# The Hazard Library
# Copyright (C) 2015, GEM Foundation
#
# This program 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.
#
# This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports :class:`Idriss2014`,
"""
from __future__ import division
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 Idriss2014(GMPE):
"""
Implements GMPE developed by Idriss 2014 and published as "An NGA-West2
Empirical Model for Estimating the Horizontal Spectral Values Generated
by Shallow Crustal Earthquakes.
(2014, Earthquake Spectra, Volume 30, No. 3, pages 1155 - 1177).
Idriss (2014) defines the GMPE only for the case in which Vs30 >= 450 m/s.
In the present implementation no check is made for the use of this model
for sites with Vs30 < 450 m/s
"""
#: Supported tectonic region type is active shallow crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#:and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
SA
])
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.RotD50`
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: Supported standard deviation types are total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
])
#: 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 Rrup
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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
mean = (self._get_magnitude_scaling_term(C, rup.mag) +
self._get_distance_scaling_term(C, rup.mag, dists.rrup) +
self._get_style_of_faulting_term(C, rup.rake) +
self._get_site_scaling_term(C, sites.vs30))
stddevs = self._get_stddevs(imt,
rup.mag,
len(dists.rrup),
stddev_types)
return mean, stddevs
def _get_magnitude_scaling_term(self, C, mag):
"""
Returns the magnitude scaling term defined in equation 3
"""
if mag < 6.75:
return C["a1_lo"] + C["a2_lo"] * mag + C["a3"] *\
((8.5 - mag) ** 2.0)
else:
return C["a1_hi"] + C["a2_hi"] * mag + C["a3"] *\
((8.5 - mag) ** 2.0)
def _get_distance_scaling_term(self, C, mag, rrup):
"""
Returns the magnitude dependent distance scaling term
"""
if mag < 6.75:
mag_factor = -(C["b1_lo"] + C["b2_lo"] * mag)
else:
mag_factor = -(C["b1_hi"] + C["b2_hi"] * mag)
return mag_factor * np.log(rrup + 10.0) + (C["gamma"] * rrup)
def _get_style_of_faulting_term(self, C, rake):
"""
Only distinction is between reverse faulting events and
normal/strike-slip. Returns the style-of-faulting factor only for
reverse events
"""
if (rake > 30.0) and (rake < 150.0):
return C["phi"]
else:
return 0.0
def _get_site_scaling_term(self, C, vs30):
"""
Returns the site scaling. For sites with Vs30 > 1200 m/s the site
amplification for Vs30 = 1200 is used
"""
site_amp = C["xi"] * np.log(1200.0) * np.ones(len(vs30))
idx = vs30 < 1200.0
site_amp[idx] = C["xi"] * np.log(vs30[idx])
return site_amp
def _get_stddevs(self, imt, mag, n_sites, stddev_types):
"""
The standard error (assumed equivalent to total standard deviation)
is defined as a function of magnitude and period (equation 4,
page 1168). For magnitudes lower than 5.0 the standard deviation is
equal to that for the case in which magnitude is 5.0. For short
periods (T < 0.05), including PGA, the standard deviation is
assumed to be equal to the case in which T = 0.05, whilst for long
periods (T > 3.0) it is assumed to be equal to the case in which
T = 3.0
"""
if mag < 5.0:
stddev_mag = 5.0
else:
stddev_mag = mag
if isinstance(imt, PGA) or (imt.period < 0.05):
total_sigma = 1.18 + 0.035 * np.log(0.05) - 0.06 * stddev_mag
elif imt.period > 3.0:
total_sigma = 1.18 + 0.035 * np.log(3.0) - 0.06 * stddev_mag
else:
total_sigma = 1.18 + 0.035 * np.log(imt.period) - 0.06 * stddev_mag
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(total_sigma + np.zeros(n_sites, dtype=float))
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT a1_lo a2_lo b1_lo b2_lo a1_hi a2_hi b1_hi b2_hi a3 xi gamma phi
pga 7.0887 0.2058 2.9935 -0.2287 9.0138 -0.0794 2.9935 -0.2287 0.0589 -0.8540 -0.0027 0.0800
0.010 7.0887 0.2058 2.9935 -0.2287 9.0138 -0.0794 2.9935 -0.2287 0.0589 -0.8540 -0.0027 0.0800
0.020 7.1157 0.2058 2.9935 -0.2287 9.0408 -0.0794 2.9935 -0.2287 0.0589 -0.8540 -0.0027 0.0800
0.030 7.2087 0.2058 2.9935 -0.2287 9.1338 -0.0794 2.9935 -0.2287 0.0589 -0.8540 -0.0027 0.0800
0.050 6.2638 0.0625 2.8664 -0.2418 7.9837 -0.1923 2.7995 -0.2319 0.0417 -0.6310 -0.0061 0.0800
0.075 5.9051 0.1128 2.9406 -0.2513 7.7560 -0.1614 2.8143 -0.2326 0.0527 -0.5910 -0.0056 0.0800
0.100 7.5791 0.0848 3.0190 -0.2516 9.4252 -0.1887 2.8131 -0.2211 0.0442 -0.7570 -0.0042 0.0800
0.150 8.0190 0.1713 2.7871 -0.2236 9.6242 -0.0665 2.4091 -0.1676 0.0329 -0.9110 -0.0046 0.0800
0.200 9.2812 0.1041 2.8611 -0.2229 11.1300 -0.1698 2.4938 -0.1685 0.0188 -0.9980 -0.0030 0.0800
0.250 9.5804 0.0875 2.8289 -0.2200 11.3629 -0.1766 2.3773 -0.1531 0.0095 -1.0420 -0.0028 0.0800
0.300 9.8912 0.0003 2.8423 -0.2284 11.7818 -0.2798 2.3772 -0.1595 -0.0039 -1.0300 -0.0029 0.0800
0.400 9.5342 0.0027 2.8300 -0.2318 11.6097 -0.3048 2.3413 -0.1594 -0.0133 -1.0190 -0.0028 0.0800
0.500 9.2142 0.0399 2.8560 -0.2337 11.4484 -0.2911 2.3477 -0.1584 -0.0224 -1.0230 -0.0021 0.0800
0.750 8.3517 0.0689 2.7544 -0.2392 10.9065 -0.3097 2.2042 -0.1577 -0.0267 -1.0560 -0.0029 0.0800
1.000 7.0453 0.1600 2.7339 -0.2398 9.8565 -0.2565 2.1493 -0.1532 -0.0198 -1.0090 -0.0032 0.0600
1.500 5.1307 0.2429 2.6800 -0.2417 8.3363 -0.2320 2.0408 -0.1470 -0.0367 -0.8980 -0.0033 0.0400
2.000 3.3610 0.3966 2.6837 -0.2450 6.8656 -0.1226 2.0013 -0.1439 -0.0291 -0.8510 -0.0032 0.0200
3.000 0.1784 0.7560 2.6907 -0.2389 4.1178 0.1724 1.9408 -0.1278 -0.0214 -0.7610 -0.0031 0.0200
4.000 -2.4301 0.9283 2.5782 -0.2514 1.8102 0.3001 1.7763 -0.1326 -0.0240 -0.6750 -0.0051 0.0000
5.000 -4.3570 1.1209 2.5468 -0.2541 0.0977 0.4609 1.7030 -0.1291 -0.0202 -0.6290 -0.0059 0.0000
7.500 -7.8275 1.4016 2.4478 -0.2593 -3.0563 0.6948 1.5212 -0.1220 -0.0219 -0.5310 -0.0057 0.0000
10.00 -9.2857 1.5574 2.3922 -0.2586 -4.4387 0.8393 1.4195 -0.1145 -0.0035 -0.5860 -0.0061 0.0000
""")