# -*- 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:`BooreEtAl1997GeometricMean`,
:class:'BooreEtAl1997GeometricMeanUnspecified'
:class:'BooreEtAl1997ArbitraryHorizontal' and
:class:'BooreEtAl1997ArbitraryHorizontalUnspecfied'
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
[docs]class BooreEtAl1997GeometricMean(GMPE):
"""
Implements GMPE developed by David M. Boore and William B. Joyner and
Thomas E. Fumal (1997). "Equations for Estimating Horizontal Response
Spectra and Peak Acceleration form Western North American Earthquakes:
A Summary of Recent Work". Seismological Research Letters. 68(1). 128 - 153
"""
#: Supported tectonic region type is active shallow crust, see
#: paragraph 'Introduction', page 99.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: peak ground velocity and peak ground acceleration, see table 3
#: pag. 110
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is geometric mean
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types are inter-event, intra-event
#: and total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: Required site parameters is Vs30.
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude, and rake.
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'rake'))
#: Required distance measure is Rjb.
REQUIRES_DISTANCES = set(('rjb', ))
[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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
mean = (self._compute_style_of_faulting_term(rup, C) +
self._compute_magnitude_scaling(rup.mag, C) +
self._compute_distance_scaling(dists.rjb, C) +
self._compute_site_term(sites.vs30, C))
stddevs = self._get_stddevs(C, stddev_types, num_sites=len(sites.vs30))
return mean, stddevs
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return standard deviations using Page 142 (Eq 4 - 5)
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigtot = np.sqrt(((C['sigma_e'] * np.ones(num_sites)) ** 2.) +
(C['sigma1'] * np.ones(num_sites)) ** 2.)
stddevs.append(sigtot)
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(C['sigma1'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['sigma_e'] + np.zeros(num_sites))
return stddevs
def _compute_distance_scaling(self, rjb, C):
"""
Compute distance-scaling term (Page 141, Eq 1)
"""
# Calculate distance according to Page 141, Eq 2.
rdist = np.sqrt((rjb ** 2.) + (C['h'] ** 2.))
return C['B5'] * np.log(rdist)
def _compute_magnitude_scaling(self, mag, C):
"""
Compute magnitude-scaling term (Page 141, Eq 1)
"""
dmag = mag - 6.
return (C['B2'] * dmag) + (C['B3'] * (dmag ** 2.))
def _compute_style_of_faulting_term(self, rup, C):
"""
Computes the coefficient to scale for reverse or strike-slip events
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 'Unspecified' case is used to refer to all other rake
angles.
"""
if np.abs(rup.rake) <= 30.0 or (180.0 - np.abs(rup.rake)) <= 30.0:
# strike-slip
return C['B1ss']
elif rup.rake > 30.0 and rup.rake < 150.0:
# reverse
return C['B1rv']
else:
# unspecified (also includes Normal faulting!)
return C['B1all']
def _compute_site_term(self, vs30, C):
"""
Compute site amplification linear term (Page 141, Eq 1)
"""
return C['Bv'] * np.log(vs30 / C['Va'])
#: Coefficient table is constructed from values in Table 8
#: Note that for periods between 0.1 s and 0.18s the inter-event term
#: is originally 0. As this was causing test warnings we have set this
#: to an arbitrarily infinitesimal number
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT B1ss B1rv B1all B2 B3 B5 Bv Va h sigma1 sigma_c sigma_r sigma_e sigma_tot
pga -0.3130 -0.1170 -0.2420 0.5270 0.0000 -0.7780 -0.3710 1396.0000 5.5700 0.4310 0.1600 0.4600 0.1840 0.4950
0.1000 1.0060 1.0870 1.0590 0.7530 -0.2260 -0.9340 -0.2120 1112.0000 6.2700 0.4400 0.1340 0.4600 1E-20 0.4600
0.1100 1.0720 1.1640 1.1300 0.7320 -0.2300 -0.9370 -0.2110 1291.0000 6.6500 0.4370 0.1410 0.4590 1E-20 0.4590
0.1200 1.1090 1.2150 1.1740 0.7210 -0.2330 -0.9390 -0.2150 1452.0000 6.9100 0.4370 0.1480 0.4610 1E-20 0.4610
0.1300 1.1280 1.2460 1.2000 0.7110 -0.2330 -0.9390 -0.2210 1596.0000 7.0800 0.4350 0.1530 0.4610 1E-20 0.4610
0.1400 1.1350 1.2610 1.2080 0.7070 -0.2300 -0.9380 -0.2280 1718.0000 7.1800 0.4350 0.1580 0.4630 1E-20 0.4630
0.1500 1.1280 1.2640 1.2040 0.7020 -0.2280 -0.9370 -0.2380 1820.0000 7.2300 0.4350 0.1630 0.4650 1E-20 0.4650
0.1600 1.1120 1.2570 1.1920 0.7020 -0.2260 -0.9350 -0.2480 1910.0000 7.2400 0.4350 0.1660 0.4660 1E-20 0.4660
0.1700 1.0900 1.2420 1.1730 0.7020 -0.2210 -0.9330 -0.2580 1977.0000 7.2100 0.4350 0.1690 0.4670 1E-20 0.4670
0.1800 1.0630 1.2220 1.1510 0.7050 -0.2160 -0.9300 -0.2700 2037.0000 7.1600 0.4350 0.1730 0.4680 0.0020 0.4680
0.1900 1.0320 1.1980 1.1220 0.7090 -0.2120 -0.9270 -0.2810 2080.0000 7.1000 0.4350 0.1760 0.4690 0.0050 0.4690
0.2000 0.9990 1.1700 1.0890 0.7110 -0.2070 -0.9240 -0.2920 2118.0000 7.0200 0.4350 0.1770 0.4700 0.0090 0.4700
0.2200 0.9250 1.1040 1.0190 0.7210 -0.1980 -0.9180 -0.3150 2158.0000 6.8300 0.4370 0.1820 0.4730 0.0160 0.4740
0.2400 0.8470 1.0330 0.9410 0.7320 -0.1890 -0.9120 -0.3380 2178.0000 6.6200 0.4370 0.1850 0.4750 0.0250 0.4750
0.2600 0.7640 0.9580 0.8610 0.7440 -0.1800 -0.9060 -0.3600 2173.0000 6.3900 0.4370 0.1890 0.4760 0.0320 0.4770
0.2800 0.6810 0.8810 0.7800 0.7580 -0.1680 -0.8990 -0.3810 2158.0000 6.1700 0.4400 0.1920 0.4800 0.0390 0.4820
0.3000 0.5980 0.8030 0.7000 0.7690 -0.1610 -0.8930 -0.4010 2133.0000 5.9400 0.4400 0.1950 0.4810 0.0480 0.4840
0.3200 0.5180 0.7250 0.6190 0.7830 -0.1520 -0.8880 -0.4200 2104.0000 5.7200 0.4420 0.1970 0.4840 0.0550 0.4870
0.3400 0.4390 0.6480 0.5400 0.7940 -0.1430 -0.8820 -0.4380 2070.0000 5.5000 0.4440 0.1990 0.4870 0.0640 0.4910
0.3600 0.3610 0.5700 0.4620 0.8060 -0.1360 -0.8770 -0.4560 2032.0000 5.3000 0.4440 0.2000 0.4870 0.0710 0.4920
0.3800 0.2860 0.4950 0.3850 0.8200 -0.1270 -0.8720 -0.4720 1995.0000 5.1000 0.4470 0.2020 0.4910 0.0780 0.4970
0.4000 0.2120 0.4230 0.3110 0.8310 -0.1200 -0.8670 -0.4870 1954.0000 4.9100 0.4470 0.2040 0.4910 0.0850 0.4990
0.4200 0.1400 0.3520 0.2390 0.8400 -0.1130 -0.8620 -0.5020 1919.0000 4.7400 0.4490 0.2050 0.4940 0.0920 0.5020
0.4400 0.0730 0.2820 0.1690 0.8520 -0.1080 -0.8580 -0.5160 1884.0000 4.5700 0.4490 0.2060 0.4940 0.0990 0.5040
0.4600 0.0050 0.2170 0.1020 0.8630 -0.1010 -0.8540 -0.5290 1849.0000 4.4100 0.4510 0.2090 0.4970 0.1040 0.5080
0.4800 -0.0580 0.1510 0.0360 0.8730 -0.0970 -0.8500 -0.5410 1816.0000 4.2600 0.4510 0.2100 0.4970 0.1110 0.5100
0.5000 -0.1220 0.0870 -0.0250 0.8840 -0.0900 -0.8460 -0.5530 1782.0000 4.1300 0.4540 0.2110 0.5010 0.1150 0.5140
0.5500 -0.2680 -0.0630 -0.1760 0.9070 -0.0780 -0.8370 -0.5790 1710.0000 3.8200 0.4560 0.2140 0.5040 0.1290 0.5200
0.6000 -0.4010 -0.2030 -0.3140 0.9280 -0.0690 -0.8300 -0.6020 1644.0000 3.5700 0.4580 0.2160 0.5060 0.1430 0.5260
0.6500 -0.5230 -0.3310 -0.4400 0.9460 -0.0600 -0.8230 -0.6220 1592.0000 3.3600 0.4610 0.2180 0.5100 0.1540 0.5330
0.7000 -0.6340 -0.4520 -0.5550 0.9620 -0.0530 -0.8180 -0.6390 1545.0000 3.2000 0.4630 0.2200 0.5130 0.1660 0.5390
0.7500 -0.7370 -0.5620 -0.6610 0.9790 -0.0460 -0.8130 -0.6530 1507.0000 3.0700 0.4650 0.2210 0.5150 0.1750 0.5440
0.8000 -0.8290 -0.6660 -0.7600 0.9920 -0.0410 -0.8090 -0.6660 1476.0000 2.9800 0.4670 0.2230 0.5180 0.1840 0.5490
0.8500 -0.9150 -0.7610 -0.8510 1.0060 -0.0370 -0.8050 -0.6760 1452.0000 2.9200 0.4670 0.2260 0.5190 0.1910 0.5530
0.9000 -0.9930 -0.8480 -0.9330 1.0180 -0.0350 -0.8020 -0.6850 1432.0000 2.8900 0.4700 0.2280 0.5220 0.2000 0.5590
0.9500 -1.0660 -0.9320 -1.0100 1.0270 -0.0320 -0.8000 -0.6920 1416.0000 2.8800 0.4720 0.2300 0.5250 0.2070 0.5640
1.0000 -1.1330 -1.0090 -1.0800 1.0360 -0.0320 -0.7980 -0.6980 1406.0000 2.9000 0.4740 0.2300 0.5270 0.2140 0.5690
1.1000 -1.2490 -1.1450 -1.2080 1.0520 -0.0300 -0.7950 -0.7060 1396.0000 2.9900 0.4770 0.2330 0.5310 0.2260 0.5770
1.2000 -1.3450 -1.2650 -1.3150 1.0640 -0.0320 -0.7940 -0.7100 1400.0000 3.1400 0.4790 0.2360 0.5340 0.2350 0.5830
1.3000 -1.4280 -1.3700 -1.4070 1.0730 -0.0350 -0.7930 -0.7110 1416.0000 3.3600 0.4810 0.2390 0.5370 0.2440 0.5900
1.4000 -1.4950 -1.4600 -1.4830 1.0800 -0.0390 -0.7940 -0.7090 1442.0000 3.6200 0.4840 0.2410 0.5410 0.2510 0.5960
1.5000 -1.5520 -1.5380 -1.5500 1.0850 -0.0440 -0.7960 -0.7040 1479.0000 3.9200 0.4860 0.2440 0.5440 0.2560 0.6010
1.6000 -1.5980 -1.6080 -1.6050 1.0870 -0.0510 -0.7980 -0.6970 1524.0000 4.2600 0.4880 0.2460 0.5460 0.2620 0.6060
1.7000 -1.6340 -1.6680 -1.6520 1.0890 -0.0580 -0.8010 -0.6890 1581.0000 4.6200 0.4900 0.2490 0.5500 0.2670 0.6110
1.8000 -1.6630 -1.7180 -1.6890 1.0870 -0.0670 -0.8040 -0.6790 1644.0000 5.0100 0.4930 0.2510 0.5530 0.2690 0.6150
1.9000 -1.6850 -1.7630 -1.7200 1.0870 -0.0740 -0.8080 -0.6670 1714.0000 5.4200 0.4930 0.2540 0.5550 0.2740 0.6190
2.0000 -1.6990 -1.8010 -1.7430 1.0850 -0.0850 -0.8120 -0.6550 1795.0000 5.8500 0.4950 0.2560 0.5570 0.2760 0.6220
""")
[docs]class BooreEtAl1997GeometricMeanUnspecified(BooreEtAl1997GeometricMean):
"""
Where the faulting mechanism need not be specified it is preferable to use
this instance of the Boore et al (1997) GMPE, which omits the need for
rake to be defined.
"""
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag',))
def _compute_style_of_faulting_term(self, rup, C):
"""
Returns only the coefficients for the 'B1all' type
"""
return C['B1all']
[docs]class BooreEtAl1997ArbitraryHorizontal(BooreEtAl1997GeometricMean):
"""
Returns the ground motion values for the arbitrary horizontal component,
rather than the geometric mean.
This version includes the corrected intra-event terms, as defined in
an erratum to the original paper:
Boore, DM (2005). "Erratum: Equations for Estimating
Horizontal Response Spectra and Peak Acceleration from Western North
American Earthquakes: A Summary of Recent Work." Seismological Research
Letters, 76(3), 368-369
"""
#: Supported intensity measure component is the arbitrary horizontal
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return standard deviations as defined in table 8, pag 121.
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(C['sigma_tot'] * np.ones(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(C['sigma_r'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['sigma_e'] + np.zeros(num_sites))
return stddevs
[docs]class BooreEtAl1997ArbitraryHorizontalUnspecified(
BooreEtAl1997ArbitraryHorizontal):
"""
As for the :class:'BooreEtAl1997Arbitrary', here defined for the case
when the style of faulting is not specified
"""
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag',))
def _compute_style_of_faulting_term(self, rup, C):
"""
Returns only the coefficients for the 'B1all' type
"""
return C['B1all']