Source code for openquake.hazardlib.gsim.arroyo_2010

# -*- 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.
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# 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:'ArroyoEtAl2010SInter'
"""
import numpy as np
from scipy.constants import g
from scipy.special import exp1

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

def _compute_mean(C, g, ctx):
    """
    Compute mean according to equation 8a, page 773.
    """
    mag = ctx.mag
    dis = ctx.rrup

    # computing r02 parameter and the average distance to the fault surface
    ro2 = 1.4447e-5 * np.exp(2.3026 * mag)
    avg = np.sqrt(dis ** 2 + ro2)

    # computing fourth term of Eq. 8a, page 773.
    trm4 = (exp1(C['c4'] * dis) - exp1(C['c4'] * avg)) / ro2

    # computing the mean
    mean = C['c1'] + C['c2'] * mag + C['c3'] * np.log(trm4)
        
    # convert from cm/s**2 to 'g'
    mean = np.log(np.exp(mean) * 1e-2 / g)
    return mean

def _get_stddevs(C):
    """
    Return standard deviations as defined in table 2, page 776.
    """
    stds = np.array([C['s_t'], C['s_e'], C['s_r']])
    return stds


[docs]class ArroyoEtAl2010SInter(GMPE): """ Implements GMPE developed by Arroyo et al. (2010) for Mexican subduction interface events and published as: Arroyo D., GarcĂ­a D., Ordaz M., Mora M. A., and Singh S. K. (2010) "Strong ground-motion relations for Mexican interplate earhquakes", J. Seismol., 14:769-785. The original formulation predict peak ground acceleration (PGA), in cm/s**2, and 5% damped pseudo-acceleration response spectra (PSA) in cm/s**2 for the geometric average of the maximum component of the two horizontal component of ground motion. The GMPE predicted values for Mexican interplate events at rock sites (NEHRP B site condition) in the forearc region. """ #: Supported tectonic region type is subduction interface, #: given that the equations have been derived using Mexican interface #: events. DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE #: Supported intensity measure types are spectral acceleration, #: and peak ground acceleration. See Table 2 in page 776. DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA} #: Supported intensity measure component is the geometric average of # the maximum of the two horizontal components. DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types are inter-event, intra-event #: and total. See Table 2, page 776. DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: No site parameters required REQUIRES_SITES_PARAMETERS = {'vs30'} #: Required rupture parameter is the magnitude REQUIRES_RUPTURE_PARAMETERS = {'mag'} #: Required distance measure is Rrup (closest distance to fault surface) 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. """ for m, imt in enumerate(imts): C = self.COEFFS[imt] mean[m] = _compute_mean(C, g, ctx) sig[m], tau[m], phi[m] = _get_stddevs(C)
#: Equation coefficients for geometric average of the maximum of the two #: horizontal components, as described in Table 2 on page 776. COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT c1 c2 c3 c4 g_e bias s_t s_e s_r 0.040 3.8123 0.8636 0.5578 0.0150 0.3962 -0.0254 0.8228 0.5179 0.6394 0.045 4.0440 0.8489 0.5645 0.0150 0.3874 -0.0285 0.8429 0.5246 0.6597 0.050 4.1429 0.8580 0.5725 0.0150 0.3731 -0.0181 0.8512 0.5199 0.6740 0.055 4.3092 0.8424 0.5765 0.0150 0.3746 0.0004 0.8583 0.5253 0.6788 0.060 4.3770 0.8458 0.5798 0.0150 0.4192 -0.0120 0.8591 0.5563 0.6547 0.065 4.5185 0.8273 0.5796 0.0150 0.3888 -0.0226 0.8452 0.5270 0.6607 0.070 4.4591 0.8394 0.5762 0.0150 0.3872 -0.0346 0.8423 0.5241 0.6594 0.075 4.5939 0.8313 0.5804 0.0150 0.3775 -0.0241 0.8473 0.5205 0.6685 0.080 4.4832 0.8541 0.5792 0.0150 0.3737 -0.0241 0.8421 0.5148 0.6664 0.085 4.5062 0.8481 0.5771 0.0150 0.3757 -0.0138 0.8344 0.5115 0.6593 0.090 4.4648 0.8536 0.5742 0.0150 0.4031 -0.0248 0.8304 0.5273 0.6415 0.095 4.3940 0.8580 0.5712 0.0150 0.4097 0.0040 0.8294 0.5309 0.6373 0.100 4.3391 0.8620 0.5666 0.0150 0.3841 -0.0045 0.8254 0.5116 0.6477 0.120 4.0505 0.8933 0.5546 0.0150 0.3589 -0.0202 0.7960 0.4768 0.6374 0.140 3.5599 0.9379 0.5350 0.0150 0.3528 -0.0293 0.7828 0.4650 0.6298 0.160 3.1311 0.9736 0.5175 0.0150 0.3324 -0.0246 0.7845 0.4523 0.6409 0.180 2.7012 1.0030 0.4985 0.0150 0.3291 -0.0196 0.7717 0.4427 0.6321 0.200 2.5485 0.9988 0.4850 0.0150 0.3439 -0.0250 0.7551 0.4428 0.6116 0.220 2.2699 1.0125 0.4710 0.0150 0.3240 -0.0205 0.7431 0.4229 0.6109 0.240 1.9130 1.0450 0.4591 0.0150 0.3285 -0.0246 0.7369 0.4223 0.6039 0.260 1.7181 1.0418 0.4450 0.0150 0.3595 -0.0220 0.7264 0.4356 0.5814 0.280 1.4039 1.0782 0.4391 0.0150 0.3381 -0.0260 0.7209 0.4191 0.5865 0.300 1.1080 1.1038 0.4287 0.0150 0.3537 -0.0368 0.7198 0.4281 0.5787 0.320 1.0652 1.0868 0.4208 0.0150 0.3702 -0.0345 0.7206 0.4384 0.5719 0.340 0.8319 1.1088 0.4142 0.0150 0.3423 -0.0381 0.7264 0.4250 0.5891 0.360 0.4965 1.1408 0.4044 0.0150 0.3591 -0.0383 0.7255 0.4348 0.5808 0.380 0.3173 1.1388 0.3930 0.0150 0.3673 -0.0264 0.7292 0.4419 0.5800 0.400 0.2735 1.1533 0.4067 0.0134 0.3956 -0.0317 0.7272 0.4574 0.5653 0.450 0.0990 1.1662 0.4127 0.0117 0.3466 -0.0267 0.7216 0.4249 0.5833 0.500 -0.0379 1.2206 0.4523 0.0084 0.3519 -0.0338 0.7189 0.4265 0.5788 0.550 -0.3512 1.2445 0.4493 0.0076 0.3529 -0.0298 0.7095 0.4215 0.5707 0.600 -0.6897 1.2522 0.4421 0.0067 0.3691 -0.0127 0.7084 0.4304 0.5627 0.650 -0.6673 1.2995 0.4785 0.0051 0.3361 -0.0192 0.7065 0.4096 0.5756 0.700 -0.7154 1.3263 0.5068 0.0034 0.3200 -0.0243 0.7070 0.3999 0.5830 0.750 -0.7015 1.2994 0.5056 0.0029 0.3364 -0.0122 0.7092 0.4113 0.5778 0.800 -0.8581 1.3205 0.5103 0.0023 0.3164 -0.0337 0.6974 0.3923 0.5766 0.850 -0.9712 1.3375 0.5201 0.0018 0.3435 -0.0244 0.6906 0.4047 0.5596 0.900 -1.0970 1.3532 0.5278 0.0012 0.3306 -0.0275 0.6923 0.3980 0.5665 0.950 -1.2346 1.3687 0.5345 0.0007 0.3264 -0.0306 0.6863 0.3921 0.5632 1.000 -1.2600 1.3652 0.5426 0.0001 0.3194 -0.0183 0.6798 0.3842 0.5608 1.100 -1.7687 1.4146 0.5342 0.0001 0.3336 -0.0229 0.6701 0.3871 0.5471 1.200 -2.1339 1.4417 0.5263 0.0001 0.3445 -0.0232 0.6697 0.3931 0.5422 1.300 -2.4122 1.4577 0.5201 0.0001 0.3355 -0.0231 0.6801 0.3939 0.5544 1.400 -2.5442 1.4618 0.5242 0.0001 0.3759 -0.0039 0.6763 0.4146 0.5343 1.500 -2.8509 1.4920 0.5220 0.0001 0.3780 -0.0122 0.6765 0.4159 0.5335 1.600 -3.0887 1.5157 0.5215 0.0001 0.3937 -0.0204 0.6674 0.4187 0.5197 1.700 -3.4884 1.5750 0.5261 0.0001 0.4130 -0.0208 0.6480 0.4164 0.4965 1.800 -3.7195 1.5966 0.5255 0.0001 0.3967 -0.0196 0.6327 0.3985 0.4914 1.900 -4.0141 1.6162 0.5187 0.0001 0.4248 -0.0107 0.6231 0.4062 0.4726 2.000 -4.1908 1.6314 0.5199 0.0001 0.3967 -0.0133 0.6078 0.3828 0.4721 2.500 -5.1104 1.7269 0.5277 0.0001 0.4302 -0.0192 0.6001 0.3936 0.4530 3.000 -5.5926 1.7515 0.5298 0.0001 0.4735 -0.0319 0.6029 0.4148 0.4375 3.500 -6.1202 1.8077 0.5402 0.0001 0.4848 -0.0277 0.6137 0.4273 0.4405 4.000 -6.5318 1.8353 0.5394 0.0001 0.5020 -0.0368 0.6201 0.4393 0.4376 4.500 -6.9744 1.8685 0.5328 0.0001 0.5085 -0.0539 0.6419 0.4577 0.4500 5.000 -7.1389 1.8721 0.5376 0.0001 0.5592 -0.0534 0.6701 0.5011 0.4449 pga 2.4862 0.9392 0.5061 0.0150 0.3850 -0.0181 0.7500 0.4654 0.5882 """)