Source code for openquake.hazardlib.gsim.idriss_2014

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2016 GEM Foundation
#
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"""
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 """)