Source code for openquake.hazardlib.gsim.climent_1994

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2022 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.

"""
Module exports :class:'ClimentEtAl1994'.
"""
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g


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


def _compute_term_1_2(ctx, C):
    """
    Compute terms 1 and 2 in equation 1 page 1.
    """
    return C['c1'] + C['c2'] * ctx.mag


def _compute_term_3_4(ctx, C):
    """
    Compute term 3 and 4 in equation 1 page 1.
    """
    cutoff = 6.056877878
    rhypo = ctx.rhypo.copy()
    rhypo[rhypo <= cutoff] = cutoff
    return C['c3'] * np.log(rhypo) + C['c4'] * rhypo


def _get_site_amplification(ctx, imt, C):
    """
    Compute the fith term of the equation (1), p. 1:
    ``c5 * S``
    """
    S = _get_site_type_dummy_variables(ctx)
    return (C['c5'] * S)


def _get_site_type_dummy_variables(ctx):
    """
    Get site type dummy variables, ``S`` (for rock and soil sites)
    """
    S = np.zeros_like(ctx.vs30)
    # S=0 for rock sites, S=1 otherwise pag 1.
    idxS = (ctx.vs30 < 760.0)
    S[idxS] = 1
    return S


def _compute_mean(C, ctx, imt):
    """
    Compute mean value for PGA and pseudo-velocity response spectrum,
    as given in equation 1. Converts also pseudo-velocity response
    spectrum values to SA, using:

      SA = (PSV * W)/ratio(SA_larger/SA_geo_mean)
       W = (2 * pi / T)
       T = period (sec)
    """
    mean = (_compute_term_1_2(ctx, C) +
            _compute_term_3_4(ctx, C) +
            _get_site_amplification(ctx, imt, C))

    # convert from m/s**2 to g for PGA and from m/s to g for PSV
    # and divided this value for the ratio(SA_larger/SA_geo_mean)
    if imt.string == "PGA":
        mean = (np.exp(mean) / g) / C['r_SA']
    else:
        W = (2. * np.pi) / imt.period
        mean = np.exp(mean) * W / g / C['r_SA']
    return np.log(mean)


[docs]class ClimentEtAl1994(GMPE): """ Implements GMPE developed by Climent, A, W. Taylor, M. Ciudad Real, W. Strauch, M. Villagran, A. Dahle, and H. Bungum. Published as a NORSAR report: "Spectral strong motion attenuation in Central Ame- rica", NORSAR Technical Report No. 2-17, 46 pp. The original formulation predict PGA (m/s*s) and 5% damped PSV (m/s) for the largest component of horizontal ground motion. In this implementation: Spectral acceleration (SA) values are obtained from PSV ones using the following formula : SA = [PSV * (2 * pi/ T)]/ratio(SA_larger/SA_geo_mean) StdDev.TOTAL=StdDev.TOTAL/sd_ratio(SA_larger/SA_geo_mean) The ratio() and sd_ratio() from Beyer and Bommer(2006) """ #: Supported tectonic region type is active shallow crust and/or #: interface subduction the authors did not distinction between shallow #: and sudbdution events (see topic 5.3 "Shallow crustal vs.subduction #: events, pag. 32). #: Any factor/parameter is used in the formulation to discriminate between #: shallow or interface tectonic regime, here this GMPE is implemented #: for active_shallow_crust only DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure types are spectral acceleration, #: and peak ground acceleration. See Table 2 in page 1865 DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA} #: Supported intensity measure component is the largest component of #: two horizontal components #: :attr:`openquake.hazardlib.const.IMC.GREATER_OF_TWO_HORIZONTAL`, #: see paragraph before table on Summary, page 1. DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = ( const.IMC.GREATER_OF_TWO_HORIZONTAL) #: Supported standard deviation types is total. #: See equation 1 on the Summary and Table 4.1, page 22. DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL} #: Required site parameters. The GMPE was developed for rock and soil #: site conditions. The parameter S in eq. 1 (see Summary) define the #: soil condition: S=0 for rock, S=1 for soil. #: Here we use the Vs30=760 as limit between the two soil conditions REQUIRES_SITES_PARAMETERS = {'vs30'} #: Required rupture parameters are magnitude. REQUIRES_RUPTURE_PARAMETERS = {'mag'} #: Required distance measure is Rhypo, explained in page 1(eq. 1) 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] mean[m] = _compute_mean(C, ctx, imt) sig[m] = C['SigmaB'] / C['r_std']
#: Equation coefficients, described in Table 4.1 on pp. 22 #: the original imt values are defined as frequencies values #: the sigma_ls was excluded COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT c1 c2 c3 c4 c5 SigmaB r_SA r_std pga -1.6870 0.5530 -0.5370 -0.00302 0.3270 0.750 1.1000 1.0200 0.025 -7.2140 0.5530 -0.5370 -0.00302 0.3270 0.750 1.1000 1.0200 0.050 -5.4870 0.4470 -0.5500 -0.00246 0.3090 0.780 1.1000 1.0200 0.100 -4.7260 0.4830 -0.5810 -0.00199 0.3810 0.800 1.2020 1.0200 0.200 -4.8760 0.6420 -0.6420 -0.00156 0.4700 0.820 1.2040 1.0200 0.500 -5.8620 0.9170 -0.7260 -0.00107 0.5660 0.820 1.2100 1.0200 1.000 -6.7440 1.0810 -0.7560 -0.00077 0.5880 0.820 1.2200 1.0200 2.000 -7.3480 1.1280 -0.7280 -0.00053 0.5360 0.790 1.2400 1.0200 4.000 -7.4410 1.0070 -0.6010 -0.00040 0.4960 0.730 1.2800 1.0200 """)