Source code for openquake.hazardlib.gsim.dowrickrhoades_2005

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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"""
Module exports :class:`DowrickRhoades2005Asc`,:class:`DowrickRhoades2005SInter`
:class:`DowrickRhoades2005SSlab`, and :class:`DowrickRhoades2005Volc`.
"""
import numpy as np

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


def _compute_mean(C, mag, rrup, hypo_depth, delta_R, delta_S,
                  delta_V, delta_I, vs30):

    """
    Compute MMI Intensity Value as per Equation in Table 5 and
    Table 7 pag 198.
    """
    # mean is calculated for all the 4 classes using the same equation.
    # For DowrickRhoades2005SSlab, the coefficients which don't appear in
    # Model 3 equationare assigned to zero

    mean = (C['A1'] + (C['A2'] + C['A2R'] * delta_R + C['A2V'] * delta_V) *
            mag + (C['A3'] + C['A3S'] * delta_S + C['A3V'] * delta_V) *
            np.log10(np.power((rrup**3 + C['d']**3), 1.0 / 3.0)) +
            C['A4'] * hypo_depth + C['A5'] * delta_I)

    # Get S site class term
    S = _get_site_class(vs30, mean)

    # Add S amplification term to mean value
    mean = mean + S

    return mean


_get_deltas = CallableDict()


@_get_deltas.add(const.TRT.ACTIVE_SHALLOW_CRUST)
def _get_deltas_1(trt, rake):
    """
    Return the value of deltas (delta_R, delta_S, delta_V, delta_I),
    as defined in "Table 5: Model 1" pag 198
    """
    # delta_R = 1 for reverse focal mechanism (45<rake<135)
    # and for interface events, 0 for all other events
    # delta_S = 1 for Strike-slip focal mechanisms (0<=rake<=45) or
    # (135<=rake<=180) or (-45<=rake<=0), 0 for all other events
    # delta_V = 1 for TVZ events, 0 for all other events
    # delta_I = 1 for interface events, 0 for all other events

    # All deltas = 0 for Model 3: Deep Region, pag 198

    delta_R, delta_S = 0, 0
    delta_V, delta_I = 0, 0

    if rake > 45.0 and rake < 135.0:
        delta_R = 1

    if (rake >= 0.0 and rake <= 45.0) or \
       (rake >= 135 and rake <= 180.0) or \
       (rake >= -180.0 and rake <= -135.0) or \
       (rake >= -45.0 and rake < 0.0):
        delta_S = 1

    return delta_R, delta_S, delta_V, delta_I


@_get_deltas.add(const.TRT.SUBDUCTION_INTERFACE)
def _get_deltas_2(trt, rake):
    """
    Return the value of deltas (delta_R, delta_S, delta_V, delta_I),
    as defined in "Table 5: Model 1" pag 198
    """
    # delta_I = 1, delta_R = 1 for interface events
    # delta_S = 0, delta_V = 0

    delta_R, delta_S = 1, 0
    delta_V, delta_I = 0, 1

    return delta_R, delta_S, delta_V, delta_I


@_get_deltas.add(const.TRT.SUBDUCTION_INTRASLAB)
def _get_deltas_3(trt, rake):
    """
    Return the value of deltas (delta_R, delta_S, delta_V, delta_I),
    as defined in "Table 5: Model 1" pag 198
    """
    # All deltas = 0 for DowrickRhoades2005SSlab Model 3: Deep Region,
    # pag 198

    delta_R, delta_S = 0, 0
    delta_V, delta_I = 0, 0

    return delta_R, delta_S, delta_V, delta_I


@_get_deltas.add(const.TRT.VOLCANIC)
def _get_deltas_4(trt, rake):
    """
    Return the value of deltas (delta_R, delta_S, delta_V, delta_I),
    as defined in "Table 5: Model 1" pag 198
    """
    # delta_V = 1 for TVZ events, 0 for all other events
    # delta_R =0, delta_S = 0, delta_I = 0

    delta_R, delta_S = 0, 0
    delta_V, delta_I = 1, 0

    return delta_R, delta_S, delta_V, delta_I


def _get_site_class(vs30, mmi_mean):
    """
    Return site class flag for:
    Class E - Very Soft Soil        vs30 < 180
    Class D - Deep or Soft Soil     vs30 >= 180 and vs30 <= 360
    Class C - Shallow Soil          vs30 > 360 and vs30 <= 760
    Class B - Rock                  vs30 > 760 and vs30 <= 1500
    Class A - Strong Rock           vs30 >= 180 and vs30 <= 360
    The S site class is equal to
        S = c1 if MMI <= 7
        S = c1 - d *(MMI - 7.0) if 7<MMI<9.5
        S = c2 if MMI >= 9.5
    """

    if vs30[0] < 180:
        c1 = 1.0
        c2 = -0.25
        d = 0.5
    elif vs30[0] >= 180 and vs30[0] <= 360:
        c1 = 0.5
        c2 = -0.125
        d = 0.25
    elif vs30[0] > 360 and vs30[0] <= 760:
        c1 = 0.
        c2 = 0.
        d = 0.
    elif vs30[0] > 760 and vs30[0] <= 1500:
        c1 = -0.5
        c2 = 0.125
        d = -0.25
    elif vs30[0] > 1500:
        c1 = -1.0
        c2 = 0.25
        d = -0.5

    S = np.zeros_like(vs30)

    for i in range(vs30.size):
        if mmi_mean[i] <= 7.0:
            S[i] += c1
        elif mmi_mean[i] > 7 and mmi_mean[i] < 9.5:
            S[i] += c1 - d * (mmi_mean[i] - 7.0)
        else:
            S[i] += c2

    return S


def _get_stddevs(C):
    """
    Return total standard deviation as described in paragraph 5.2 pag 200.
    """
    # interevent stddev
    sigma_inter = C['tau']
    # intraevent std
    sigma_intra = C['sigma']
    # equation in section 5.2 page 200
    return [np.sqrt(sigma_intra**2 + sigma_inter**2), sigma_inter, sigma_intra]


[docs]class DowrickRhoades2005Asc(GMPE): """ Implements IPE developed by D.J. Dowrick and D.A. Rhoades published as "Revised models for attenuation of Modified Mercalli Intensity in New Zealand earthquakes", Bulletin of the New Zealand Society for Earthquake Engineering, v.38, no. 4, p. 185-214, December 2005. URL: http://www.nzsee.org.nz/db/Bulletin/Archive/38(4)0185.pdf Last accessed 20 November 2015. This class implements the IPE for Active Shallow Crust for different faulting types. """ #: Supported tectonic region type for base class is 'active shallow crust' DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure type is MMI. DEFINED_FOR_INTENSITY_MEASURE_TYPES = {MMI} #: Supported intensity measure component is the horizontal component DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL #: Supported standard deviation types are Inter, Intra and Total # (see description in paragraph 5.2 page 200 ) DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: The only site parameter is vs30 used to map to site class to distinguish # between rock, stiff soil and soft soil REQUIRES_SITES_PARAMETERS = {'vs30'} #: Required rupture parameters are magnitude, and rake and hypocentral # depth rake is for determining fault style flags. Hypo depth is for # subduction GMPEs REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'hypo_depth'} #: Required distance measure is rrup (paragraphy x, page xx) which is # defined as nearest distance to the source. 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. """ trt = self.DEFINED_FOR_TECTONIC_REGION_TYPE for m, imt in enumerate(imts): C = self.COEFFS[imt] # Deltas for Tectonic Region Type and rake angles delta_R, delta_S, delta_V, delta_I = _get_deltas(trt, ctx.rake) mean[m] = _compute_mean(C, ctx.mag, ctx.rrup, ctx.hypo_depth, delta_R, delta_S, delta_V, delta_I, ctx.vs30) sig[m], tau[m], phi[m] = _get_stddevs(C)
#: Coefficient table (table 5, page 198) COEFFS = CoeffsTable(table="""\ IMT A1 A2 A2R A2V A3 A3S A3V A4 A5 d tau sigma MMI 4.74 1.23 0.042 0.292 -3.613 0.100 -1.76 0.007 -0.42 10.28 0.21 0.38 """)
[docs]class DowrickRhoades2005SInter(DowrickRhoades2005Asc): """ Implements IPE developed by D.J. Dowrick and D.A. Rhoades published as "Revised models for attenuation of Modified Mercalli Intensity in New Zealand earthquakes", Bulletin of the New Zealand Society for Earthquake Engineering, v.38, no. 4, p. 185-214, December 2005. URL: http://www.nzsee.org.nz/db/Bulletin/Archive/38(4)0185.pdf Last accessed 20 November 2015. This class implements the IPE for Subduction Interface events """ DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
[docs]class DowrickRhoades2005SSlab(DowrickRhoades2005Asc): """ Implements IPE developed by D.J. Dowrick and D.A. Rhoades published as "Revised models for attenuation of Modified Mercalli Intensity in New Zealand earthquakes", Bulletin of the New Zealand Society for Earthquake Engineering, v.38, no. 4, p. 185-214, December 2005. URL: http://www.nzsee.org.nz/db/Bulletin/Archive/38(4)0185.pdf Last accessed 20 November 2015. This class implements the IPE for Subduction Slab events """ DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB #: Coefficient table (table 7, page 198) COEFFS = CoeffsTable(table="""\ IMT A1 A2 A2R A2V A3 A3S A3V A4 A5 d tau sigma MMI 3.76 1.48 0.0 0.0 -3.50 0.0 0.0 0.0031 0.0 0.0 0.27 0.42 """)
[docs]class DowrickRhoades2005Volc(DowrickRhoades2005Asc): """ Implements IPE developed by D.J. Dowrick and D.A. Rhoades published as "Revised models for attenuation of Modified Mercalli Intensity in New Zealand earthquakes", Bulletin of the New Zealand Society for Earthquake Engineering, v.38, no. 4, p. 185-214, December 2005. URL: http://www.nzsee.org.nz/db/Bulletin/Archive/38(4)0185.pdf Last accessed 20 November 2015. This class implements the IPE for events with a volcanic source """ DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.VOLCANIC