# Source code for openquake.hazardlib.gsim.somerville_2009

```# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2022 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:`SomervilleEtAl2009NonCratonic`,
:class:`SomervilleEtAl2009YilgarnCraton`
"""
import numpy as np

from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA

def _compute_mean(C, mag, rjb):
"""
Compute mean value, see table 2.
"""
m1 = 6.4
r1 = 50.
h = 6.
R = np.sqrt(rjb ** 2 + h ** 2)
R1 = np.sqrt(r1 ** 2 + h ** 2)
less_r1 = rjb < r1
ge_r1 = rjb >= r1

mean = (C['c1'] + C['c4'] * (mag - m1) * np.log(R) + C['c5'] * rjb +
C['c8'] * (8.5 - mag) ** 2)

mean[less_r1] += C['c3'] * np.log(R[less_r1])
mean[ge_r1] += (C['c3'] * np.log(R1) +
C['c6'] * (np.log(R[ge_r1]) - np.log(R1)))
mean += np.where(mag < m1, C['c2'] * (mag - m1), C['c7'] * (mag - m1))

return mean

[docs]class SomervilleEtAl2009NonCratonic(GMPE):
"""
Implements GMPE developed by P. Somerville, R. Graves, N. Collins, S. G.
Song, S. Ni, and P. Cummins for Non-Cratonic Australia published in "Source
and Ground Motion Models for Australian Earthquakes", Report to Geoscience
Australia (2009). Document available at:
http://www.ga.gov.au/cedda/publications/193?yp=2009
"""
#: The supported tectonic region type is stable continental region
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL

#: The supported intensity measure types are PGA, PGV, and SA, see table
#: 3
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}

#: The supported intensity measure component is set to 'average
#: horizontal', however the original paper does not report this information
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL

#: The supported standard deviations is total, see tables 3
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}

#: no site parameters are defined, the GMPE is calibrated for Vs30 = 865
#: m/s (provisionally set to 800 for compatibility with SiteTerm class)
REQUIRES_SITES_PARAMETERS = set()
DEFINED_FOR_REFERENCE_VELOCITY = 800.

#: The required rupture parameter is magnitude, see table 2
REQUIRES_RUPTURE_PARAMETERS = {'mag'}

#: The required distance parameter is 'Joyner-Boore' distance, see table 2
REQUIRES_DISTANCES = {'rjb'}

[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.

Implement equations as defined in table 2.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
mean[m] = _compute_mean(C, ctx.mag, ctx.rjb)
sig[m] = C['sigma']

#: Coefficients taken from table 3
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT     c1       c2        c3       c4        c5        c6        c7        c8       sigma
pgv     5.07090  0.52780  -0.85740  0.17700  -0.00501  -0.61190   0.80660  -0.03800  0.6417
pga     1.03780 -0.03970  -0.79430  0.14450  -0.00618  -0.72540  -0.03590  -0.09730  0.5685
0.010   1.05360 -0.04190  -0.79390  0.14450  -0.00619  -0.72660  -0.03940  -0.09740  0.5684
0.020   1.05680 -0.03920  -0.79680  0.14550  -0.00617  -0.73230  -0.03930  -0.09600  0.5684
0.030   1.13530 -0.04790  -0.80920  0.15000  -0.00610  -0.76410  -0.05710  -0.09210  0.5681
0.040   1.30000 -0.07020  -0.83150  0.15920  -0.00599  -0.82850  -0.09810  -0.08530  0.5676
0.050   1.47680 -0.09310  -0.83330  0.15600  -0.00606  -0.86740  -0.12740  -0.09130  0.5670
0.075   1.70220 -0.05160  -0.80720  0.14560  -0.00655  -0.87690  -0.10970  -0.08690  0.5663
0.100   1.65720  0.15080  -0.77590  0.13100  -0.00708  -0.77830   0.01690  -0.05980  0.5659
0.150   1.94440 -0.09620  -0.75000  0.11670  -0.00698  -0.69490  -0.13320  -0.12530  0.5659
0.200   1.82720 -0.06230  -0.73430  0.11940  -0.00677  -0.64380  -0.09570  -0.11920  0.5669
0.250   1.74380 -0.02530  -0.72480  0.11950  -0.00646  -0.63740  -0.06250  -0.11650  0.5678
0.3003  1.80560 -0.27020  -0.73190  0.13490  -0.00606  -0.66440  -0.17470  -0.14340  0.5708
0.400   1.88750 -0.37820  -0.70580  0.09960  -0.00589  -0.58770  -0.24420  -0.21890  0.5697
0.500   2.03760 -0.79590  -0.69730  0.11470  -0.00565  -0.59990  -0.48670  -0.29690  0.5739
0.750   1.93060 -0.80280  -0.74510  0.11220  -0.00503  -0.59460  -0.50120  -0.34990  0.5876
1.000   1.60380 -0.47800  -0.86950  0.07320  -0.00569  -0.41590   0.06360  -0.33730  0.6269
1.4993  0.47740  0.90960  -1.02440  0.11060  -0.00652  -0.19000   1.09610  -0.10660  0.7517
2.000  -0.25810  1.37770  -1.01000  0.10310  -0.00539  -0.27340   1.50330  -0.04530  0.8036
3.0003 -0.96360  1.14690  -0.88530  0.10380  -0.00478  -0.40420   1.54130  -0.11020  0.8219
4.000  -1.46140  1.07950  -0.80490  0.10960  -0.00395  -0.46040   1.41960  -0.14700  0.8212
5.000  -1.61160  0.74860  -0.78100  0.09650  -0.00307  -0.46490   1.24090  -0.22170  0.8240
7.5019 -2.35310  0.35190  -0.64340  0.09590  -0.00138  -0.68260   0.92880  -0.31230  0.7957
10.000 -3.26140  0.69730  -0.62760  0.12920  -0.00155  -0.61980   1.01050  -0.24550  0.7602
""")

[docs]class SomervilleEtAl2009YilgarnCraton(SomervilleEtAl2009NonCratonic):
"""
Implements GMPE developed by P. Somerville, R. Graves, N. Collins, S. G.
Song, S. Ni, and P. Cummins for Yilgarn Craton published in "Source
and Ground Motion Models for Australian Earthquakes", Report to Geoscience
Australia (2009). Document available at:
http://www.ga.gov.au/cedda/publications/193?yp=2009

Extends
:class:`openquake.hazardlib.gsim.somerville_2009.SomervilleEtAl2009NonCratonic`
because the same functional form is used, only the coefficents differ.
"""

#: Coefficients taken from table 4
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT     c1        c2        c3       c4        c5        c6        c7        c8       sigma
pgv     5.23440   1.58530  -1.01540  0.21400  -0.00341  -0.91610   1.12980   0.14810  0.6606
pga     1.54560   1.45650  -1.11510  0.16640  -0.00567  -1.04900   1.05530   0.20000  0.5513
0.010   1.55510   1.46380  -1.11460  0.16620  -0.00568  -1.04840   1.05850   0.20140  0.5512
0.020   2.33800   1.38060  -1.22970  0.18010  -0.00467  -1.39850   0.95990   0.20130  0.5510
0.030   2.48090   1.37540  -1.17620  0.17120  -0.00542  -1.38720   0.96930   0.19280  0.5508
0.040   2.31450   1.60250  -1.12600  0.17150  -0.00629  -1.27910   1.07040   0.23560  0.5509
0.050   2.26860   1.55840  -1.07340  0.14710  -0.00709  -1.08910   1.10750   0.20670  0.5510
0.075   1.97070   1.68030  -1.01540  0.14560  -0.00737  -0.91930   1.18290   0.22170  0.5514
0.100   1.71030   1.75070  -0.99330  0.13820  -0.00746  -0.78140   1.29390   0.23790  0.5529
0.150   1.52310   1.69160  -0.96310  0.13330  -0.00713  -0.67330   1.22430   0.21020  0.5544
0.200   1.36830   1.57940  -0.94720  0.13640  -0.00677  -0.62690   1.17760   0.18950  0.5558
0.250   1.40180   1.28940  -0.94410  0.14360  -0.00617  -0.67070   1.05610   0.14590  0.5583
0.3003  1.45000   1.04630  -0.94880  0.14760  -0.00581  -0.68700   0.94040   0.11040  0.5602
0.400   1.44150   0.92820  -0.91830  0.11320  -0.00576  -0.59520   0.86280   0.04060  0.5614
0.500   1.40380   0.69160  -0.91010  0.13480  -0.00557  -0.62390   0.71230   0.00620  0.5636
0.750   1.50840   0.75800  -0.99010  0.11260  -0.00458  -0.69040   0.68590  -0.05630  0.5878
1.000   2.10630   0.38180  -1.08680  0.07950  -0.00406  -0.90340   0.61850  -0.18250  0.6817
1.4993  2.55790  -0.84270  -0.81810  0.07650  -0.00220  -1.35320  -0.25440  -0.46660  0.8514
2.000   2.39600  -1.39950  -0.70440  0.06770  -0.00366  -0.90860  -0.64320  -0.59600  0.8646
3.0003  0.96040  -0.46120  -0.70450  0.06450  -0.00429  -0.51190  -0.16430  -0.46310  0.8424
4.000   0.12190  -0.06980  -0.75910  0.08490  -0.00374  -0.41450   0.12350  -0.39250  0.8225
5.000  -0.84240   0.53160  -0.79600  0.10330  -0.00180  -0.62130   0.53680  -0.27570  0.8088
7.5019 -1.92260   0.63760  -0.81900  0.14550  -0.00066  -0.75740   0.69020  -0.23290  0.7808
10.000 -2.60330   0.59060  -0.80940  0.16090  -0.00106  -0.68550   0.70350  -0.22910  0.7624
""")
```