# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2018 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:`Allen2012`
"""
import numpy as np
from scipy.constants import g
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import SA, PGA
[docs]class Allen2012(GMPE):
"""
Implements GMPE developed by T. Allen and published as "Stochastic ground-
motion prediction equations for southeastern Australian earthquakes using
updated source and attenuation parameters", 2012, Geoscience Australia
Record 2012/69. Document available at:
https://www.ga.gov.au/products/servlet/controller?event=GEOCAT_DETAILS&catno=74133
"""
#: Supported tectonic region type is stable continental crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types is spectral acceleration, see table 7,
#: page 35, and PGA (coefficients assumed to be the same of SA(0.01))
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is the median horizontal component
#: see table 7, page 35
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.MEDIAN_HORIZONTAL
#: Supported standard deviation type is only total, see table 7, page 35
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: No site parameters are needed, the GMPE is calibrated for average South
#: East Australia site conditions (assumed consistent to Vs30 = 820 m/s)
#: see paragraph 'Executive Summary', page VII
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude and hypocentral depth, see
#: paragraph 'Regression of Model Coefficients', page 32 and tables 7 and
#: 8, pages 35, 36
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth'))
#: Required distance measure is closest distance to rupture, see paragraph
#: 'Regression of Model Coefficients', page 32
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.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
if rup.hypo_depth < 10:
C = self.COEFFS_SHALLOW[imt]
else:
C = self.COEFFS_DEEP[imt]
mean = self._compute_mean(C, rup.mag, dists.rrup)
stddevs = self._get_stddevs(C, stddev_types, dists.rrup.shape[0])
return mean, stddevs
def _compute_mean(self, C, mag, rrup):
"""
Compute mean value according to equation 18, page 32.
"""
# see table 3, page 14
R1 = 90.
R2 = 150.
# see equation 19, page 32
m_ref = mag - 4
r1 = R1 + C['c8'] * m_ref
r2 = R2 + C['c11'] * m_ref
assert r1 > 0
assert r2 > 0
g0 = np.log10(
np.sqrt(np.minimum(rrup, r1) ** 2 + (1 + C['c5'] * m_ref) ** 2)
)
g1 = np.maximum(np.log10(rrup / r1), 0)
g2 = np.maximum(np.log10(rrup / r2), 0)
mean = (C['c0'] + C['c1'] * m_ref + C['c2'] * m_ref ** 2 +
(C['c3'] + C['c4'] * m_ref) * g0 +
(C['c6'] + C['c7'] * m_ref) * g1 +
(C['c9'] + C['c10'] * m_ref) * g2)
# convert from log10 to ln and units from cm/s2 to g
mean = np.log((10 ** mean) * 1e-2 / g)
return mean
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return total standard deviation.
"""
# standard deviation is converted from log10 to ln
std_total = np.log(10 ** C['sigma'])
stddevs = []
for _ in stddev_types:
stddevs.append(np.zeros(num_sites) + std_total)
return stddevs
#: Coefficients for shallow events taken from Excel file produced by Trevor
#: Allen and provided by Geoscience Australia (20120821.GMPE_coeffs.xls)
#: (coefficients in the original report are not correct)
COEFFS_SHALLOW = CoeffsTable(sa_damping=5, table="""\
IMT c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 sigma
pga 3.258600 0.505400 -0.069300 -1.838600 0.158000 1.246600 -0.204500 -0.044100 -5.108100 -2.861200 0.252000 -0.691100 0.412000
0.0100 3.258600 0.505400 -0.069300 -1.838600 0.158000 1.246600 -0.204500 -0.044100 -5.108100 -2.861200 0.252000 -0.691100 0.412000
0.0200 3.368300 0.496200 -0.062000 -1.807800 0.136300 1.247500 -0.486200 0.016300 -4.701900 -2.863100 0.248200 -0.939300 0.438300
0.0300 3.510700 0.470500 -0.059900 -1.852300 0.142300 1.433600 -0.544500 0.014800 -4.977800 -2.849200 0.249500 -1.070600 0.431000
0.0500 3.545000 0.476800 -0.062800 -1.836800 0.140300 1.459500 -0.488900 -0.010600 -5.116200 -3.072400 0.302500 -1.229400 0.399400
0.0750 3.516000 0.491900 -0.067900 -1.806300 0.142400 1.418400 -0.340700 -0.042800 -4.987400 -3.251800 0.305900 -0.760200 0.380500
0.1000 3.458400 0.514700 -0.072800 -1.773900 0.142300 1.374600 -0.215200 -0.061100 -4.836000 -3.286000 0.267700 -0.189000 0.372000
0.1500 3.295600 0.580400 -0.081900 -1.700200 0.131400 1.285500 -0.062700 -0.067200 -4.664000 -3.122100 0.156200 0.632700 0.363700
0.2000 3.136200 0.641600 -0.091600 -1.647500 0.127200 1.214000 0.071500 -0.080400 -4.682900 -2.934700 0.107400 1.033900 0.359400
0.2500 2.998000 0.692000 -0.101400 -1.614900 0.130400 1.159500 0.207800 -0.104600 -4.805400 -2.789000 0.113000 1.191100 0.357500
0.3000 2.872100 0.735800 -0.110100 -1.593400 0.135100 1.120600 0.318800 -0.124400 -4.854500 -2.680300 0.130700 1.166500 0.355800
0.4000 2.623100 0.817700 -0.123900 -1.565400 0.139800 1.082300 0.433000 -0.127100 -4.466500 -2.539500 0.135800 0.651700 0.354400
0.5000 2.398100 0.888800 -0.133900 -1.547600 0.139900 1.070500 0.465800 -0.105600 -3.820000 -2.457700 0.115600 -0.063200 0.352200
0.7500 1.943700 1.010800 -0.147100 -1.526700 0.140400 1.050100 0.475600 -0.092400 -3.422000 -2.406200 0.124500 -1.012700 0.349500
1.0000 1.616000 1.078400 -0.151400 -1.521700 0.144500 1.025200 0.481200 -0.123500 -4.045000 -2.438100 0.188700 -1.099200 0.348700
1.4999 1.192500 1.102000 -0.142300 -1.539500 0.160400 1.008700 0.503600 -0.159200 -4.247400 -2.498400 0.255800 -0.692900 0.349200
2.0000 0.928600 1.073700 -0.126300 -1.563900 0.175100 1.016400 0.521900 -0.163800 -3.754600 -2.526600 0.266400 -0.295300 0.348400
3.0003 0.573800 1.010900 -0.095300 -1.587900 0.184800 1.047900 0.513700 -0.157400 -3.782600 -2.535600 0.268200 -0.057000 0.346700
4.0000 0.339500 0.953600 -0.071200 -1.603600 0.188400 1.070600 0.509100 -0.158000 -4.200800 -2.564400 0.286000 -0.106100 0.345700
""")
#: Coefficients for deep events taken from Excel file produced by Trevor
#: Allen and provided by Geoscience Australia (20120821.GMPE_coeffs.xls)
#: (coefficients in the original report are not correct)
COEFFS_DEEP = CoeffsTable(sa_damping=5, table="""\
IMT c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 sigma
pga 3.383000 0.603400 -0.090500 -1.928900 0.175400 1.114000 -0.182200 -0.012600 -4.697400 -3.149000 0.315200 -0.724200 0.365300
0.0100 3.383000 0.603400 -0.090500 -1.928900 0.175400 1.114000 -0.182200 -0.012600 -4.697400 -3.149000 0.315200 -0.724200 0.365300
0.0200 3.556500 0.590400 -0.085600 -1.939400 0.162100 1.195400 -0.456100 0.033800 -4.858800 -3.091900 0.301200 -1.151800 0.389700
0.0300 3.706900 0.528100 -0.084300 -1.972900 0.185500 1.165300 -0.454800 0.001600 -4.683500 -3.284900 0.393800 -1.287100 0.384000
0.0500 3.738800 0.546200 -0.083500 -1.936900 0.165000 1.428100 -0.439900 0.001200 -4.335200 -3.477700 0.416800 -1.086700 0.355800
0.0750 3.671800 0.584400 -0.089300 -1.887900 0.157800 1.501000 -0.298600 -0.033500 -4.189500 -3.552900 0.399000 -1.230800 0.339200
0.1000 3.578800 0.626600 -0.097200 -1.847800 0.157300 1.512500 -0.162900 -0.057900 -4.055200 -3.517900 0.347100 -1.158900 0.332300
0.1500 3.377900 0.727600 -0.112800 -1.779600 0.147600 1.627700 -0.009000 -0.045100 -3.627400 -3.285000 0.182100 -0.189600 0.327100
0.2000 3.182600 0.820500 -0.128300 -1.732500 0.144300 1.648100 0.122900 -0.043000 -3.485400 -3.059000 0.103500 0.163500 0.324700
0.2500 3.004000 0.898700 -0.143200 -1.701000 0.148300 1.572900 0.259800 -0.063200 -3.597500 -2.883800 0.104700 -0.138500 0.324600
0.3000 2.842900 0.963400 -0.155600 -1.679100 0.153700 1.490100 0.368900 -0.084300 -3.750900 -2.749300 0.126100 -0.592800 0.324500
0.4000 2.550100 1.064800 -0.171800 -1.652100 0.159400 1.436400 0.460800 -0.095500 -3.856300 -2.559700 0.134600 -1.180600 0.324800
0.5000 2.303500 1.139300 -0.180700 -1.636700 0.160300 1.472500 0.462600 -0.083300 -3.790200 -2.436500 0.111300 -1.410700 0.322500
0.7500 1.821900 1.248000 -0.186000 -1.614500 0.157900 1.602600 0.453000 -0.076500 -3.630900 -2.380700 0.115500 -1.495100 0.318800
1.0000 1.478900 1.296500 -0.181800 -1.603100 0.156700 1.682600 0.486800 -0.101400 -3.612200 -2.471300 0.182000 -1.424700 0.318000
1.4999 1.070600 1.274400 -0.161100 -1.625600 0.172500 1.700600 0.526100 -0.134900 -3.722900 -2.564400 0.248000 -0.994700 0.316100
2.0000 0.840700 1.205900 -0.139000 -1.663900 0.193800 1.657500 0.538500 -0.147500 -3.764200 -2.581400 0.259700 -0.585400 0.314200
3.0003 0.534400 1.095900 -0.105400 -1.707400 0.217800 1.598000 0.597500 -0.167000 -3.159600 -2.706200 0.311300 -0.575300 0.311300
4.0000 0.320200 1.025000 -0.084500 -1.730700 0.229100 1.570300 0.640300 -0.176500 -2.737500 -2.811400 0.352600 -0.854700 0.309700
""")