Source code for openquake.hazardlib.gsim.allen_2012_ipe

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"""
Module exports :class:'AllenEtAl2012',
                      'AllenEtAl2012Rhypo'
"""
import numpy as np

from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import MMI
from openquake.baselib.general import CallableDict


_compute_distance_term = CallableDict()


@_compute_distance_term.add('rrup')
def _compute_distance_term_rrup(kind, C, rrup, mag):
    """
    Returns the distance scaling term
    """
    exponent_term = (1.0 + C["c3"] * np.exp(mag - 5.)) ** 2.
    return C["c2"] * np.log(np.sqrt(rrup ** 2. + exponent_term))


@_compute_distance_term.add('rhypo')
def _compute_distance_term_rhypo(kind, C, rhypo, mag):
    """
    Returns the distance scaling term
    """
    r_m = C["m1"] + C["m2"] * np.exp(mag - 5.)
    f_r = C["c2"] * np.log(np.sqrt(rhypo ** 2. + r_m ** 2.))
    # For distances greater than 50 km an anelastic term is added
    idx = rhypo > 50.0
    f_r[idx] += C["c4"] * np.log(rhypo[idx] / 50.)
    return f_r


def _compute_magnitude_term(C, mag):
    """
    Returns the magnitude scaling term
    """
    return C["c0"] + C["c1"] * mag


[docs]class AllenEtAl2012(GMPE):
    """
    Implements the Intensity Prediction Equation of Allen, Wald and Worden
    (2012) for Modified Mercalli Intensity in Active Crustal Regions
    Allen, T. I., Wald, D. J. and Worden, C. B. (2012) Intensity attenuation
    in active crustal regions, J. Seismology, 16: 409 - 433

    This class implements the version using rupture distance, neglecting
    site amplification
    """
    #: The GMPE is derived from induced earthquakes
    DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST

    #: Supported intensity measure types are peak ground acceleration
    #: and peak ground velocity
    DEFINED_FOR_INTENSITY_MEASURE_TYPES = {MMI}

    #: Supported intensity measure component is not considered for IPEs, so
    #: we assume equivalent to 'average horizontal'
    DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN

    #: Supported standard deviation types is total.
    DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}

    #: No required site parameters (in the present version)
    REQUIRES_SITES_PARAMETERS = set()

    #: Required rupture parameters are magnitude (ML is used)
    REQUIRES_RUPTURE_PARAMETERS = {'mag'}

    #: Required distance measure is rupture distance
    REQUIRES_DISTANCES = {'rrup'}

[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]
            [dist_type] = self.REQUIRES_DISTANCES
            dist = getattr(ctx, dist_type)
            mean[m] = (_compute_magnitude_term(C, ctx.mag) +
                       _compute_distance_term(dist_type, C, dist, ctx.mag))
            # the total standard deviation, which is a function of distance
            sig[m] = C["s1"] + C["s2"] / (1.0 + (dist / C["s3"]) ** 2.)

    COEFFS = CoeffsTable(sa_damping=5, table="""
    IMT     c0     c1      c2     c3    s1     s2    s3
    mmi  3.950  0.913  -1.107  0.813  0.72   0.23  44.7
    """)


[docs]class AllenEtAl2012Rhypo(AllenEtAl2012):
    """
    Version of the Allen, Wald and Worden (2012) GSIM for hypocentral distance
    """
    #: Required distance measure is hypocentral distance
    REQUIRES_DISTANCES = {'rhypo'}

    COEFFS = CoeffsTable(sa_damping=5, table="""
    IMT     c0     c1      c2   c3     c4      m1      m2     s1     s2    s3
    mmi  2.085  1.428  -1.402  0.0  0.078  -0.209   2.042   0.82   0.37  22.9
    """)