Source code for openquake.hazardlib.gsim.hong_goda_2007

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (c) 2013-2022 GEM Foundation
#
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"""
module exports :class:`HongGoda2007RotD100`.
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA

CONSTS = {"Vref": 760.0, "v1": 180.0, "v2": 300.0}


def _compute_pga_rock(C_PGA, mag, rjb):
    """
    Returns the PGA (g) on rock, as defined in equation 15
    """
    return np.exp(_compute_linear_magnitude_term(C_PGA, mag) +
                  _compute_simple_distance_term(C_PGA, rjb))


def _compute_linear_magnitude_term(C, mag):
    """
    Computes the linear part of the magnitude term
    """
    return C["b1"] + C["b2"] * (mag - 7.0)


def _compute_nonlinear_magnitude_term(C, mag):
    """
    Computes the non-linear magnitude term
    """
    return _compute_linear_magnitude_term(C, mag) + C["b3"] * (
        (mag - 7.0) ** 2.)


def _compute_simple_distance_term(C, rjb):
    """
    The distance term for the PGA case ignores magnitude (equation 15)
    """
    return C["b4"] * np.log(np.sqrt(rjb ** 2. + C["h"] ** 2.))


def _compute_magnitude_distance_term(C, rjb, mag):
    """
    Returns the magntude dependent distance term
    """
    rval = np.sqrt(rjb ** 2. + C["h"] ** 2.)
    return (C["b4"] + C["b5"] * (mag - 4.5)) * np.log(rval)


def _get_site_amplification(C_AMP, vs30, pga_rock):
    """
    Gets the site amplification term based on equations 7 and 8 of
    Atkinson & Boore (2006)
    """
    # Get nonlinear term
    bnl = _get_bnl(C_AMP, vs30)
    #
    f_nl_coeff = np.log(60.0 / 100.0) * np.ones_like(vs30)
    idx = pga_rock > 60.0
    f_nl_coeff[idx] = np.log(pga_rock[idx] / 100.0)
    return np.log(np.exp(
        C_AMP["blin"] * np.log(vs30 / CONSTS["Vref"]) + bnl * f_nl_coeff))


def _get_bnl(C_AMP, vs30):
    """
    Gets the nonlinear term, given by equation 8 of Atkinson & Boore 2006
    """
    # Default case 8d
    bnl = np.zeros_like(vs30)
    if np.all(vs30 >= CONSTS["Vref"]):
        return bnl
    # Case 8a
    bnl[vs30 < CONSTS["v1"]] = C_AMP["b1sa"]
    # Cade 8b
    idx = np.logical_and(vs30 > CONSTS["v1"],
                         vs30 <= CONSTS["v2"])

    if np.any(idx):
        bnl[idx] = (C_AMP["b1sa"] - C_AMP["b2sa"]) *\
            (np.log(vs30[idx] / CONSTS["v2"]) /
             np.log(CONSTS["v1"] / CONSTS["v2"])) + C_AMP["b2sa"]
    # Case 8c
    idx = np.logical_and(vs30 > CONSTS["v2"],
                         vs30 < CONSTS["Vref"])
    if np.any(idx):
        bnl[idx] = C_AMP["b2sa"] *\
            np.log(vs30[idx] / CONSTS["Vref"]) /\
            np.log(CONSTS["v2"] / CONSTS["Vref"])
    return bnl


def _get_stddevs(C):
    """
    Returns the standard deviations given in Table 2
    """
    return [C["sigtot"], C['sig1'], C['sig2']]


[docs]class HongGoda2007(GMPE): """ Implements GMPE developed for RotD100 ground motion as defined by Hong, H. P. and Goda, K. (2007), "Orientation-Dependent Ground Motion Measure for Seismic Hazard Assessment", Bull. Seism. Soc. Am. 97(5), 1525 - 1538 This is really an experimental GMPE in which the amplification term is taken directly from Atkinson & Boore (2006) rather than constrained by the records themselves. There may exist a possible units issue as the amplification function for AB2006 is in cm/s/s whereas the GMPE here is given in g """ #: The supported tectonic region type is active shallow crust DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: The supported intensity measure types are PGA, PGV, and SA DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA} #: The supported intensity measure component is RotD100 DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD100 #: The supported standard deviations are total, inter and intra event, see #: table 4.a, pages 22-23 DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: The required site parameter is vs30, see equation 1, page 20. REQUIRES_SITES_PARAMETERS = {'vs30'} #: The required rupture parameters are magnitude REQUIRES_RUPTURE_PARAMETERS = {'mag'} #: The required distance parameter is 'Joyner-Boore' distance REQUIRES_DISTANCES = {'rjb'} #: GMPE not tested against independent implementation non_verified = True
[docs] def compute(self, ctx, imts, mean, sig, tau, phi): """ See :meth:`superclass method <.base.GroundShakingIntensityModel.compute>` for spec of input and result values. Implements equation 14 of Hong & Goda (2007) """ C_PGA = self.COEFFS[PGA()] # Gets the PGA on rock - need to convert from g to cm/s/s pga_rock = _compute_pga_rock(C_PGA, ctx.mag, ctx.rjb) * 980.665 for m, imt in enumerate(imts): C = self.COEFFS[imt] C_AMP = self.COEFFS_AMP[imt] # Get the mean ground motion value mean[m] = (_compute_nonlinear_magnitude_term(C, ctx.mag) + _compute_magnitude_distance_term(C, ctx.rjb, ctx.mag) + _get_site_amplification(C_AMP, ctx.vs30, pga_rock)) # Get standard deviations sig[m], tau[m], phi[m] = _get_stddevs(C)
COEFFS = CoeffsTable(sa_damping=5, table="""\ imt b1 b2 b3 b4 b5 h sig1 sig2 sigtot pga 1.365 0.349 0.000 -1.123 0.062 5.9 0.184 0.449 0.485 pgv 5.540 0.931 0.000 -0.866 -0.009 3.8 0.248 0.494 0.553 0.10 2.305 -0.084 -0.054 -1.461 0.167 8.2 0.218 0.467 0.515 0.15 2.605 -0.045 -0.044 -1.514 0.179 8.6 0.218 0.473 0.521 0.20 2.514 0.234 -0.053 -1.204 0.067 8.4 0.166 0.499 0.526 0.25 2.228 0.369 0.000 -1.118 0.057 6.9 0.170 0.495 0.523 0.30 1.762 0.515 0.000 -0.878 0.003 4.7 0.182 0.510 0.541 0.40 1.608 0.577 0.000 -0.898 0.012 4.9 0.234 0.528 0.577 0.50 1.713 0.837 0.000 -0.843 -0.041 6.0 0.216 0.542 0.584 0.60 1.451 0.924 -0.030 -0.755 -0.066 5.0 0.274 0.557 0.621 0.70 1.138 0.740 -0.093 -0.838 -0.014 4.2 0.320 0.581 0.664 0.80 0.781 0.549 -0.182 -0.834 0.005 3.4 0.316 0.591 0.670 0.90 0.763 0.484 -0.197 -0.960 0.052 4.0 0.324 0.594 0.677 1.00 0.763 0.359 -0.270 -1.024 0.067 4.9 0.326 0.593 0.677 1.10 0.827 0.596 -0.333 -0.819 -0.032 4.6 0.346 0.584 0.679 1.20 0.853 0.845 -0.328 -0.689 -0.093 4.3 0.358 0.578 0.680 1.30 0.682 0.921 -0.322 -0.634 -0.108 4.0 0.362 0.576 0.681 1.40 0.540 0.954 -0.303 -0.635 -0.103 3.8 0.362 0.574 0.678 1.50 0.433 1.005 -0.294 -0.617 -0.109 3.7 0.352 0.568 0.668 1.60 0.289 0.988 -0.302 -0.617 -0.103 3.6 0.364 0.566 0.673 1.70 0.102 0.976 -0.301 -0.611 -0.093 3.4 0.378 0.564 0.679 1.80 -0.098 0.965 -0.310 -0.588 -0.088 3.0 0.380 0.560 0.676 1.90 -0.216 0.936 -0.325 -0.601 -0.079 2.9 0.380 0.561 0.677 2.00 -0.379 0.693 -0.308 -0.759 -0.001 2.7 0.364 0.562 0.670 2.20 -0.549 0.643 -0.336 -0.776 0.011 2.5 0.378 0.570 0.684 2.40 -0.663 0.772 -0.325 -0.706 -0.016 2.3 0.402 0.570 0.697 2.60 -0.747 0.909 -0.302 -0.655 -0.039 2.3 0.404 0.575 0.703 2.80 -0.883 1.024 -0.259 -0.630 -0.045 2.2 0.414 0.584 0.716 3.00 -0.955 1.027 -0.265 -0.677 -0.029 2.3 0.420 0.594 0.728 """) COEFFS_AMP = CoeffsTable(sa_damping=5, table="""\ imt blin b1sa b2sa pgv -0.60000 -0.49500 -0.06000 pga -0.36100 -0.64100 -0.14400 0.02500 -0.33000 -0.62400 -0.11500 0.03125 -0.32200 -0.61800 -0.10800 0.04000 -0.31400 -0.60900 -0.10500 0.05000 -0.28600 -0.64300 -0.10500 0.06289 -0.24900 -0.64200 -0.10500 0.07937 -0.23200 -0.63700 -0.11700 0.10000 -0.25000 -0.59500 -0.13200 0.12500 -0.26000 -0.56000 -0.14000 0.15873 -0.28000 -0.52800 -0.18500 0.20000 -0.30600 -0.52100 -0.18500 0.25000 -0.39000 -0.51800 -0.16000 0.31250 -0.44500 -0.51300 -0.13000 0.40000 -0.50000 -0.50800 -0.09500 0.50000 -0.60000 -0.49500 -0.06000 0.62500 -0.67000 -0.48000 -0.03100 0.76923 -0.69000 -0.46500 -0.00200 1.00000 -0.70000 -0.44000 0.00000 1.58730 -0.72600 -0.39500 0.00000 2.00000 -0.73000 -0.37500 0.00000 3.12500 -0.74000 -0.33000 0.00000 4.00000 -0.74500 -0.31000 0.00000 5.00000 -0.75200 -0.30000 0.00000 """)