Source code for openquake.hazardlib.gsim.afshari_stewart_2016

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
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#
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# (at your option) any later version.
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"""
Module exports :class:`AfshariStewart2016`,
               :class:`AfshariStewart2016Japan`
"""
import numpy as np

from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import RSD595, RSD575, RSD2080

CONSTANTS = {"mstar": 6.0,
             "r1": 10.0,
             "r2": 50.0,
             "v1": 600.0,
             "dz1ref": 200.0}

_get_lnmu_z1 = CallableDict()


@_get_lnmu_z1.add("CAL")
def _get_lnmu_z1_1(region, vs30):
    """
    Returns the z1.0 normalisation term for California (equation 11)
    """
    return (-7.15 / 4.) * np.log(
        (vs30 ** 4. + 570.94 ** 4) / (1360.0 ** 4. + 570.94 ** 4.)) -\
        np.log(1000.0)


@_get_lnmu_z1.add("JPN")
def _get_lnmu_z1_2(region, vs30):
    """
    Returns the z1.0 normalisation term for Japan (equation 12)
    """
    return (-5.23 / 2.) * np.log(
        (vs30 ** 2. + 412.39 ** 2) / (1360.0 ** 2. + 412.39 ** 2.)) -\
        np.log(1000.0)


def _get_phi(C, mag):
    """
    Returns the magnitude dependent intra-event standard deviation (phi)
    (equation 15)
    """
    if mag < 5.5:
        return C["phi1"]
    elif mag < 5.75:
        return C["phi1"] + (C["phi2"] - C["phi1"]) * ((mag - 5.5) / 0.25)
    else:
        return C["phi2"]


def _get_sof_terms(C, rake):
    """
    Returns the style-of-faulting scaling parameters
    """
    if rake >= 45.0 and rake <= 135.0:
        # Reverse faulting
        return C["b0R"], C["b1R"]
    elif rake <= -45. and rake >= -135.0:
        # Normal faulting
        return C["b0N"], C["b1N"]
    else:
        # Strike slip
        return C["b0SS"], C["b1SS"]


def _get_tau(C, mag):
    """
    Returns magnitude dependent inter-event standard deviation (tau)
    (equation 14)
    """
    if mag < 6.5:
        return C["tau1"]
    elif mag < 7.:
        return C["tau1"] + (C["tau2"] - C["tau1"]) * ((mag - 6.5) / 0.5)
    else:
        return C["tau2"]


[docs]def get_distance_term(C, rrup): """ Returns the distance scaling term in equation 7 """ f_p = C["c1"] * rrup idx = np.logical_and(rrup > CONSTANTS["r1"], rrup <= CONSTANTS["r2"]) f_p[idx] = (C["c1"] * CONSTANTS["r1"]) +\ C["c2"] * (rrup[idx] - CONSTANTS["r1"]) idx = rrup > CONSTANTS["r2"] f_p[idx] = C["c1"] * CONSTANTS["r1"] +\ C["c2"] * (CONSTANTS["r2"] - CONSTANTS["r1"]) +\ C["c3"] * (rrup[idx] - CONSTANTS["r2"]) return f_p
[docs]def get_magnitude_term(C, ctx): """ Returns the magnitude scaling term in equation 3 """ b0, stress_drop = _get_sof_terms(C, ctx.rake) if ctx.mag <= C["m1"]: return b0 else: # Calculate moment (equation 5) m_0 = 10.0 ** (1.5 * ctx.mag + 16.05) # Get stress-drop scaling (equation 6) if ctx.mag > C["m2"]: stress_drop += (C["b2"] * (C["m2"] - CONSTANTS["mstar"]) + (C["b3"] * (ctx.mag - C["m2"]))) else: stress_drop += (C["b2"] * (ctx.mag - CONSTANTS["mstar"])) stress_drop = np.exp(stress_drop) # Get corner frequency (equation 4) f0 = 4.9 * 1.0E6 * 3.2 * ((stress_drop / m_0) ** (1. / 3.)) return 1. / f0
[docs]def get_site_amplification(region, C, ctx): """ Returns the site amplification term """ # Gets delta normalised z1 dz1 = ctx.z1pt0 - np.exp(_get_lnmu_z1(region, ctx.vs30)) f_s = C["c5"] * dz1 # Calculates site amplification term f_s[dz1 > CONSTANTS["dz1ref"]] = (C["c5"] * CONSTANTS["dz1ref"]) idx = ctx.vs30 > CONSTANTS["v1"] f_s[idx] += (C["c4"] * np.log(CONSTANTS["v1"] / C["vref"])) idx = np.logical_not(idx) f_s[idx] += (C["c4"] * np.log(ctx.vs30[idx] / C["vref"])) return f_s
[docs]def get_stddevs(C, mag): """ Returns the standard deviations """ tau = _get_tau(C, mag) phi = _get_phi(C, mag) return [np.sqrt(tau ** 2. + phi ** 2.), tau, phi]
[docs]class AfshariStewart2016(GMPE): """ Implements the GMPE of Afshari & Stewart (2016) for relative significant duration for 5 - 75 %, 5 - 95 % and 20 - 80 % Arias Intensity. Afshari, K. and Stewart, J. P. (2016) "Physically Parameterized Prediction Equations for Signficant Duration in Active Crustal Regions", Earthquake Spectra, 32(4), 2057 - 2081 """ region = "CAL" #: Supported tectonic region type is active shallow crust DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure types are 5 - 95 % Arias and 5 - 75 % Arias #: significant duration DEFINED_FOR_INTENSITY_MEASURE_TYPES = {RSD595, RSD575, RSD2080} #: Supported intensity measure component is the geometric mean horizontal #: component DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation type is only total, see table 7, page 35 DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: Requires vs30 REQUIRES_SITES_PARAMETERS = {'vs30', 'z1pt0'} #: Required rupture parameters are magnitude and top of rupture depth REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'} #: Required distance measure is closest distance to rupture REQUIRES_DISTANCES = {'rrup'}
[docs] def compute(self, ctx, 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] = (np.log(get_magnitude_term(C, ctx) + get_distance_term(C, ctx.rrup)) + get_site_amplification(self.region, C, ctx)) sig[m], tau[m], phi[m] = get_stddevs(C, ctx.mag)
COEFFS = CoeffsTable(sa_damping=5, table="""\ imt m1 m2 b0N b0R b0SS b0U b1N b1R b1SS b1U b2 b3 c1 c2 c3 c4 c5 vref tau1 tau2 phi1 phi2 rsd575 5.35 7.15 1.555 0.7806 1.2790 1.280 4.992 7.061 5.578 5.576 0.9011 -1.684 0.1159 0.1065 0.0682 -0.2246 0.0006 368.2 0.28 0.25 0.54 0.41 rsd595 5.2 7.40 2.541 1.6120 2.3020 2.182 3.170 4.536 3.467 3.628 0.9443 -3.911 0.3165 0.2539 0.0932 -0.3183 0.0006 369.9 0.25 0.19 0.43 0.35 rsd2080 5.2 7.40 1.409 0.7729 0.8804 0.8822 4.778 6.579 6.188 6.182 0.7414 -3.164 0.0646 0.0865 0.0373 -0.4237 0.0005 369.6 0.30 0.19 0.56 0.45 """)
[docs]class AfshariStewart2016Japan(AfshariStewart2016): """ Adaption of the Afshari & Stewart (2016) GMPE for relative significant duration for the case when the Japan basin model is preferred """ region = "JPN"