Source code for openquake.hazardlib.gsim.akkar_cagnan_2010

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2022 GEM Foundation
#
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"""
Module exports :class:`AkkarCagnan2010`.
"""
import numpy as np
from scipy.constants import g

from openquake.hazardlib.gsim.atkinson_boore_2006 import (
     _get_site_amplification_linear, _get_site_amplification_non_linear)
from openquake.hazardlib.gsim.boore_atkinson_2008 import BooreAtkinson2008
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA

# c1 is the reference magnitude, fixed to 6.5
# see paragraph 'Functional Form', p. 2982
c1 = 6.5


def _compute_faulting_style_term(C, rake):
    """
    Compute and return fifth and sixth terms in equations (1a)
    and (1b), pages 2981 and 2982, respectively.
    """
    Fn = (rake > -135.0) & (rake < -45.0)
    Fr = (rake > 45.0) & (rake < 135.0)
    return C['a8'] * Fn + C['a9'] * Fr


def _compute_linear_magnitude_term(C, mag):
    """
    Compute and return second term in equations (1a)
    and (1b), pages 2981 and 2982, respectively.
    """
    return np.where(mag <= c1, C['a2'] * (mag - c1), C['a3'] * (mag - c1))


def _compute_logarithmic_distance_term(C, mag, rjb):
    """
    Compute and return fourth term in equations (1a)
    and (1b), pages 2981 and 2982, respectively.
    """
    return (C['a5'] + C['a6'] * (mag - c1)) * np.log(
        np.sqrt(rjb ** 2 + C['a7'] ** 2))


def _compute_mean(C, mag, rjb, rake):
    """
    Compute and return mean value without site conditions,
    that is equations (1a) and (1b), p.2981-2982.
    """
    mean = (C['a1'] +
            _compute_linear_magnitude_term(C, mag) +
            _compute_quadratic_magnitude_term(C, mag) +
            _compute_logarithmic_distance_term(C, mag, rjb) +
            _compute_faulting_style_term(C, rake))

    return mean


def _compute_quadratic_magnitude_term(C, mag):
    """
    Compute and return third term in equations (1a)
    and (1b), pages 2981 and 2982, respectively.
    """
    return C['a4'] * (8.5 - mag) ** 2


def _get_stddevs(C):
    """
    Return standard deviations as defined in table 3, p. 2985.
    """
    return [np.sqrt(C['sigma'] ** 2 + C['tau'] ** 2), C['tau'], C['sigma']]


[docs]class AkkarCagnan2010(GMPE): """ Implements GMPE developed by Sinnan Akkar and Zehra Cagnan and published as "A Local Ground-Motion Predictive Model for Turkey, and Its Comparison with Other Regional and Global Ground-Motion Models" (2010, Bulletin of the Seismological Society of America, Volume 100, No. 6, pages 2978-2995). It uses the same site response function used in Boore and Atkinson 2008. """ #: Supported tectonic region type is active shallow crust (the #: equations being developed for Turkey, see paragraph 'Strong Motion #: Databank', p. 2981) DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure types are spectral acceleration, #: peak ground velocity and peak ground acceleration, see paragraph # 'Functional Form', p. 2981 DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA} #: Supported intensity measure component is geometric mean #: of two horizontal components : #: attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, see paragraph #: 'Functional Form', p. 2981. DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types are inter-event, intra-event #: and total, see Table 3, p. 2985. DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: Required site parameters is Vs30. #: See paragraph 'Functionl Form', p. 2981. REQUIRES_SITES_PARAMETERS = {'vs30'} #: Required rupture parameters are magnitude, and rake. #: See paragraph 'Functional Form', p. 2981. REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'} #: Required distance measure is Rjb. #: See paragraph 'Functional Form', p. 2981. REQUIRES_DISTANCES = {'rjb'}
[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. """ # compute median PGA on rock, needed to compute non-linear site # amplification C = self.COEFFS_AC10[PGA()] pga4nl = np.exp( _compute_mean(C, ctx.mag, ctx.rjb, ctx.rake)) * 1e-2 / g for m, imt in enumerate(imts): C = self.COEFFS_AC10[imt] C_SR = self.COEFFS_SOIL_RESPONSE[imt] # compute full mean value by adding site amplification terms # (but avoiding recomputing mean on rock for PGA) if imt.string == "PGA": mean[m] = (np.log(pga4nl) + _get_site_amplification_linear(ctx.vs30, C_SR) + _get_site_amplification_non_linear( ctx.vs30, pga4nl, C_SR)) else: mean[m] = (_compute_mean(C, ctx.mag, ctx.rjb, ctx.rake) + _get_site_amplification_linear(ctx.vs30, C_SR) + _get_site_amplification_non_linear( ctx.vs30, pga4nl, C_SR)) # convert from cm/s**2 to g for SA (PGA is already computed in g) if imt.string[:2] == "SA": mean[m] = np.log(np.exp(mean[m]) * 1e-2 / g) sig[m], tau[m], phi[m] = _get_stddevs(C)
#: Coefficient table (from Table 3, p. 2985) #: sigma is the 'intra-event' standard deviation, #: while tau is the 'inter-event' standard deviation COEFFS_AC10 = CoeffsTable(sa_damping=5, table="""\ IMT a1 a2 a3 a4 a5 a6 a7 a8 a9 sigma tau pgv 5.60931 -0.513 -0.695 -0.25800 -0.90393 0.21576 5.57472 -0.10481 0.07791 0.6154 0.526 pga 8.92418 -0.513 -0.695 -0.18555 -1.25594 0.18105 7.33617 -0.02125 0.01851 0.6527 0.5163 0.03 8.85984 -0.513 -0.695 -0.17123 -1.25132 0.18421 7.46968 -0.0134 0.03512 0.6484 0.5148 0.05 9.05262 -0.513 -0.695 -0.15516 -1.28796 0.1984 7.26552 0.02076 0.01484 0.6622 0.5049 0.075 9.56670 -0.513 -0.695 -0.13840 -1.38817 0.20246 8.03646 0.07311 0.02492 0.6849 0.5144 0.10 9.85606 -0.513 -0.695 -0.11563 -1.43846 0.21833 8.84202 0.11044 -0.00620 0.7001 0.5182 0.15 10.43715 -0.513 -0.695 -0.17897 -1.46786 0.15588 9.39515 0.03555 0.19751 0.6958 0.549 0.20 10.63516 -0.513 -0.695 -0.21034 -1.44625 0.11590 9.60868 -0.03536 0.18594 0.6963 0.5562 0.25 10.12551 -0.513 -0.695 -0.25565 -1.27388 0.09426 7.54353 -0.10685 0.13574 0.7060 0.5585 0.30 10.12745 -0.513 -0.695 -0.27020 -1.26899 0.08352 8.03144 -0.10685 0.13574 0.6718 0.5735 0.40 9.47855 -0.513 -0.695 -0.30498 -1.09793 0.06082 6.24042 -0.11197 0.16555 0.6699 0.5857 0.50 8.95147 -0.513 -0.695 -0.29877 -1.01703 0.09099 5.67936 -0.10118 0.23546 0.6455 0.5782 0.75 8.10498 -0.513 -0.695 -0.3349 -0.84365 0.08647 4.93842 -0.0456 0.10993 0.6463 0.6168 1.00 7.61737 -0.513 -0.695 -0.35366 -0.75840 0.09623 4.12590 -0.01936 0.19729 0.6485 0.6407 1.50 7.20427 -0.513 -0.695 -0.39858 -0.70134 0.11219 3.46535 -0.02618 0.21977 0.6300 0.6751 2.00 6.70845 -0.513 -0.695 -0.39528 -0.70766 0.12032 3.8822 -0.03215 0.20584 0.6243 0.6574 """) COEFFS_SOIL_RESPONSE = BooreAtkinson2008.COEFFS_SOIL_RESPONSE