Source code for openquake.hazardlib.gsim.idriss_2014

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
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#
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"""
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 """)