Source code for openquake.hazardlib.gsim.campbell_2003

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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"""
Module exports :class:`Campbell2003`, :class:`Campbell2003SHARE`,
:class:`Campbell2003MblgAB1987NSHMP2008`,
:class:`Campbell2003MblgJ1996NSHMP2008`,
:class:`Campbell2003MwNSHMP2008`
"""
import numpy as np

from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib.gsim.utils import (
    mblg_to_mw_atkinson_boore_87,
    mblg_to_mw_johnston_96,
    clip_mean)
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA

_compute_mean = CallableDict()


@_compute_mean.add("base")
def _compute_mean_1(kind, C, mag, rrup):
    """
    Compute mean value according to equation 30, page 1021.
    """
    mean = (C['c1'] +
            _compute_term1(C, mag) +
            _compute_term2(C, mag, rrup) +
            _compute_term3(C, rrup))
    return mean


@_compute_mean.add("Mblg87", "Mblg96", "Mw")
def _compute_mean_2(kind, C, mag, rrup):
    """
    Compute mean value (Equation 30 in USGS report)
    """
    mean = np.zeros_like(rrup)

    mean += C['c1'] + C['c2'] * mag + C['c3'] * (8.5 - mag) ** 2

    idx = rrup > 70.
    mean[idx] += C['c7'] * (np.log(rrup[idx]) - np.log(70.))

    idx = rrup > 130.
    mean[idx] += C['c8'] * (np.log(rrup[idx]) - np.log(130.))

    R = np.sqrt(
        rrup ** 2 + (C['c5'] * np.exp(C['c6'] * mag)) ** 2)
    mean += C['c4'] * np.log(R) + (C['c9'] + C['c10'] * mag) * rrup

    return mean


def _compute_term1(C, mag):
    """
    This computes the term f1 in equation 31, page 1021
    """
    return (C['c2'] * mag) + C['c3'] * (8.5 - mag) ** 2


def _compute_term2(C, mag, rrup):
    """
    This computes the term f2 in equation 32, page 1021
    """
    c78_factor = (C['c7'] * np.exp(C['c8'] * mag)) ** 2
    R = np.sqrt(rrup ** 2 + c78_factor)

    return C['c4'] * np.log(R) + (C['c5'] + C['c6'] * mag) * rrup


def _compute_term3(C, rrup):
    """
    This computes the term f3 in equation 34, page 1021 but corrected
    according to the erratum.
    """
    f3 = np.zeros_like(rrup)

    idx_between_70_130 = (rrup > 70) & (rrup <= 130)
    idx_greater_130 = rrup > 130

    f3[idx_between_70_130] = (
        C['c9'] * (np.log(rrup[idx_between_70_130]) - np.log(70)))

    f3[idx_greater_130] = (
        C['c9'] * (np.log(rrup[idx_greater_130]) - np.log(70)) +
        C['c10'] * (np.log(rrup[idx_greater_130]) - np.log(130)))

    return f3


_convert_magnitude = CallableDict()


@_convert_magnitude.add("Mblg87")
def _convert_magnitude_1(kind, mag):
    """
    Convert magnitude from Mblg to Mw using Atkinson and Boore 1987
    equation.
    """
    return mblg_to_mw_atkinson_boore_87(mag)


@_convert_magnitude.add("Mblg96")
def _convert_magnitude_2(kind, mag):
    """
    Convert magnitude from Mblg to Mw using Johnston 1996 equation.
    """
    return mblg_to_mw_johnston_96(mag)


@_convert_magnitude.add("Mw")
def _convert_magnitude_3(kind, mag):
    """
    Return magnitude value unchanged
    """
    return mag


[docs]class Campbell2003(GMPE): """ Implements GMPE developed by K.W Campbell and published as "Prediction of Strong Ground Motion Using the Hybrid Empirical Method and Its Use in the Development of Ground Motion (Attenuation) Relations in Eastern North America" (Bulletting of the Seismological Society of America, Volume 93, Number 3, pages 1012-1033, 2003). The class implements also the corrections given in the erratum (2004). """ kind = "base" #: Supported tectonic region type is stable continental crust given that #: the equations have been derived for Eastern North America. DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL #: Supported intensity measure types are spectral acceleration, #: and peak ground acceleration, see table 6, page 1022 (PGA is assumed #: to be equal to SA at 0.01 s) DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA} #: Supported intensity measure component is the geometric mean of #: two horizontal components #: :attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation type is only total, see equation 35, page #: 1021 DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL} #: No site parameters are needed REQUIRES_SITES_PARAMETERS = set() #: Required rupture parameter is only magnitude, see equation 30 page #: 1021. REQUIRES_RUPTURE_PARAMETERS = {'mag'} #: Required distance measure is closest distance to rupture, see equation #: 30 page 1021. REQUIRES_DISTANCES = {'rrup'}
[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. """ for m, imt in enumerate(imts): C = self.COEFFS[imt] mean[m] = _compute_mean(self.kind, C, ctx.mag, ctx.rrup) sig[m] = np.where(ctx.mag < 7.16, C['c11'] + C['c12'] * ctx.mag, C['c13'])
#: Coefficient tables are constructed from the electronic suplements of #: the original paper. COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 pga 0.0305 0.633 -0.0427 -1.591 -0.00428 0.000483 0.683 0.416 1.140 -0.873 1.030 -0.0860 0.414 0.020 1.3535 0.630 -0.0404 -1.787 -0.00388 0.000497 1.020 0.363 0.851 -0.715 1.030 -0.0860 0.414 0.030 1.1860 0.622 -0.0362 -1.691 -0.00367 0.000501 0.922 0.376 0.759 -0.922 1.030 -0.0860 0.414 0.050 0.3736 0.616 -0.0353 -1.469 -0.00378 0.000500 0.630 0.423 0.771 -1.239 1.042 -0.0838 0.443 0.075 -0.0395 0.615 -0.0353 -1.383 -0.00421 0.000486 0.491 0.463 0.955 -1.349 1.052 -0.0838 0.453 0.100 -0.1475 0.613 -0.0353 -1.369 -0.00454 0.000460 0.484 0.467 1.096 -1.284 1.059 -0.0838 0.460 0.150 -0.1901 0.616 -0.0478 -1.368 -0.00473 0.000393 0.461 0.478 1.239 -1.079 1.068 -0.0838 0.469 0.200 -0.4328 0.617 -0.0586 -1.320 -0.00460 0.000337 0.399 0.493 1.250 -0.928 1.077 -0.0838 0.478 0.300 -0.6906 0.609 -0.0786 -1.280 -0.00414 0.000263 0.349 0.502 1.241 -0.753 1.081 -0.0838 0.482 0.500 -0.5907 0.534 -0.1379 -1.216 -0.00341 0.000194 0.318 0.503 1.166 -0.606 1.098 -0.0824 0.508 0.750 -0.5429 0.480 -0.1806 -1.184 -0.00288 0.000160 0.304 0.504 1.110 -0.526 1.105 -0.0806 0.528 1.000 -0.6104 0.451 -0.2090 -1.158 -0.00255 0.000141 0.299 0.503 1.067 -0.482 1.110 -0.0793 0.543 1.500 -0.9666 0.441 -0.2405 -1.135 -0.00213 0.000119 0.304 0.500 1.029 -0.438 1.099 -0.0771 0.547 2.000 -1.4306 0.459 -0.2552 -1.124 -0.00187 0.000103 0.310 0.499 1.015 -0.417 1.093 -0.0758 0.551 3.000 -2.2331 0.492 -0.2646 -1.121 -0.00154 0.000084 0.310 0.499 1.014 -0.393 1.090 -0.0737 0.562 4.000 -2.7975 0.507 -0.2738 -1.119 -0.00135 0.000074 0.294 0.506 1.018 -0.386 1.092 -0.0722 0.575 """)
[docs]class Campbell2003SHARE(Campbell2003): """ Extends :class:`~openquake.hazardlib.gsim.campbell_2003.Campbell2003` and introduces adjustments for style of faulting and default rock soil conditions as needed by the SHARE (http://www.share-eu.org/) project. """ #: Required rupture parameters are magnitude and rake REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'} #: Shear-wave velocity for reference soil conditions in [m s-1] DEFINED_FOR_REFERENCE_VELOCITY = 800.
[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. """ super().compute(ctx, imts, mean, sig, tau, phi) for m, imt in enumerate(imts): # extract faulting style and rock adjustment coefficients for the # given imt C_ADJ = self.COEFFS_FS_ROCK[imt] # apply faulting style and rock adjustment factor for mean and std mean[m] = np.log(np.exp(mean[m]) * _compute_faulting_style_term( C_ADJ['Frss'], self.CONSTS_FS['pR'], self.CONSTS_FS['Fnss'], self.CONSTS_FS['pN'], ctx.rake) * C_ADJ['AFrock'])
#: Coefficients for faulting style and rock adjustment COEFFS_FS_ROCK = CoeffsTable(sa_damping=5, table="""\ IMT Frss AFrock pga 1.220000 0.735106 0.020000 1.192000 0.474275 0.030000 1.178000 0.423049 0.050000 1.150000 0.550323 0.075000 1.115000 0.730061 0.100000 1.080000 0.888509 0.150000 1.150000 1.094622 0.200000 1.190000 1.197291 0.300000 1.230000 1.288309 0.500000 1.230000 1.311421 0.750000 1.199444 1.298212 1.000000 1.196667 1.265762 1.500000 1.191111 1.197583 2.000000 1.140000 1.215779 3.000000 1.140000 1.215779 4.000000 1.140000 1.215779 """) #: Constants for faulting style adjustment CONSTS_FS = {'Fnss': 0.95, 'pN': 0.01, 'pR': 0.81}
def _compute_faulting_style_term(Frss, pR, Fnss, pN, rake): """ Compute SHARE faulting style adjustment term. """ term = np.full_like(rake, np.power(Frss, - pR) * np.power(Fnss, - pN)) term[(rake > 30.0) & (rake <= 150.0)] = ( np.power(Frss, 1 - pR) * np.power(Fnss, -pN)) term[(rake > -120.0) & (rake <= -60.0)] = ( np.power(Frss, - pR) * np.power(Fnss, 1 - pN)) return term
[docs]class Campbell2003MblgAB1987NSHMP2008(Campbell2003): """ Implement GMPE developed by Ken Campbell and described in "Development of semi-empirical attenuation relationships for the CEUS", U.S. Geological Survey, Award 01HQGR0011, final report. Document available at: http://earthquake.usgs.gov/research/external/reports/01HQGR0011.pdf This GMPE is used by the National Seismic Hazard Mapping Project (NSHMP) for the 2008 central and eastern US hazard model. This class replicates the algorithm as implemented in ``subroutine getCampCEUS`` in the ``hazgridXnga2.f`` Fortran code available at: http://earthquake.usgs.gov/hazards/products/conterminous/2008/software/ The class assumes rupture magnitude to be in Mblg scale (given that MFDs for central and eastern US are given in this scale). Mblg is converted to Mw using Atkinson and Boore 1987 conversion equation Coefficients are given for the B/C (firm rock) conditions. """ kind = "Mblg87" #: Shear-wave velocity for reference soil conditions in [m s-1] DEFINED_FOR_REFERENCE_VELOCITY = 760.
[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. """ mag = _convert_magnitude(self.kind, ctx.mag) for m, imt in enumerate(imts): C = self.COEFFS[imt] mean[m] = _compute_mean(self.kind, C, mag, ctx.rrup) mean[m] = clip_mean(imt, mean[m]) sig[m] = np.where(mag < 7.16, C['c11'] + C['c12'] * mag, C['c13'])
#: Coefficient tables extracted from ``subroutine getCampCEUS`` in #: ``hazgridXnga2.f`` COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 pga 0.4492 0.633 -0.0427 -1.591 0.683 0.416 1.140 -0.873 -0.00428 0.000483 1.030 -0.0860 0.414 0.1 0.4064 0.613 -0.0353 -1.369 0.484 0.467 1.096 -1.284 -0.00454 0.00046 1.059 -0.0838 0.460 0.2 0.1325 0.617 -0.0586 -1.32 0.399 0.493 1.25 -0.928 -0.0046 0.000337 1.077 -0.0838 0.478 0.3 -0.1483 0.609 -0.0786 -1.28 0.349 0.502 1.241 -0.753 -0.00414 0.000263 1.081 -0.0838 0.482 0.5 -0.1333 0.534 -0.1379 -1.216 0.318 0.503 1.116 -0.606 -0.00341 0.000194 1.098 -0.0824 0.508 1.0 -0.3177 0.451 -0.2090 -1.158 0.299 0.503 1.067 -0.482 -0.00255 0.000141 1.110 -0.0793 0.543 2.0 -1.2483 0.459 -0.2552 -1.124 0.310 0.499 1.015 -0.417 -0.00187 0.000103 1.093 -0.0758 0.551 """)
[docs]class Campbell2003MblgJ1996NSHMP2008(Campbell2003MblgAB1987NSHMP2008): """ Extend :class:`Campbell2003MblgAB1987NSHMP2008` but uses Johnston 1996 equation for converting Mblg to Mw """ kind = "Mblg96"
[docs]class Campbell2003MwNSHMP2008(Campbell2003MblgAB1987NSHMP2008): """ Extend :class:`Campbell2003MblgAB1987NSHMP2008` but assumes magnitude to be in Mw scale, so no converion is applied. """ kind = "Mw"