# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2023 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:`Bradley2013`, :class:`Bradley2013Volc`,
:class:`Bradley2013ChchCBD`,
:class:`Bradley2013ChchWest`, :class:`Bradley2013ChchEast`,
:class:`Bradley2013ChchNorth`,
:class:`Bradley2013ChchCBDAdditionalSigma`,
:class:`Bradley2013ChchWestAdditionalSigma`,
:class:`Bradley2013ChchEastAdditionalSigma`,
:class:`Bradley2013ChchNorthAdditionalSigma`.
:class:`Bradley2013ChchMaps`.
:class:`Bradley2013ChchMapsAdditionalSigma`.
"""
import copy
import numpy as np
import shapely
from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib.gsim.abrahamson_2014 import get_epistemic_sigma
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
cbd_polygon = shapely.geometry.Polygon(
[(172.6259, -43.5209), (172.6505, -43.5209),
(172.6505, -43.5399), (172.6124, -43.5400),
(172.6123, -43.5289), (172.6124, -43.5245),
(172.6220, -43.5233)])
def _adjust_mean_model(region, in_cshm, in_cbd, imt_per, b13_mean):
dL2L = dS2S = np.array(np.zeros(np.shape(b13_mean)))
# If the site is in the CBD polygon, get dL2L and dS2S terms
# Only apply the dL2L term only to sites located in the CBD.
dL2L[in_cbd & in_cshm] = _get_dL2L(imt_per)
dS2S[in_cbd & in_cshm] = _get_dS2S(region, imt_per)
return b13_mean + dL2L + dS2S
def _check_in_cbd_polygon(lons, lats):
"""
Checks if site is located within the CBD polygon. The boundaries of
the polygon implemented here are from the 'Central City' Zoning Map
in the Christchurch District Plan. See Figure 4.4 of Van Houtte and
Abbott (2019).
"""
points = [shapely.geometry.Point(lons[ind], lats[ind])
for ind in np.arange(len(lons))]
in_cbd = np.array([cbd_polygon.contains(point) for point in points])
return in_cbd
def _get_SRF_phi(imt_per):
"""
Table 7 and equation 19 of 2013 report. NB change in notation,
2013 report calls this term 'sigma' but it is referred to here
as phi.
"""
if imt_per < 0.6:
srf = 0.8
elif 0.6 <= imt_per < 1:
srf = _interp_function(0.7, 0.8, 1, 0.6, imt_per)
elif 1 <= imt_per <= 10:
srf = _interp_function(0.6, 0.7, 10, 1, imt_per)
else:
srf = 1
return srf
def _get_SRF_sigma(imt_per):
"""
Table 8 and equation 19 of 2013 report. NB change in notation,
2013 report calls this term 'sigma_t' but it is referred to
here as sigma. Note that Table 8 is identical to Table 7 in
the 2013 report.
"""
if imt_per < 0.6:
srf = 0.8
elif 0.6 <= imt_per < 1:
srf = _interp_function(0.7, 0.8, 1, 0.6, imt_per)
elif 1 <= imt_per <= 10:
srf = _interp_function(0.6, 0.7, 10, 1, imt_per)
else:
srf = 1
return srf
def _get_SRF_tau(imt_per):
"""
Table 6 and equation 19 of 2013 report.
"""
if imt_per < 1:
srf = 0.87
elif 1 <= imt_per < 5:
srf = _interp_function(0.58, 0.87, 5, 1, imt_per)
elif 5 <= imt_per <= 10:
srf = 0.58
else:
srf = 1
return srf
[docs]def set_adjusted_stddevs(
clsname, additional_sigma, ctx, C, ln_y_ref,
exp1, exp2, in_cshm, in_cbd, imt_per, sig, tau, phi):
# aftershock flag is zero, we consider only main shock.
AS = 0
Fmeasured = ctx.vs30measured
Finferred = ~ctx.vs30measured
# eq. 19 to calculate inter-event standard error
mag_test = np.clip(ctx.mag - 5., 0., 2.)
t = C['tau1'] + (C['tau2'] - C['tau1']) / 2 * mag_test
# b and c coeffs from eq. 10
b = C['phi2'] * (exp1 - exp2)
c = C['phi4']
y_ref = np.exp(ln_y_ref)
# eq. 20
NL = b * y_ref / (y_ref + c)
sigma = (
# first line of eq. 20
(C['sig1'] + 0.5 * (C['sig2'] - C['sig1']) * mag_test + C['sig4'] * AS)
# second line
* np.sqrt(C['sig3'] * Finferred + 0.7 * Fmeasured + (1 + NL) ** 2))
if "Maps" in clsname:
# Get sigma reduction factors if site is in CBD polygon.
srf_sigma = np.array(np.ones(np.shape(in_cbd)))
srf_phi = np.array(np.ones(np.shape(in_cbd)))
srf_tau = np.array(np.ones(np.shape(in_cbd)))
srf_sigma[in_cshm & in_cbd] = _get_SRF_sigma(imt_per)
srf_phi[in_cshm & in_cbd] = _get_SRF_phi(imt_per)
# The tau reduction term is not used in this implementation
# srf_tau[in_cbd == True] = _get_SRF_tau(imt_per)
# Add 'additional sigma' specified in the Canterbury Seismic
# Hazard Model to total sigma, eq. 21
scaled_sigma = np.sqrt((1 + NL) ** 2 * t ** 2 + sigma ** 2) * srf_sigma
sig[:] = np.sqrt(scaled_sigma ** 2 + additional_sigma ** 2)
scaled_phi = sigma * srf_phi
phi[:] = np.sqrt(scaled_phi ** 2 + additional_sigma ** 2 / 2)
scaled_tau = np.abs((1 + NL) * t) * srf_tau
tau[:] = np.sqrt(scaled_tau ** 2 + additional_sigma ** 2 / 2)
return
# Get sigma reduction factors
srf_sigma = _get_SRF_sigma(imt_per)
srf_phi = _get_SRF_phi(imt_per)
srf_tau = _get_SRF_tau(imt_per)
# Add 'additional sigma' specified in the Canterbury Seismic
# Hazard Model to total sigma. This equals zero for the base model.
# eq. 21
scaled_sigma = np.sqrt((1 + NL) ** 2 * t**2 + sigma**2) * srf_sigma
sig[:] += np.sqrt(scaled_sigma ** 2 + additional_sigma ** 2)
scaled_phi = sigma * srf_phi
phi[:] += np.sqrt(scaled_phi ** 2 + additional_sigma ** 2 / 2)
scaled_tau = np.abs((1 + NL) * t) * srf_tau
tau[:] += np.sqrt(scaled_tau ** 2 + additional_sigma ** 2 / 2)
def _get_dL2L(imt_per):
"""
Table 3 and equation 19 of 2013 report.
"""
if imt_per < 0.18:
dL2L = -0.06
elif 0.18 <= imt_per < 0.35:
dL2L = _interp_function(0.12, -0.06, 0.35, 0.18, imt_per)
elif 0.35 <= imt_per <= 10:
dL2L = _interp_function(0.65, 0.12, 10, 0.35, imt_per)
else:
dL2L = 0
return dL2L
_get_dS2S = CallableDict()
@_get_dS2S.add("CBD")
def _get_dS2S_1(region, imt_per):
"""
Table 4 of 2013 report
"""
if imt_per == 0:
dS2S = 0.05
elif 0 < imt_per < 0.15:
dS2S = _interp_function(-0.15, 0.05, 0.15, 0, imt_per)
elif 0.15 <= imt_per < 0.45:
dS2S = _interp_function(0.4, -0.15, 0.45, 0.15, imt_per)
elif 0.45 <= imt_per < 3.2:
dS2S = 0.4
elif 3.2 <= imt_per < 5:
dS2S = _interp_function(0.08, 0.4, 5, 3.2, imt_per)
elif 5 <= imt_per <= 10:
dS2S = 0.08
else:
dS2S = 0
return dS2S
@_get_dS2S.add("West")
def _get_dS2S_2(region, imt_per):
"""
The parameters of this function have been digitised from Figure 8a
of the Bradley (2013b) report, as the actual parameters are not
provided in the report, and could not be provided by the author
(B. Bradley, pers. comm. 01/02/2019).
"""
if imt_per == 0:
dS2S = -0.2
elif 0 < imt_per < 0.85:
dS2S = _interp_function(-0.55, -0.2, 0.85, 0, imt_per)
elif 0.85 <= imt_per < 1.4:
dS2S = _interp_function(-0.18, -0.55, 1.4, 0.85, imt_per)
elif 1.4 <= imt_per < 3.2:
dS2S = -0.18
elif 3.2 <= imt_per < 5:
dS2S = _interp_function(0.22, -0.18, 5, 3.2, imt_per)
elif 5 <= imt_per <= 10:
dS2S = 0.22
else:
dS2S = 0
return dS2S
@_get_dS2S.add("East")
def _get_dS2S_3(region, imt_per):
"""
The parameters of this function have been digitised from Figure 9a
of the Bradley (2013b) report, as the actual parameters are not
provided in the report, and could not be provided by the author
(B. Bradley, pers. comm. 01/02/2019).
"""
if 0 <= imt_per <= 0.25:
dS2S = 0.05
elif 0.25 < imt_per < 1.5:
dS2S = _interp_function(0.15, 0.05, 1.5, 0.25, imt_per)
elif 1.5 <= imt_per <= 10:
dS2S = _interp_function(0.1, 0.15, 10, 1.5, imt_per)
else:
dS2S = 0
return dS2S
@_get_dS2S.add("North")
def _get_dS2S_4(region, imt_per):
"""
The parameters of this function have been digitised from Figure 10a
of the Bradley (2013b) report, as the actual parameters are not
provided in the report, and could not be provided by the author
(B. Bradley, pers. comm. 01/02/2019).
"""
if imt_per == 0:
dS2S = -0.31
elif 0 < imt_per < 0.2:
dS2S = _interp_function(-0.4, -0.31, 0.2, 0, imt_per)
elif 0.2 <= imt_per < 0.6:
dS2S = _interp_function(0.2, -0.4, 0.6, 0.2, imt_per)
elif 0.6 <= imt_per <= 10:
dS2S = 0.2
else:
dS2S = 0
return dS2S
def _get_ln_y_ref(trt, ctx, C):
"""
Get an intensity on a reference soil.
Implements eq. 4 in Bradley 2013. This is the same as Chiou and
Youngs 2008, with addition of TVZ attentuation term, and addition of
c8 which constains the ZTOR. Note that the TVZ scaling is set to 1
(i.e. no TVZ attenuation)
"""
# Taupo Volcanic Zone Path Distance. Set to zero.
rtvz = ctx.rrup if trt == const.TRT.VOLCANIC else 0.
# reverse faulting flag
Frv = np.zeros_like(ctx.rake)
Frv[(30 <= ctx.rake) & (ctx.rake <= 150)] = 1.
# normal faulting flag
Fnm = np.zeros_like(ctx.rake)
Fnm[(-120 <= ctx.rake) & (ctx.rake <= -60)] = 1.
# hanging wall flag
Fhw = ctx.rx >= 0
# aftershock flag. always zero since we only consider main shock
AS = 0
ln_y_ref = (
# first line of eq. 4 in Bradley 2013
C['c1']
+ (C['c1a'] * Frv
+ C['c1b'] * Fnm
+ C['c7'] * (np.clip(ctx.ztor, -np.inf, C['c8']) - 4))
* (1 - AS)
+ (C['c10'] + C['c7a'] * (ctx.ztor - 4)) * AS
# second line
+ C['c2'] * (ctx.mag - 6)
+ ((C['c2'] - C['c3']) / C['cn'])
* np.log(1 + np.exp(C['cn'] * (C['cm'] - ctx.mag)))
# third line
+ C['c4']
* np.log(ctx.rrup
+ C['c5']
* np.cosh(C['c6'] * np.maximum(ctx.mag - C['chm'], 0)))
# fourth line
+ (C['c4a'] - C['c4'])
* np.log(np.sqrt(ctx.rrup ** 2 + C['crb'] ** 2))
# fifth line
+ (C['cg1'] + C['cg2'] / (np.cosh(np.maximum(ctx.mag - C['cg3'], 0))))
# sixth line
* ((1 + C['ctvz'] * (rtvz / ctx.rrup)) * ctx.rrup)
# seventh line
+ C['c9'] * Fhw
* np.tanh(ctx.rx
* (np.cos(np.radians(ctx.dip)) ** 2)
/ C['c9a'])
* (1 - np.sqrt(ctx.rjb ** 2 + ctx.ztor ** 2)
/ (ctx.rrup + 0.001)))
return ln_y_ref
def _get_mean(ctx, C, ln_y_ref, exp1, exp2, v1):
"""
Add site effects to an intensity.
Implements eq. 5
"""
# we do not support estimating of basin depth and instead
# rely on it being available (since we require it).
z1pt0 = ctx.z1pt0
# we consider random variables being zero since we want
# to find the exact mean value.
eta = epsilon = 0
ln_y = (
# first line of eq. 13b
ln_y_ref + C['phi1'] *
np.log(np.clip(ctx.vs30, -np.inf, v1) / 1130)
# second line
+ C['phi2'] * (exp1 - exp2)
* np.log((np.exp(ln_y_ref) + C['phi4']) / C['phi4'])
# third line
+ C['phi5']
* (1.0 - 1.0 / np.cosh(
C['phi6'] * (z1pt0 - C['phi7']).clip(0, np.inf)))
+ C['phi8'] / np.cosh(0.15 * (z1pt0 - 15).clip(0, np.inf))
# fourth line
+ eta + epsilon)
return ln_y
[docs]def set_stddevs(additional_sigma, ctx, C,
ln_y_ref, exp1, exp2, sig, tau, phi):
# aftershock flag is zero, we consider only main shock.
AS = 0
Fmeasured = ctx.vs30measured
Finferred = 1 - ctx.vs30measured
# eq. 19 to calculate inter-event standard error
mag_test = np.clip(ctx.mag - 5., 0., 2.)
t = C['tau1'] + (C['tau2'] - C['tau1']) / 2 * mag_test
# b and c coeffs from eq. 10
b = C['phi2'] * (exp1 - exp2)
c = C['phi4']
y_ref = np.exp(ln_y_ref)
# eq. 20
NL = b * y_ref / (y_ref + c)
sigma = (
# first line of eq. 20
(C['sig1']
+ 0.5 * (C['sig2'] - C['sig1']) * mag_test
+ C['sig4'] * AS)
# second line
* np.sqrt((C['sig3'] * Finferred + 0.7 * Fmeasured)
+ (1 + NL) ** 2))
# Add 'additional sigma' specified in the Canterbury Seismic
# Hazard Model to total sigma
# eq. 21
unscaled_sigma_tot = np.sqrt((1 + NL) ** 2 * t ** 2 + sigma ** 2)
sig[:] = np.sqrt(unscaled_sigma_tot ** 2 + additional_sigma ** 2)
phi[:] = np.sqrt(sigma ** 2 + additional_sigma ** 2 / 2)
# this is implied in eq. 21
unscaled_tau = np.abs((1 + NL) * t)
tau[:] = np.sqrt(unscaled_tau ** 2 + additional_sigma ** 2 / 2)
def _get_v1(imt):
"""
Calculates Bradley's V1 term. Equation 2 (page 1814) and 6 (page 1816)
based on SA period
"""
T = imt.period
if T == 0:
v1 = 1800.
else:
v1a = np.clip((1130 * (T / 0.75)**-0.11), 1130, np.inf)
v1 = np.clip(v1a, -np.inf, 1800.)
return v1
def _interp_function(y_ip1, y_i, t_ip1, t_i, imt_per):
"""
Generic interpolation function used in equation 19 of 2013 report.
"""
return y_i + (y_ip1 - y_i) / (t_ip1 - t_i) * (imt_per - t_i)
[docs]class Bradley2013(GMPE):
"""
Implements GMPE developed by Brendan Bradley for Active Shallow Crust
Earthquakes for New Zealand, and published as "A New Zealand-Specific
Pseudospectral Acceleration Ground-Motion Prediction Equation for Active
Shallow Crustal Earthquakes Based on Foreign Models" (2013, Bulletin of
the Seismological Society of America, Volume 103, No. 3, pages 1801-1822).
This model is modified from Chiou and Youngs, 2008 and has been adapted
for New Zealand conditions. Specifically, the modifications are related to:
1) small magnitude scaling;
2) scaling of short period ground motion from normal faulting events in
volcanic crust;
3) scaling of ground motions on very hard rock sites;
4) anelastic attenuation in the New Zealand crust;
5) consideration of the increates anelastic attenuation in the Taupo
Volcanic Zone (not implemented in this model, use Bradley2013Volc)
"""
#: Supported tectonic region type is active shallow crust, see page 1801
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: peak ground velocity and peak ground acceleration. Note that PGV is
#: the Chiou & Youngs PGV and has not been modified for New Zealand.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is geometric mean
#: of two horizontal components
#: attr:`~openquake.hazardlib.const.IMC.GEOMETRIC_MEAN`,
#: see abstract page 1801.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation types are inter-event, intra-event
#: and total, see chapter "Variance model".
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameters are Vs30 (eq. 13b), Vs30 measured flag (eq. 20)
#: and Z1.0 (eq. 13b).
REQUIRES_SITES_PARAMETERS = {'vs30', 'vs30measured', 'z1pt0'}
#: Required rupture parameters are magnitude, rake (eq. 13a and 13b),
#: dip (eq. 13a) and ztor (eq. 13a).
REQUIRES_RUPTURE_PARAMETERS = {'dip', 'rake', 'mag', 'ztor'}
#: Required distance measures are RRup, Rjb and Rx (all are in eq. 13a).
REQUIRES_DISTANCES = {'rrup', 'rjb', 'rx'}
additional_sigma = 0.
def __init__(self, sigma_mu_epsilon=0.0):
self.sigma_mu_epsilon = sigma_mu_epsilon
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
trt = self.DEFINED_FOR_TECTONIC_REGION_TYPE
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
# intensity on a reference soil is used for both mean
# and stddev calculations.
ln_y_ref = _get_ln_y_ref(trt, ctx, C)
# exp1 and exp2 are parts of eq. 7
exp1 = np.exp(C['phi3'] * (ctx.vs30.clip(-np.inf, 1130) - 360))
exp2 = np.exp(C['phi3'] * (1130 - 360))
# v1 is the period dependent site term. The Vs30 above which, the
# amplification is constant
v1 = _get_v1(imt)
mean[m] = _get_mean(ctx, C, ln_y_ref, exp1, exp2, v1)
mean[m] += (self.sigma_mu_epsilon*get_epistemic_sigma(ctx))
set_stddevs(self.additional_sigma, ctx, C, ln_y_ref, exp1, exp2,
sig[m], tau[m], phi[m])
#: Coefficient tables are constructed from values in tables 1, 2 and 3
#: (pages 197, 198 and 199) in Chiou & Youngs,2008. Only Coefficients c1,
#: c1b, c3, cm, c8, cg1, cg2, ctvz are modified by Bradley 2013.
#: Spectral acceleration is defined for damping of 5%, see page 208 (CY08).
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c2 c3 c4 c4a crb chm cg3 c1 c1a c1b cn cm c5 c6 c7 c7a c8 c9 c9a c10 cg1 cg2 ctvz phi1 phi2 phi3 phi4 phi5 phi6 phi7 phi8 tau1 tau2 sig1 sig2 sig3 sig4
pga 1.06 1.50000 -2.1 -0.5 50.0 3.0 4.0 -1.1985 0.1000 -0.4550 2.996 5.85000 6.1600 0.4893 0.0512 0.0860 10.00 0.7900 1.5005 -0.3218 -0.00960 -0.00480 2.000 -0.4417 -0.1417 -0.007010 0.102151 0.2289 0.014996 580.0 0.0700 0.3437 0.2637 0.4458 0.3459 0.8000 0.0663
0.010 1.06 1.50299 -2.1 -0.5 50.0 3.0 4.0 -1.1958 0.1000 -0.4550 2.996 5.81711 6.1600 0.4893 0.0512 0.0860 10.00 0.7900 1.5005 -0.3218 -0.00960 -0.00481 2.000 -0.4417 -0.1417 -0.007010 0.102151 0.2289 0.014996 580.0 0.0700 0.3437 0.2637 0.4458 0.3459 0.8000 0.0663
0.020 1.06 1.50845 -2.1 -0.5 50.0 3.0 4.0 -1.1756 0.1000 -0.4550 3.292 5.80023 6.1580 0.4892 0.0512 0.0860 10.00 0.8129 1.5028 -0.3323 -0.00970 -0.00486 2.000 -0.4340 -0.1364 -0.007279 0.108360 0.2289 0.014996 580.0 0.0699 0.3471 0.2671 0.4458 0.3459 0.8000 0.0663
0.030 1.06 1.51549 -2.1 -0.5 50.0 3.0 4.0 -1.0909 0.1000 -0.4550 3.514 5.78659 6.1550 0.4890 0.0511 0.0860 10.00 0.8439 1.5071 -0.3394 -0.01010 -0.00503 2.000 -0.4177 -0.1403 -0.007354 0.119888 0.2289 0.014996 580.0 0.0701 0.3603 0.2803 0.4535 0.3537 0.8000 0.0663
0.040 1.06 1.52380 -2.1 -0.5 50.0 3.0 4.0 -0.9793 0.1000 -0.4550 3.563 5.77472 6.1508 0.4888 0.0508 0.0860 10.00 0.8740 1.5138 -0.3453 -0.01050 -0.00526 2.000 -0.4000 -0.1591 -0.006977 0.133641 0.2289 0.014996 579.9 0.0702 0.3718 0.2918 0.4589 0.3592 0.8000 0.0663
0.050 1.06 1.53319 -2.1 -0.5 50.0 3.0 4.0 -0.8549 0.1000 -0.4550 3.547 5.76402 6.1441 0.4884 0.0504 0.0860 10.00 0.8996 1.5230 -0.3502 -0.01090 -0.00549 2.000 -0.3903 -0.1862 -0.006467 0.148927 0.2290 0.014996 579.9 0.0701 0.3848 0.3048 0.4630 0.3635 0.8000 0.0663
0.075 1.06 1.56053 -2.1 -0.5 50.0 3.0 4.0 -0.6008 0.1000 -0.4540 3.448 5.74056 6.1200 0.4872 0.0495 0.0860 10.00 0.9442 1.5597 -0.3579 -0.01170 -0.00588 2.000 -0.4040 -0.2538 -0.005734 0.190596 0.2292 0.014996 579.6 0.0686 0.3878 0.3129 0.4702 0.3713 0.8000 0.0663
0.10 1.06 1.59241 -2.1 -0.5 50.0 3.0 4.0 -0.4700 0.1000 -0.4530 3.312 5.72017 6.0850 0.4854 0.0489 0.0860 10.00 0.9677 1.6104 -0.3604 -0.01170 -0.00591 2.000 -0.4423 -0.2943 -0.005604 0.230662 0.2297 0.014996 579.2 0.0646 0.3835 0.3152 0.4747 0.3769 0.8000 0.0663
0.15 1.06 1.66640 -2.1 -0.5 50.0 3.0 4.0 -0.4139 0.1000 -0.4500 3.044 5.68493 5.9871 0.4808 0.0479 0.0860 10.00 0.9660 1.7549 -0.3565 -0.01110 -0.00540 2.000 -0.5162 -0.3113 -0.005845 0.266468 0.2326 0.014988 577.2 0.0494 0.3719 0.3128 0.4798 0.3847 0.8000 0.0612
0.20 1.06 1.75021 -2.1 -0.5 50.0 3.0 4.0 -0.5237 0.1000 -0.4149 2.831 5.65435 5.8699 0.4755 0.0471 0.0860 10.00 0.9334 1.9157 -0.3470 -0.01000 -0.00479 2.000 -0.5697 -0.2927 -0.006141 0.255253 0.2386 0.014964 573.9 -0.0019 0.3601 0.3076 0.4816 0.3902 0.8000 0.0530
0.25 1.06 1.84052 -2.1 -0.5 50.0 3.0 4.0 -0.6678 0.1000 -0.3582 2.658 5.62686 5.7547 0.4706 0.0464 0.0860 10.50 0.8946 2.0709 -0.3379 -0.00910 -0.00427 2.000 -0.6109 -0.2662 -0.006439 0.231541 0.2497 0.014881 568.5 -0.0479 0.3522 0.3047 0.4815 0.3946 0.7999 0.0457
0.30 1.06 1.93480 -2.1 -0.5 50.0 3.0 4.0 -0.8277 0.0999 -0.3113 2.505 5.60162 5.6527 0.4665 0.0458 0.0860 11.00 0.8590 2.2005 -0.3314 -0.00820 -0.00384 2.500 -0.6444 -0.2405 -0.006704 0.207277 0.2674 0.014639 560.5 -0.0756 0.3438 0.3005 0.4801 0.3981 0.7997 0.0398
0.40 1.06 2.12764 -2.1 -0.5 50.0 3.0 4.0 -1.1284 0.0997 -0.2646 2.261 5.55602 5.4997 0.4607 0.0445 0.0850 12.00 0.8019 2.3886 -0.3256 -0.00690 -0.00317 3.200 -0.6931 -0.1975 -0.007125 0.165464 0.3120 0.013493 540.0 -0.0960 0.3351 0.2984 0.4758 0.4036 0.7988 0.0312
0.50 1.06 2.31684 -2.1 -0.5 50.0 3.0 4.0 -1.3926 0.0991 -0.2272 2.087 5.51513 5.4029 0.4571 0.0429 0.0830 13.00 0.7578 2.5000 -0.3189 -0.00590 -0.00272 3.500 -0.7246 -0.1633 -0.007435 0.133828 0.3610 0.011133 512.9 -0.0998 0.3353 0.3036 0.4710 0.4079 0.7966 0.0255
0.75 1.06 2.73064 -2.1 -0.5 50.0 3.0 4.0 -1.8664 0.0936 -0.1620 1.812 5.38632 5.2900 0.4531 0.0387 0.0690 14.00 0.6788 2.6224 -0.2702 -0.00450 -0.00209 4.500 -0.7708 -0.1028 -0.008120 0.085153 0.4353 0.006739 441.9 -0.0765 0.3429 0.3205 0.4621 0.4157 0.7792 0.0175
1.0 1.06 3.03000 -2.1 -0.5 50.0 3.0 4.0 -2.1935 0.0766 -0.1400 1.648 5.31000 5.2480 0.4517 0.0350 0.0450 15.00 0.6196 2.6690 -0.2059 -0.00370 -0.00175 5.000 -0.7990 -0.0699 -0.008444 0.058595 0.4629 0.005749 391.8 -0.0412 0.3577 0.3419 0.4581 0.4213 0.7504 0.0133
1.5 1.06 3.43384 -2.1 -0.5 50.0 3.0 4.0 -2.6883 0.0022 -0.1184 1.511 5.29995 5.2194 0.4507 0.0280 0.0134 16.00 0.5101 2.6985 -0.0852 -0.00280 -0.00142 5.400 -0.8382 -0.0425 -0.007707 0.031787 0.4756 0.005544 348.1 0.0140 0.3769 0.3703 0.4493 0.4213 0.7136 0.0090
2.0 1.06 3.67464 -2.1 -0.5 50.0 3.0 4.0 -3.1040 -0.0591 -0.1100 1.470 5.32730 5.2099 0.4504 0.0213 0.0040 18.00 0.3917 2.7085 0.0160 -0.00230 -0.00143 5.800 -0.8663 -0.0302 -0.004792 0.019716 0.4785 0.005521 332.5 0.0544 0.4023 0.4023 0.4459 0.4213 0.7035 0.0068
3.0 1.06 3.64933 -2.1 -0.5 50.0 3.0 4.0 -3.7085 -0.0931 -0.1040 1.456 5.43850 5.2040 0.4501 0.0106 0.0010 19.00 0.1244 2.7145 0.1876 -0.00190 -0.00115 6.000 -0.9032 -0.0129 -0.001828 0.009643 0.4796 0.005517 324.1 0.1232 0.4406 0.4406 0.4433 0.4213 0.7006 0.0045
4.0 1.06 3.60999 -2.1 -0.5 50.0 3.0 4.0 -4.1486 -0.0982 -0.1020 1.465 5.59770 5.2020 0.4501 0.0041 0.0000 19.75 0.0086 2.7164 0.3378 -0.00180 -0.00104 6.150 -0.9231 -0.0016 -0.001523 0.005379 0.4799 0.005517 321.7 0.1859 0.4784 0.4784 0.4424 0.4213 0.7001 0.0034
5.0 1.06 3.50000 -2.1 -0.5 50.0 3.0 4.0 -4.4881 -0.0994 -0.1010 1.478 5.72760 5.2010 0.4500 0.0010 0.0000 20.00 0.0000 2.7172 0.4579 -0.00170 -0.00099 6.300 -0.9222 0.0000 -0.001440 0.003223 0.4799 0.005517 320.9 0.2295 0.5074 0.5074 0.4420 0.4213 0.7000 0.0027
7.5 1.06 3.45000 -2.1 -0.5 50.0 3.0 4.0 -5.0891 -0.0999 -0.1010 1.498 5.98910 5.2000 0.4500 0.0000 0.0000 20.00 0.0000 2.7177 0.7514 -0.00170 -0.00094 6.425 -0.8346 0.0000 -0.001369 0.001134 0.4800 0.005517 320.3 0.2660 0.5328 0.5328 0.4416 0.4213 0.7000 0.0018
10.0 1.06 3.45000 -2.1 -0.5 50.0 3.0 4.0 -5.5530 -0.1000 -0.1000 1.502 6.19300 5.2000 0.4500 0.0000 0.0000 20.00 0.0000 2.7180 1.1856 -0.00170 -0.00091 6.550 -0.7332 0.0000 -0.001361 0.000515 0.4800 0.005517 320.1 0.2682 0.5542 0.5542 0.4414 0.4213 0.7000 0.0014
""")
[docs]class Bradley2013Volc(Bradley2013):
"""
Extend :class:`Bradley2013` for earthquakes with paths across the Taupo
Volcanic Zone (rtvz) that have increased anelastic attenuation.
Implements GMPE developed by Brendan Bradley for Active Shallow Crust
Earthquakes for New Zealand, and published as "A New Zealand-Specific
Pseudospectral Acceleration Ground-Motion Prediction Equation for Active
Shallow Crustal Earthquakes Based on Foreign Models" (2013, Bulletin of
the Seismological Society of America, Volume 103, No. 3, pages 1801-1822).
This model is modified from Chiou and Youngs, 2008 and has been adapted
for New Zealand conditions. Specifically, the modifications are related to:
1) small magnitude scaling;
2) scaling of short period ground motion from normal faulting events in
volcanic crust;
3) scaling of ground motions on very hard rock sites;
4) anelastic attenuation in the New Zealand crust;
5) consideration of the increates anelastic attenuation in the Taupo
Volcanic Zone (rtvz is equal to rrup)
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC
[docs]class Bradley2013LHC(Bradley2013):
"""
Extend :class:`Bradley2013` to provide the model in terms of the larger
of two as-recorded horizontal components. This definition is required
by New Zealand building design standards.
"""
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = \
const.IMC.GREATER_OF_TWO_HORIZONTAL
#: This implementation is non-verified because this version of the
#: model has not been published, nor is independent code available.
non_verified = True
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
super().compute(ctx, imts, mean, sig, tau, phi)
for m, imt in enumerate(imts):
mean[m] += convert_to_LHC(imt)
[docs]class Bradley2013VolcLHC(Bradley2013LHC):
"""
Extend :class:`Bradley2013LHC` for earthquakes with paths across the Taupo
Volcanic Zone (rtvz) that have increased anelastic attenuation.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC
[docs]def convert_to_LHC(imt):
"""
Converts from GMRotI50 to Larger of two horizontal components using
global equation of:
Boore, D and Kishida, T (2016). Relations between some horizontal-
component ground-motion intensity measures used in practice.
Bulletin of the Seismological Society of America, 107(1), 334-343.
doi:10.1785/0120160250
No standard deviation modification required.
"""
# get period t
t = imt.period or 0.01
T1 = 0.08
T2 = 0.56
T3 = 4.40
T4 = 8.70
R1 = 1.106
R2 = 1.158
R3 = 1.178
R4 = 1.241
R5 = 1.241
min1 = min(R1 + (R2 - R1) / np.log(T2 / T1) * np.log(t / T1),
R2 + (R3 - R2) / np.log(T3 / T2) * np.log(t / T2))
min2 = min(R3 + (R4 - R3) / np.log(T4 / T3) * np.log(t / T3), R5)
Ratio = max(R1, max(min1, min2))
SF = np.log(Ratio)
return SF
[docs]class Bradley2013bChchCBD(Bradley2013LHC):
"""
Implements GMPE developed by Brendon Bradley for Christchurch subregions,
and published as:
Bradley, B. (2013). "Systematic ground motion observations in the
Canterbury earthquakes and region-specific nonergodic empirical ground
motion modelling"" (2013), University of Canterbury Research Report
2013-03, Department of Civil Engineering, University of Canterbury,
Christchurch, New Zealand."
This model was also published as:
Bradley, B. (2015). Systematic Ground Motion Observations in the Canterbury
Earthquakes And Region-Specific Non-Ergodic Empirical Ground Motion
Modeling. Earthquake Spectra: August 2015, Vol. 31, No. 3, pp. 1735-1761.
but this implementation has been developed from the information in the 2013
report.
The original code by the author could not be made available at the time of
development of this code. For this reason, this implementation is untested
and marked as non_verified.
It appears from the model documentation that the dL2L and dS2S terms are
relative to a baseline Vs30 value of 250 m/s and a baseline Z1 value of
330 m, although this is unconfirmed.
"""
region = "CBD"
non_verified = True
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
trt = self.DEFINED_FOR_TECTONIC_REGION_TYPE
ctx = copy.copy(ctx)
# Fix site parameters for consistent dS2S application.
ctx.vs30 = np.array([250])
ctx.z1pt0 = np.array([330])
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imt_per = imt.period
# intensity on a reference soil is used for both mean
# and stddev calculations.
ln_y_ref = _get_ln_y_ref(trt, ctx, C)
# exp1 and exp2 are parts of eq. 7
exp1 = np.exp(C['phi3'] * (ctx.vs30.clip(-np.inf, 1130) - 360))
exp2 = np.exp(C['phi3'] * (1130 - 360))
# v1 is the period dependent site term. The Vs30 above which, the
# amplification is constant
v1 = _get_v1(imt)
# Get log-mean from regular unadjusted model
b13a_mean = _get_mean(ctx, C, ln_y_ref, exp1, exp2, v1)
# Adjust mean and standard deviation
mean[m] = b13a_mean + _get_dL2L(imt_per) + _get_dS2S(
self.region, imt_per)
mean[m] += convert_to_LHC(imt)
set_adjusted_stddevs(
self.__class__.__name__, self.additional_sigma, ctx,
C, ln_y_ref, exp1, exp2, 0, 0, imt_per, sig[m], tau[m], phi[m])
[docs]class Bradley2013bChchWest(Bradley2013bChchCBD):
"""
Extend :class:`Bradley2013bChchCBD` to implement the 'extended western
suburbs' dS2S model.
"""
region = "West"
[docs]class Bradley2013bChchEast(Bradley2013bChchCBD):
"""
Extend :class:`Bradley2013bChchCBD` to implement the 'eastern
suburbs' dS2S model.
"""
region = "East"
[docs]class Bradley2013bChchNorth(Bradley2013bChchCBD):
"""
Extend :class:`Bradley2013bChchCBD` to implement the 'northern
suburbs' dS2S model.
"""
region = "North"
[docs]class Bradley2013bChchCBDAdditionalSigma(Bradley2013bChchCBD):
"""
Extend :class:`Bradley2013ChchCBD` to implement the 'additional
epistemic uncertainty' version of the model in:
Gerstenberger, M., McVerry, G., Rhoades, D., Stirling, M. 2014.
"Seismic hazard modelling for the recovery of Christchurch",
Earthquake Spectra, 30(1), 17-29.
"""
additional_sigma = .35
[docs]class Bradley2013bChchWestAdditionalSigma(Bradley2013bChchWest):
"""
Extend :class:`Bradley2013ChchWest` to implement the 'additional
epistemic uncertainty' version of the model in:
Gerstenberger, M., McVerry, G., Rhoades, D., Stirling, M. 2014.
"Seismic hazard modelling for the recovery of Christchurch",
Earthquake Spectra, 30(1), 17-29.
"""
additional_sigma = .35
[docs]class Bradley2013bChchEastAdditionalSigma(Bradley2013bChchEast):
"""
Extend :class:`Bradley2013ChchEast` to implement the 'additional
epistemic uncertainty' version of the model in:
Gerstenberger, M., McVerry, G., Rhoades, D., Stirling, M. 2014.
"Seismic hazard modelling for the recovery of Christchurch",
Earthquake Spectra, 30(1), 17-29.
"""
additional_sigma = .35
[docs]class Bradley2013bChchNorthAdditionalSigma(Bradley2013bChchNorth):
"""
Extend :class:`Bradley2013ChchNorth` to implement the 'additional
epistemic uncertainty' version of the model in:
Gerstenberger, M., McVerry, G., Rhoades, D., Stirling, M. 2014.
"Seismic hazard modelling for the recovery of Christchurch",
Earthquake Spectra, 30(1), 17-29.
"""
additional_sigma = .35
[docs]class Bradley2013AdditionalSigma(Bradley2013LHC):
"""
Extend :class:`Bradley2013LHC` to implement the 'additional
epistemic uncertainty' version of the model in:
Gerstenberger, M., McVerry, G., Rhoades, D., Stirling, M. 2014.
"Seismic hazard modelling for the recovery of Christchurch",
Earthquake Spectra, 30(1), 17-29.
"""
additional_sigma = .35
[docs]class Bradley2013bChchMaps(Bradley2013bChchCBD):
"""
Implements GMPE developed by Brendon Bradley for Christchurch subregions,
and published as ""Systematic ground motion observations in the Canterbury
earthquakes and region-specific nonergodic empirical ground motion
modelling"" (2013), University of Canterbury Research Report 2013-03,
Department of Civil Engineering, University of Canterbury, Christchurch,
New Zealand.
The original code by the author was not made available at the time of
development of this code. For this reason, this implementation is untested.
It appears from the model documentation that the CBD dL2L and dS2S are
relative to a baseline Vs30 value of 250 m/s and a baseline Z1 value of
330 m, although this is unconfirmed.
Only the CBD subregion dS2S term is implemented here, because of
difficulties defining the boundaries of other subregions. Full details
behind the choices here are detailed in:
Van Houtte and Abbott (2019), "Implementation of the GNS Canterbury
Seismic Hazard Model in the OpenQuake Engine", Lower Hutt (NZ): GNS
Science. 38 p. (GNS Science report; 2019/11). doi:10.21420/1AEM-PZ85.
"""
#: Required site parameters are Vs30 (eq. 13b), Vs30 measured flag (eq. 20)
#: and Z1.0 (eq. 13b), longitude and latitude.
REQUIRES_SITES_PARAMETERS = {'vs30', 'vs30measured', 'z1pt0', 'lon', 'lat'}
#: This implementation is non-verified because the author of the model does
#: not have code that can be made available.
non_verified = True
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
ctx = copy.copy(ctx)
trt = self.DEFINED_FOR_TECTONIC_REGION_TYPE
name = self.__class__.__name__
# Check if the sites are located in the CBD polygon
in_cbd = _check_in_cbd_polygon(ctx.lon, ctx.lat)
# Fix CBD site terms before dS2S modification.
ctx.vs30[in_cbd] = 250
ctx.z1pt0[in_cbd] = 330
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imt_per = imt.period
# intensity on a reference soil is used for both mean
# and stddev calculations.
ln_y_ref = _get_ln_y_ref(trt, ctx, C)
# exp1 and exp2 are parts of eq. 7
exp1 = np.exp(C['phi3'] * (ctx.vs30.clip(-np.inf, 1130) - 360))
exp2 = np.exp(C['phi3'] * (1130 - 360))
# v1 is the period dependent site term. The Vs30 above which, the
# amplification is constant
v1 = _get_v1(imt)
# Get log-mean from regular unadjusted model
b13_mean = _get_mean(ctx, C, ln_y_ref, exp1, exp2, v1)
# Adjust mean and standard deviation
mean[m] = _adjust_mean_model(
self.region, ctx.in_cshm, in_cbd, imt_per, b13_mean)
mean[m] += convert_to_LHC(imt)
set_adjusted_stddevs(
name, self.additional_sigma, ctx, C, ln_y_ref, exp1, exp2,
ctx.in_cshm, in_cbd, imt_per, sig[m], tau[m], phi[m])
[docs]class Bradley2013bChchMapsAdditionalSigma(Bradley2013bChchMaps):
"""
Extend :class:`Bradley2013ChchNorth` to implement the 'additional
epistemic uncertainty' version of the model in:
Gerstenberger, M., McVerry, G., Rhoades, D., Stirling, M. 2014.
"Seismic hazard modelling for the recovery of Christchurch",
Earthquake Spectra, 30(1), 17-29.
"""
additional_sigma = .35
