Source code for openquake.hazardlib.gsim.travasarou_2003

# -*- coding: utf-8 -*-
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"""
Module exports :class:`Travasarou2003`,
"""
import numpy as np

from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import IA


def _get_stddevs(ctx, arias):
    """
    Return standard deviations as defined in table 1, p. 200.
    """
    # Magnitude dependent inter-event term (Eq. 13)
    tau = 0.611 - 0.047 * (ctx.mag - 4.7)
    tau[ctx.mag < 4.7] = 0.611
    tau[ctx.mag > 7.6] = 0.475

    # Retrieve site-class dependent sigma
    sigma1, sigma2 = _get_intra_event_sigmas(ctx)
    sigma = np.copy(sigma1)

    # Implements the nonlinear intra-event sigma (Eq. 14)
    idx = arias >= 0.125
    sigma[idx] = sigma2[idx]
    idx = np.logical_and(arias > 0.013, arias < 0.125)
    sigma[idx] = sigma1[idx] - 0.106 * np.log(arias[idx] / 0.0132)
    sigma_total = np.sqrt(tau ** 2. + sigma ** 2.)
    return [sigma_total, tau, sigma]


def _get_intra_event_sigmas(ctx):
    """
    The intra-event term nonlinear and dependent on both the site class
    and the expected ground motion. In this case the sigma coefficients
    are determined from the site class as described below Eq. 14
    """
    sigma1 = 1.18 * np.ones_like(ctx.vs30)
    sigma2 = 0.94 * np.ones_like(ctx.vs30)

    idx1 = np.logical_and(ctx.vs30 >= 360.0, ctx.vs30 < 760.0)
    idx2 = ctx.vs30 < 360.0
    sigma1[idx1] = 1.17
    sigma2[idx1] = 0.93
    sigma1[idx2] = 0.96
    sigma2[idx2] = 0.73
    return sigma1, sigma2


def _compute_magnitude(ctx, C):
    """
    Compute the first term of the equation described on p. 1144:

    ``c1 + c2 * (M - 6) + c3 * log(M / 6)``
    """
    return C['c1'] + C['c2'] * (ctx.mag - 6.0) + (
        C['c3'] * np.log(ctx.mag / 6.0))


def _compute_distance(ctx, C):
    """
    Compute the second term of the equation described on p. 1144:

    `` c4 * np.log(sqrt(R ** 2. + h ** 2.)
    """
    return C["c4"] * np.log(np.sqrt(ctx.rrup ** 2. + C["h"] ** 2.))


def _get_site_amplification(ctx, C):
    """
    Compute the third term of the equation described on p. 1144:

    ``(s11 + s12 * (M - 6)) * Sc + (s21 + s22 * (M - 6)) * Sd`
    """
    Sc, Sd = _get_site_type_dummy_variables(ctx)
    return (C["s11"] + C["s12"] * (ctx.mag - 6.0)) * Sc +\
        (C["s21"] + C["s22"] * (ctx.mag - 6.0)) * Sd


def _get_site_type_dummy_variables(ctx):
    """
    Get site type dummy variables, ``Sc`` (for soft and stiff soil ctx)
    and ``Sd`` (for rock ctx).
    """
    Sc = np.zeros_like(ctx.vs30)
    Sd = np.zeros_like(ctx.vs30)
    # Soft soil; Vs30 < 360 m/s. Page 199.
    Sd[ctx.vs30 < 360.0] = 1.
    # Stiff soil 360 <= Vs30 < 760
    Sc[np.logical_and(ctx.vs30 >= 360.0, ctx.vs30 < 760.0)] = 1.
    return Sc, Sd


def _get_mechanism(ctx, C):
    """
    Compute the fourth term of the equation described on p. 199:

    ``f1 * Fn + f2 * Fr``
    """
    Fn, Fr = _get_fault_type_dummy_variables(ctx)
    return (C['f1'] * Fn) + (C['f2'] * Fr)


def _get_fault_type_dummy_variables(ctx):
    """
    The original classification considers four style of faulting categories
    (normal, strike-slip, reverse-oblique and reverse).
    """
    Fn, Fr = np.zeros_like(ctx.rake), np.zeros_like(ctx.rake)
    Fn[(ctx.rake >= -112.5) & (ctx.rake <= -67.5)] = 1.  # normal
    Fr[(ctx.rake >= 22.5) & (ctx.rake <= 157.5)] = 1.
    # joins both the reverse and reverse-oblique categories
    return Fn, Fr


[docs]class TravasarouEtAl2003(GMPE): """ Implements the ground motion prediction equation for Arias Intensity given by Travasarou et al., (2003): Travasarou, T., Bray, J. D. and Abrahamson, N. A. (2003) "Emprical Attenuation Relationship for Arias Intensity", Earthquake Engineering and Structural Dynamics, 32: 1133 - 1155 Ground motion records are generally taken from active shallow crustal regions """ #: Supported tectonic region type is 'active shallow crust' DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Set of :mod:`intensity measure types <openquake.hazardlib.imt>` #: this GSIM can calculate. A set should contain classes from module #: :mod:`openquake.hazardlib.imt`. DEFINED_FOR_INTENSITY_MEASURE_TYPES = {IA} #: Supported intensity measure component is actually the arithmetic mean of #: two horizontal components - we find this to be equivalent to #: :attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL` DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types are inter-event, intra-event #: and total, see equations 13 - 15 DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: Required site parameter is only Vs30 (used to distinguish rock #: and stiff and soft soil). REQUIRES_SITES_PARAMETERS = {'vs30'} #: Required rupture parameters are magnitude and rake (eq. 1, page 199). REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'} #: Required distance measure is RRup (eq. 1, page 199). REQUIRES_DISTANCES = {'rrup'} #: No independent tests - verification against paper non_verified = True
[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] # Implements mean model (equation 12) mean[m] = (_compute_magnitude(ctx, C) + _compute_distance(ctx, C) + _get_site_amplification(ctx, C) + _get_mechanism(ctx, C)) sig[m], tau[m], phi[m] = _get_stddevs(ctx, np.exp(mean[m]))
#: For Ia, coefficients are taken from table 3 COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT c1 c2 c3 c4 h s11 s12 s21 s22 f1 f2 ia 2.800 -1.981 20.72 -1.703 8.78 0.454 0.101 0.479 0.334 -0.166 0.512 """)