Source code for openquake.hazardlib.gsim.idriss_2014
# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2023 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:`Idriss2014`,
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
def _get_magnitude_scaling_term(C, mag):
"""
Returns the magnitude scaling term defined in equation 3
"""
res = C["a1_hi"] + C["a2_hi"] * mag + C["a3"] * (8.5 - mag) ** 2.0
below = mag < 6.75
res[below] = (C["a1_lo"] + C["a2_lo"] * mag[below] + C["a3"] *
(8.5 - mag[below]) ** 2.0)
return res
def _get_distance_scaling_term(C, mag, rrup):
"""
Returns the magnitude dependent distance scaling term
"""
mag_factor = -(C["b1_hi"] + C["b2_hi"] * mag)
mag_factor[mag < 6.75] = -(C["b1_lo"] + C["b2_lo"] * mag[mag < 6.75])
return mag_factor * np.log(rrup + 10.0) + (C["gamma"] * rrup)
def _get_style_of_faulting_term(C, rake):
"""
Only distinction is between reverse faulting events and
normal/strike-slip. Returns the style-of-faulting factor only for
reverse events
"""
res = np.zeros_like(rake)
res[(rake > 30.) & (rake < 150.)] = C["phi"]
return res
def _get_site_scaling_term(C, vs30):
"""
Returns the site scaling. For ctx 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_stddev(imt, mag):
"""
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
"""
stddev_mag = np.clip(mag, 5.0, None)
if imt.string == "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
return total_sigma
[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 ctx 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 = {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 = {const.StdDev.TOTAL}
#: Required site parameters is Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude, and rake.
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'}
#: Required distance measure is Rrup
REQUIRES_DISTANCES = {'rrup'}
#: The reference Vs30. See paper.
DEFINED_FOR_REFERENCE_VELOCITY = 2000
[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.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
mean[m] = (_get_magnitude_scaling_term(C, ctx.mag) +
_get_distance_scaling_term(C, ctx.mag, ctx.rrup) +
_get_style_of_faulting_term(C, ctx.rake) +
_get_site_scaling_term(C, ctx.vs30))
sig[m] = _get_stddev(imt, ctx.mag)
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
""")
