Source code for openquake.hazardlib.gsim.skarlatoudis_2013

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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"""
Module exports :class:`SkarlatoudisEtAlSSlab2013`.
"""
import numpy as np
from scipy.constants import g

from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA


def _compute_distance(ctx, C):
    """
    equation 3 pag 1960:

    ``c31 * logR + c32 * (R-Rref)``
    """
    rref = 1.0
    c31 = -1.7
    return (c31 * np.log10(ctx.rhypo) + C['c32'] * (ctx.rhypo - rref))


def _compute_magnitude(ctx, C):
    """
    equation 3 pag 1960:

    c1 + c2(M-5.5)
    """
    m_h = 5.5
    return C['c1'] + (C['c2'] * (ctx.mag - m_h))


def _get_site_amplification(ctx, C):
    """
    Compute the fourth term of the equation 3:
    The functional form Fs in Eq. (1) represents the site amplification and
    it is given by FS = c61*S + c62*SS , where c61 and c62 are the
    coefficients to be determined through the regression analysis,
    while S and SS are dummy variables used to denote NEHRP site category
    C and D respectively
    Coefficents for categories A and B are set to zero
    """
    S, SS = _get_site_type_dummy_variables(ctx)

    return (C['c61'] * S) + (C['c62'] * SS)


def _get_site_type_dummy_variables(ctx):
    """
    Get site type dummy variables, three different site classes,
    based on the shear wave velocity intervals in the uppermost 30 m, Vs30,
    according to the NEHRP:
    class A-B: Vs30 > 760 m/s
    class C: Vs30 = 360 − 760 m/s
    class D: Vs30 < 360 m/s

    """
    S = np.zeros(len(ctx.vs30))
    SS = np.zeros(len(ctx.vs30))

    # Class C; 180 m/s <= Vs30 <= 360 m/s.
    idx = (ctx.vs30 < 360.0)
    SS[idx] = 1.0
    # Class B; 360 m/s <= Vs30 <= 760 m/s. (NEHRP)
    idx = (ctx.vs30 >= 360.0) & (ctx.vs30 < 760)
    S[idx] = 1.0

    return S, SS


def _compute_forearc_backarc_term(C, ctx):
    """
    Compute back-arc term of Equation 3

    """
    # flag 1 (R < 335 & R >= 205)
    flag1 = np.zeros(len(ctx.rhypo))
    ind1 = np.logical_and((ctx.rhypo < 335), (ctx.rhypo >= 205))
    flag1[ind1] = 1.0
    # flag 2 (R >= 335)
    flag2 = np.zeros(len(ctx.rhypo))
    ind2 = (ctx.rhypo >= 335)
    flag2[ind2] = 1.0
    # flag 3 (R < 240 & R >= 140)
    flag3 = np.zeros(len(ctx.rhypo))
    ind3 = np.logical_and((ctx.rhypo < 240), (ctx.rhypo >= 140))
    flag3[ind3] = 1.0
    # flag 4 (R >= 240)
    flag4 = np.zeros(len(ctx.rhypo))
    ind4 = (ctx.rhypo >= 240)
    flag4[ind4] = 1.0

    A = flag1 * ((205 - ctx.rhypo)/150) + flag2
    B = flag3 * ((140 - ctx.rhypo)/100) + flag4
    if (ctx.hypo_depth < 80):
        FHR = A
    else:
        FHR = B

    H0 = 100
    # Heaviside function
    if (ctx.hypo_depth >= H0):
        H = 1
    else:
        H = 0

    # ARC = 0 for back-arc - ARC = 1 for forearc
    ARC = np.zeros(len(ctx.backarc))
    idxarc = (ctx.backarc == 1)
    ARC[idxarc] = 1.0

    return ((C['c41'] * (1 - ARC) * H) + (C['c42'] * (1 - ARC) * H * FHR) +
            (C['c51'] * ARC * H) + (C['c52'] * ARC * H * FHR))


[docs]class SkarlatoudisEtAlSSlab2013(GMPE): """ Implements GMPEs developed by A.A.Skarlatoudis, C.B.Papazachos, B.N.Margaris, C.Ventouzi, I.Kalogeras and EGELADOS group published as "Ground-Motion Prediction Equations of Intermediate-Depth Earthquakes in the Hellenic Arc, Southern Aegean Subduction Area“, Bull Seism Soc Am, DOI 10.1785/0120120265 SA are given up to 4 s. The regressions are developed considering the RotD50 (Boore, 2010) of the as-recorded horizontal components """ #: Supported tectonic region type is ‘subduction intraslab’ because the #: equations have been derived from data from Hellenic Arc events, as #: explained in the 'Introduction'. DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB #: 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 = {PGA, PGV, SA} #: Supported intensity measure component is the RotD50 of two #: horizontal components DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50 #: Supported standard deviation types are inter-event, intra-event #: and total, page 1961 DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: Required site parameter is Vs30 and backarc flag REQUIRES_SITES_PARAMETERS = {'vs30', 'backarc'} #: Required rupture parameters are magnitude and hypocentral depth REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'} #: Required distance measure is Rhypo. REQUIRES_DISTANCES = {'rhypo'}
[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] imean = (_compute_magnitude(ctx, C) + _compute_distance(ctx, C) + _get_site_amplification(ctx, C) + _compute_forearc_backarc_term(C, ctx)) stp = np.array([C['epsilon'], C['tau'], C['sigma']]) # Convert units to g, # but only for PGA and SA (not PGV) if imt.string.startswith(("SA", "PGA")): mean[m] = np.log((10.0 ** (imean - 2.0)) / g) else: # PGV mean[m] = np.log(10.0 ** imean) # Return stddevs in terms of natural log scaling sig[m], tau[m], phi[m] = np.log(10.0 ** stp)
# mean_LogNaturale = np.log((10 ** mean) * 1e-2 / g) #: Coefficients from SA from Table 1 #: Coefficients from PGA e PGV from Table 5 COEFFS = CoeffsTable(sa_damping=5, table=""" IMT c1 c2 c32 c41 c42 c51 c52 c61 c62 sigma tau epsilon pga 4.229 0.877 -0.00206 -0.481 -0.152 0.425 0.303 0.267 0.491 0.352 0.112 0.369 pgv 2.965 1.069 -0.00178 -0.264 0.018 0.390 0.333 0.408 0.599 0.315 0.144 0.346 0.010 4.235 0.876 -0.00206 -0.482 -0.153 0.425 0.304 0.265 0.488 0.353 0.111 0.370 0.025 4.119 0.877 -0.00202 -0.490 -0.140 0.415 0.326 0.301 0.511 0.352 0.103 0.367 0.050 4.320 0.863 -0.00212 -0.483 -0.178 0.410 0.286 0.245 0.475 0.376 0.095 0.388 0.100 4.565 0.867 -0.00244 -0.515 -0.185 0.452 0.371 0.234 0.442 0.404 0.066 0.410 0.200 4.613 0.842 -0.00199 -0.596 -0.221 0.396 0.291 0.289 0.469 0.379 0.154 0.409 0.400 4.463 0.926 -0.00190 -0.427 -0.110 0.459 0.295 0.298 0.516 0.322 0.141 0.351 1.000 3.952 1.102 -0.00178 -0.199 0.112 0.316 0.442 0.371 0.512 0.305 0.201 0.365 2.000 3.281 1.260 -0.00106 -0.136 0.055 0.196 0.352 0.408 0.578 0.277 0.203 0.343 4.000 2.588 1.384 -0.00039 -0.179 -0.046 0.113 0.189 0.264 0.475 0.278 0.176 0.329 """)
[docs]class SkarlatoudisEtAlSSlab2013_scaled(SkarlatoudisEtAlSSlab2013): """ Implements GMPEs developed by A.A.Skarlatoudis, C.B.Papazachos, B.N.Margaris, C.Ventouzi, I.Kalogeras and EGELADOS group published as "Ground-Motion Prediction Equations of Intermediate-Depth Earthquakes in the Hellenic Arc, Southern Aegean Subduction Area“, Bull Seism Soc Am, DOI 10.1785/0120120265 Application of a scaling factor that converts the prediction of SkarlatoudisEtAlSSlab2013 to the corresponding prediction for the Maximum value. """ COEFFS = CoeffsTable(sa_damping=5, table=""" IMT c1 c2 c32 c41 c42 c51 c52 c61 c62 sigma tau epsilon pga 4.269325379 0.877 -0.00206 -0.481 -0.152 0.425 0.303 0.267 0.491 0.352 0.112 0.369 0.05 4.358898212 0.863 -0.00212 -0.483 -0.178 0.410 0.286 0.245 0.475 0.376 0.095 0.388 0.1 4.60851946 0.867 -0.00244 -0.515 -0.185 0.452 0.371 0.234 0.442 0.404 0.066 0.410 0.15 4.634792233 0.855 -0.00222 -0.556 -0.203 0.424 0.331 0.262 0.456 0.392 0.110 0.410 0.2 4.66206289 0.842 -0.00199 -0.596 -0.221 0.396 0.291 0.289 0.469 0.379 0.154 0.409 0.3 4.59000098 0.884 -0.00195 -0.512 -0.166 0.428 0.293 0.294 0.493 0.351 0.148 0.380 0.4 4.5183401 0.926 -0.00190 -0.427 -0.110 0.459 0.295 0.298 0.516 0.322 0.141 0.351 0.5 4.431948234 0.955 -0.00188 -0.389 -0.073 0.435 0.320 0.310 0.515 0.319 0.151 0.353 0.75 4.22140226 1.029 -0.00183 -0.294 0.020 0.376 0.381 0.341 0.514 0.312 0.176 0.359 1 4.005961507 1.102 -0.00178 -0.199 0.112 0.316 0.442 0.371 0.512 0.305 0.201 0.365 2 3.336034124 1.260 -0.00106 -0.136 0.055 0.196 0.352 0.408 0.578 0.277 0.203 0.343 3 2.99174758 1.322 -0.00073 -0.158 0.005 0.155 0.271 0.336 0.527 0.278 0.190 0.336 4 2.647374059 1.384 -0.00039 -0.179 -0.046 0.113 0.189 0.264 0.475 0.278 0.176 0.329 pgv 3.008558747 1.069 -0.00178 -0.264 0.018 0.390 0.333 0.408 0.599 0.315 0.144 0.346 """)