_and_tables.pdf
"""
#: Supported tectonic region type is stable continental, given
#: that the equations have been derived for Eastern North America
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are spectral acceleration,
#: peak ground velocity and peak ground acceleration, see paragraph
#: 'Methodology and Model Parameters', p. 2182
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is horizontal
#: :attr:`~openquake.hazardlib.const.IMC.HORIZONTAL`,
#: see paragraph 'Results', pag 2190, and caption to table 6, p. 2192
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL
#: Supported standard deviation type is total, see table 6
#: and 9, p. 2192 and 2202, respectively.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
#: Required site parameters is Vs30.
#: See paragraph 'Equations for soil sites', p. 2200
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameter is magnitude (see
#: paragraph 'Methodology and Model Parameters', p. 2182)
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is Rrup.
#: See paragraph 'Methodology and Model Parameters', p. 2182
REQUIRES_DISTANCES = {'rrup'}
REQUIRES_ATTRIBUTES = {'mag_eq', 'scale_fac'}
CUTOFF_RRUP = 0.
kind = '2006'
def __init__(self, mag_eq="NA", scale_fac=0, **kwargs):
assert mag_eq in "Mblg87 Mblg96 Mw NA", mag_eq
super().__init__(**kwargs)
self.mag_eq = mag_eq
self.scale_fac = scale_fac
# used in the "Modified" version
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
if self.CUTOFF_RRUP: # for SGS subclass
ctx.rrup[ctx.rrup <= self.CUTOFF_RRUP] = self.CUTOFF_RRUP
for m, imt in enumerate(imts):
if self.mag_eq == "NA":
if 'Modified' in self.__class__.__name__:
# stress drop scaling factor is now a property of magnitude
scale_fac = _get_stress_drop_scaling_factor(ctx.mag)
else:
scale_fac = 0
mean[m] = _get_mean(
self, ctx.vs30, ctx.mag, ctx.rrup, imt,
scale_fac=scale_fac)
set_sig(self.kind, None, sig[m], tau[m], phi[m])
else:
mag = _convert_magnitude(self.mag_eq, ctx.mag)
# stress drop scaling factor defined in subroutine getAB06
mean[m] = _get_mean(
self, ctx.vs30, mag, ctx.rrup, imt,
scale_fac=self.scale_fac)
mean[m] = clip_mean(imt, mean[m])
set_sig(self.kind, None, sig[m], tau[m], phi[m])
# notice the presence of a dummy parameter `C` to keep the same
# interface as the base class BooreAtkinson2008
#: Hard rock coefficents, table 6, pag 2192,
#: coefficient values taken from Fortran implementation of Dave Boore
#: (higher precision than in the paper)
COEFFS_HARD_ROCK = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10
5.000 -5.408E+00 1.714E+00 -9.012E-02 -2.537E+00 2.267E-01 -1.268E+00 1.162E-01 9.792E-01 -1.767E-01 -1.757E-04
4.000 -5.791E+00 1.916E+00 -1.071E-01 -2.441E+00 2.113E-01 -1.162E+00 1.018E-01 1.012E+00 -1.824E-01 -2.010E-04
3.125 -6.038E+00 2.080E+00 -1.221E-01 -2.367E+00 2.002E-01 -1.073E+00 8.950E-02 1.002E+00 -1.803E-01 -2.306E-04
2.500 -6.169E+00 2.211E+00 -1.348E-01 -2.299E+00 1.898E-01 -9.860E-01 7.860E-02 9.683E-01 -1.765E-01 -2.823E-04
2.000 -6.183E+00 2.302E+00 -1.442E-01 -2.223E+00 1.770E-01 -9.370E-01 7.067E-02 9.518E-01 -1.768E-01 -3.220E-04
1.587 -6.043E+00 2.342E+00 -1.496E-01 -2.157E+00 1.662E-01 -8.704E-01 6.047E-02 9.207E-01 -1.734E-01 -3.748E-04
1.250 -5.724E+00 2.324E+00 -1.505E-01 -2.104E+00 1.565E-01 -8.202E-01 5.186E-02 8.563E-01 -1.661E-01 -4.329E-04
1.000 -5.272E+00 2.264E+00 -1.483E-01 -2.069E+00 1.497E-01 -8.132E-01 4.666E-02 8.262E-01 -1.622E-01 -4.862E-04
0.794 -4.604E+00 2.132E+00 -1.406E-01 -2.062E+00 1.468E-01 -7.974E-01 4.345E-02 7.748E-01 -1.558E-01 -5.790E-04
0.629 -3.917E+00 1.987E+00 -1.314E-01 -2.045E+00 1.419E-01 -7.818E-01 4.297E-02 7.878E-01 -1.590E-01 -6.948E-04
0.500 -3.216E+00 1.826E+00 -1.201E-01 -2.018E+00 1.344E-01 -8.134E-01 4.437E-02 8.839E-01 -1.751E-01 -7.704E-04
0.397 -2.437E+00 1.649E+00 -1.084E-01 -2.051E+00 1.363E-01 -8.426E-01 4.483E-02 7.386E-01 -1.557E-01 -8.509E-04
0.315 -1.721E+00 1.483E+00 -9.739E-02 -2.080E+00 1.382E-01 -8.893E-01 4.869E-02 6.101E-01 -1.389E-01 -9.538E-04
0.251 -1.121E+00 1.342E+00 -8.722E-02 -2.082E+00 1.349E-01 -9.714E-01 5.628E-02 6.140E-01 -1.432E-01 -1.055E-03
0.199 -6.153E-01 1.227E+00 -7.886E-02 -2.087E+00 1.312E-01 -1.120E+00 6.788E-02 6.055E-01 -1.459E-01 -1.125E-03
0.158 -1.455E-01 1.123E+00 -7.143E-02 -2.116E+00 1.302E-01 -1.303E+00 8.311E-02 5.617E-01 -1.438E-01 -1.182E-03
0.125 2.144E-01 1.054E+00 -6.664E-02 -2.154E+00 1.295E-01 -1.608E+00 1.046E-01 4.273E-01 -1.303E-01 -1.153E-03
0.100 4.797E-01 1.017E+00 -6.404E-02 -2.201E+00 1.270E-01 -2.007E+00 1.326E-01 3.371E-01 -1.266E-01 -1.047E-03
0.079 6.906E-01 9.974E-01 -6.276E-02 -2.262E+00 1.246E-01 -2.487E+00 1.636E-01 2.139E-01 -1.207E-01 -8.469E-04
0.063 9.109E-01 9.802E-01 -6.208E-02 -2.360E+00 1.263E-01 -2.972E+00 1.910E-01 1.069E-01 -1.173E-01 -5.786E-04
0.050 1.105E+00 9.719E-01 -6.197E-02 -2.466E+00 1.276E-01 -3.390E+00 2.144E-01 -1.391E-01 -9.839E-02 -3.167E-04
0.040 1.264E+00 9.680E-01 -6.232E-02 -2.581E+00 1.317E-01 -3.644E+00 2.276E-01 -3.506E-01 -8.126E-02 -1.225E-04
0.031 1.436E+00 9.592E-01 -6.276E-02 -2.714E+00 1.400E-01 -3.728E+00 2.343E-01 -5.430E-01 -6.448E-02 -3.230E-05
0.025 1.522E+00 9.597E-01 -6.351E-02 -2.813E+00 1.458E-01 -3.654E+00 2.362E-01 -6.544E-01 -5.500E-02 -4.848E-05
pga 9.069E-01 9.830E-01 -6.595E-02 -2.698E+00 1.594E-01 -2.795E+00 2.120E-01 -3.011E-01 -6.532E-02 -4.484E-04
pgv -1.442E+00 9.909E-01 -5.848E-02 -2.701E+00 2.155E-01 -2.436E+00 2.659E-01 8.479E-02 -6.927E-02 -3.734E-04
""")
#: Coefficients for NEHRP BC boundary (Vs30 = 760 m/s), table 9, pag 2202
#: coefficient values taken from Fortran implementation of Dave Boore
#: (higher precision than in the paper)
COEFFS_BC = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10
5.000 -4.852E+00 1.580E+00 -8.066E-02 -2.530E+00 2.216E-01 -1.426E+00 1.361E-01 6.340E-01 -1.413E-01 -1.608E-04
4.000 -5.256E+00 1.787E+00 -9.785E-02 -2.435E+00 2.068E-01 -1.307E+00 1.210E-01 7.340E-01 -1.560E-01 -1.959E-04
3.125 -5.590E+00 1.972E+00 -1.136E-01 -2.331E+00 1.908E-01 -1.204E+00 1.099E-01 8.449E-01 -1.723E-01 -2.452E-04
2.500 -5.800E+00 2.126E+00 -1.278E-01 -2.257E+00 1.790E-01 -1.123E+00 9.539E-02 8.911E-01 -1.797E-01 -2.601E-04
2.000 -5.853E+00 2.233E+00 -1.385E-01 -2.195E+00 1.688E-01 -1.037E+00 8.002E-02 8.666E-01 -1.790E-01 -2.860E-04
1.587 -5.754E+00 2.287E+00 -1.450E-01 -2.131E+00 1.582E-01 -9.568E-01 6.762E-02 8.670E-01 -1.789E-01 -3.429E-04
1.250 -5.489E+00 2.289E+00 -1.476E-01 -2.081E+00 1.501E-01 -9.000E-01 5.794E-02 8.208E-01 -1.719E-01 -4.070E-04
1.000 -5.058E+00 2.233E+00 -1.454E-01 -2.030E+00 1.408E-01 -8.744E-01 5.412E-02 7.922E-01 -1.697E-01 -4.886E-04
0.794 -4.446E+00 2.119E+00 -1.387E-01 -2.009E+00 1.356E-01 -8.576E-01 4.976E-02 7.084E-01 -1.589E-01 -5.751E-04
0.629 -3.748E+00 1.973E+00 -1.294E-01 -1.997E+00 1.313E-01 -8.417E-01 4.820E-02 6.772E-01 -1.557E-01 -6.763E-04
0.500 -3.007E+00 1.803E+00 -1.178E-01 -1.982E+00 1.274E-01 -8.466E-01 4.698E-02 6.670E-01 -1.546E-01 -7.676E-04
0.397 -2.281E+00 1.629E+00 -1.054E-01 -1.967E+00 1.227E-01 -8.880E-01 5.033E-02 6.839E-01 -1.582E-01 -8.587E-04
0.315 -1.560E+00 1.455E+00 -9.312E-02 -1.977E+00 1.209E-01 -9.466E-01 5.576E-02 6.499E-01 -1.558E-01 -9.552E-04
0.251 -8.756E-01 1.293E+00 -8.193E-02 -2.014E+00 1.226E-01 -1.027E+00 6.341E-02 5.808E-01 -1.491E-01 -1.053E-03
0.199 -3.056E-01 1.156E+00 -7.211E-02 -2.038E+00 1.220E-01 -1.147E+00 7.375E-02 5.082E-01 -1.430E-01 -1.140E-03
0.158 1.194E-01 1.057E+00 -6.473E-02 -2.054E+00 1.190E-01 -1.355E+00 9.160E-02 5.164E-01 -1.503E-01 -1.178E-03
0.125 5.356E-01 9.647E-01 -5.835E-02 -2.110E+00 1.205E-01 -1.672E+00 1.156E-01 3.433E-01 -1.322E-01 -1.130E-03
0.100 7.818E-01 9.235E-01 -5.555E-02 -2.165E+00 1.191E-01 -2.097E+00 1.483E-01 2.847E-01 -1.319E-01 -9.897E-04
0.079 9.667E-01 9.033E-01 -5.476E-02 -2.249E+00 1.215E-01 -2.530E+00 1.775E-01 1.001E-01 -1.147E-01 -7.724E-04
0.063 1.109E+00 8.875E-01 -5.386E-02 -2.334E+00 1.229E-01 -2.881E+00 2.007E-01 -3.189E-02 -1.069E-01 -5.483E-04
0.050 1.209E+00 8.830E-01 -5.441E-02 -2.440E+00 1.295E-01 -3.035E+00 2.133E-01 -2.098E-01 -8.997E-02 -4.145E-04
0.040 1.261E+00 8.789E-01 -5.515E-02 -2.536E+00 1.388E-01 -2.994E+00 2.158E-01 -3.908E-01 -6.746E-02 -3.881E-04
0.031 1.191E+00 8.884E-01 -5.642E-02 -2.577E+00 1.451E-01 -2.840E+00 2.121E-01 -4.370E-01 -5.866E-02 -4.329E-04
0.025 1.052E+00 9.030E-01 -5.768E-02 -2.571E+00 1.483E-01 -2.652E+00 2.065E-01 -4.084E-01 -5.769E-02 -5.122E-04
pga 5.233E-01 9.686E-01 -6.196E-02 -2.439E+00 1.465E-01 -2.335E+00 1.912E-01 -8.695E-02 -8.285E-02 -6.304E-04
pgv -1.662E+00 1.050E+00 -6.035E-02 -2.496E+00 1.840E-01 -2.301E+00 2.500E-01 1.268E-01 -8.704E-02 -4.266E-04
""")
COEFFS_STRESS = CoeffsTable(sa_damping=5, table="""\
IMT delta M1 Mh
pga 0.15 0.50 5.50
0.025 0.15 0.00 5.00
0.031 0.15 0.00 5.00
0.04 0.15 0.00 5.00
0.05 0.15 0.00 5.00
0.063 0.15 0.17 5.17
0.079 0.15 0.34 5.34
0.1 0.15 0.50 5.50
0.126 0.15 1.15 5.67
0.158 0.15 1.85 5.84
0.199 0.15 2.50 6.00
0.251 0.15 2.90 6.12
0.315 0.15 3.30 6.25
0.397 0.15 3.65 6.37
0.5 0.15 4.00 6.50
0.629 0.15 4.17 6.70
0.794 0.15 4.34 6.95
1.00 0.15 4.50 7.20
1.25 0.15 4.67 7.45
1.587 0.15 4.84 7.70
2.0 0.15 5.00 8.00
2.5 0.15 5.25 8.12
3.125 0.15 5.50 8.25
4.0 0.15 5.75 8.37
5.0 0.15 6.00 8.50
pgv 0.11 2.00 5.50
""")
#: Table 3, pag. 110. + coefficient values for additional frequencies
#: extracted from Fortran code implementing soil response function
#: developed by the original author (ab06_fmrvs_evaluate_gmpes.for
#: available at http://www.daveboore.com/pubs_online.html - see code
#: available for Atkinson, G. M. and D. M. Boore (2006). Earthquake ground
#: -motion prediction equations for eastern North America)
COEFFS_SOIL_RESPONSE = CoeffsTable(sa_damping=5, table="""\
IMT blin b1 b2
pgv -0.60 -0.50 -0.06
pga -0.36 -0.64 -0.14
0.010 -0.36 -0.64 -0.14
0.020 -0.34 -0.63 -0.12
0.030 -0.33 -0.62 -0.11
0.040 -0.31 -0.61 -0.11
0.050 -0.29 -0.64 -0.11
0.060 -0.25 -0.64 -0.11
0.075 -0.23 -0.64 -0.11
0.090 -0.23 -0.64 -0.12
0.100 -0.25 -0.60 -0.13
0.120 -0.26 -0.56 -0.14
0.150 -0.28 -0.53 -0.18
0.170 -0.29 -0.53 -0.19
0.200 -0.31 -0.52 -0.19
0.240 -0.38 -0.52 -0.16
0.250 -0.39 -0.52 -0.16
0.300 -0.44 -0.52 -0.14
0.360 -0.48 -0.51 -0.11
0.400 -0.50 -0.51 -0.10
0.460 -0.55 -0.50 -0.08
0.500 -0.60 -0.50 -0.06
0.600 -0.66 -0.49 -0.03
0.750 -0.69 -0.47 -0.00
0.850 -0.69 -0.46 -0.00
1.000 -0.70 -0.44 -0.00
1.500 -0.72 -0.40 -0.00
2.000 -0.73 -0.38 -0.00
3.000 -0.74 -0.34 -0.00
4.000 -0.75 -0.31 -0.00
5.000 -0.75 -0.291 -0.00
7.500 -0.692 -0.247 -0.00
10.00 -0.650 -0.215 -0.00
""")
add_alias("AtkinsonBoore2006MblgAB1987bar140NSHMP2008",
AtkinsonBoore2006, mag_eq="Mblg87", scale_fac=0.)
add_alias("AtkinsonBoore2006MblgJ1996bar140NSHMP2008",
AtkinsonBoore2006, mag_eq="Mblg96", scale_fac=0.)
add_alias("AtkinsonBoore2006Mwbar140NSHMP2008", AtkinsonBoore2006,
mag_eq="Mw", scale_fac=0.)
add_alias("AtkinsonBoore2006MblgAB1987bar200NSHMP2008",
AtkinsonBoore2006, mag_eq="Mblg87", scale_fac=0.5146)
add_alias("AtkinsonBoore2006MblgJ1996bar200NSHMP2008",
AtkinsonBoore2006, mag_eq="Mblg96", scale_fac=0.5146)
add_alias("AtkinsonBoore2006Mwbar200NSHMP2008",
AtkinsonBoore2006, mag_eq="Mw", scale_fac=0.5146)
[docs]class AtkinsonBoore2006Modified2011(AtkinsonBoore2006):
"""
This GMPE modifies the original implementation of :class:
`AtkinsonBoore2006` with the magnitude dependent stress-drop scaling
factor proposed in Atkinson & Boore (2011)
Atkinson, G. A. and Boore D. M. (2011) Modifications to Existing
Ground-Motion Prediciton Equations in Light of New Data. Bulletin of the
Seismological Society of America, 101(3), 1121 - 1135
"""
[docs]class AtkinsonBoore2006SGS(AtkinsonBoore2006):
"""
This class extends the original base class
:class:`openquake.hazardlib.gsim.atkinson_boore_2006.AtkinsonBoore2006`
by introducing a distance filter for the near field, as implemented
by SGS for the national PSHA model for Saudi Arabia.
"""
CUTOFF_RRUP = 5.