Source code for openquake.hazardlib.gsim.campbell_bozorgnia_2003

# -*- coding: utf-8 -*-
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"""
Module exports :class:`CampbellBozorgnia2003NSHMP2007`.
"""
import numpy as np

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


def _get_mean(C, mag, rake, dip, rrup, rjb):
    """
    Return mean value (eq. 1, page 319).
    """
    f1 = _compute_magnitude_scaling(C, mag)
    f2 = _compute_distance_scaling(C, mag, rrup)
    f3 = _compute_faulting_mechanism(C, rake, dip)
    f4 = _compute_far_source_soil_effect(C)
    f5 = _compute_hanging_wall_effect(C, rjb, rrup, dip, mag)
    return C['c1'] + f1 + C['c4'] * np.log(np.sqrt(f2)) + f3 + f4 + f5


def _compute_magnitude_scaling(C, mag):
    """
    Compute and return magnitude scaling term (eq.2, page 319)
    """
    return C['c2'] * mag + C['c3'] * (8.5 - mag) ** 2


def _compute_distance_scaling(C, mag, rrup):
    """
    Compute distance scaling term (eq.3, page 319).

    The distance scaling assumes the near-source effect of local site
    conditions due to 50% very firm soil and soft rock and 50% firm rock.
    """
    g = C['c5'] + C['c6'] * 0.5 + C['c7'] * 0.5

    return rrup ** 2 + (np.exp(
        C['c8'] * mag + C['c9'] * (8.5 - mag) ** 2) * g) ** 2


def _compute_faulting_mechanism(C, rake, dip):
    """
    Compute faulting mechanism term (see eq. 5, page 319).

    Reverse faulting is defined as occurring on steep faults (dip > 45)
    and rake in (22.5, 157.5).

    Thrust faulting is defined as occurring on shallow dipping faults
    (dip <=45) and rake in (22.5, 157.5)
    """
    # flag for reverse faulting
    frv = (dip > 45) & (22.5 <= rake) & (rake <= 157.5)
    # flag for thrust faulting
    fth = (dip <= 45) & (22.5 <= rake) & (rake <= 157.5)
    return C['c10'] * frv + C['c11'] * fth


def _compute_far_source_soil_effect(C):
    """
    Compute far-source effect of local site conditions (see eq. 6,
    page 319) assuming 'firm rock' conditions.
    """
    return C['c14']


def _compute_hanging_wall_effect(C, rjb, rrup, dip, mag):
    """
    Compute hanging-wall effect (see eq. 7, 8, 9 and 10 page 319).
    Considers correct version of equation 8 as given in the erratum and not
    in the original paper.
    """
    # eq. 8 (to be noticed that the USGS-NSHMP implementation defines
    # the hanging-wall term for all rjb distances, while in the original
    # manuscript, hw is computed only for rjb < 5). Again the 'firm rock'
    # is considered
    hw = np.zeros_like(rjb)
    hw[dip <= 70.] = (5. - rjb[dip <= 70.]) / 5.

    # eq. 9
    f_m = np.clip(mag - 5.5, None, 1.)

    # eq. 10
    f_rrup = C['c15'] + np.zeros_like(rrup)
    idx = rrup < 8
    f_rrup[idx] *= rrup[idx] / 8

    # eq. 7 (to be noticed that the f3 factor is not included
    # while this is defined in the original manuscript)
    f_hw = hw * f_m * f_rrup

    return f_hw


[docs]class CampbellBozorgnia2003NSHMP2007(GMPE): """ Implements GMPE developed by Kenneth W. Campbell and Yousef Bozorgnia and published as "Updated Near-Source Ground-Motion (Attenuation) Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Responce Spectra", Bulletin of the Seismological Society of America, Vol. 93, No. 1, pp. 314-331, 2003. The class implement the equation as modified by the United States Geological Survey - National Seismic Hazard Mapping Project (USGS-NSHMP) for the 2007 Alaska model (http://earthquake.usgs.gov/hazards/products/ak/2007/). The class replicates the equation as coded in ``subroutine getCamp2000`` in ``hazFXv7.f`` available from http://earthquake.usgs.gov/hazards/products/ak/2007/software/. The equation compute mean value for the 'firm rock' conditon. """ #: Supported tectonic region type is 'active shallow crust' (see Abstract) DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure types are PGA and SA (see Abstract) DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA} #: Supported intensity measure component is the geometric mean of two #: horizontal components (see paragraph 'Strong-Motion Database', page 316) DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation type is Total (see equations 11, 12 pp. 319 #: 320) DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL} #: No ctx parameters are required. Mean value is computed for #: 'firm rock'. DEFINED_FOR_REFERENCE_VELOCITY = 760. REQUIRES_SITES_PARAMETERS = set() #: Required rupture parameters are magnitude, rake and dip (eq. 1 and #: following, page 319). REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'dip'} #: Required distance measure are RRup and Rjb (eq. 1 and following, #: page 319). REQUIRES_DISTANCES = {'rrup', '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. """ for m, imt in enumerate(imts): C = self.COEFFS[imt] mean[m] = _get_mean( C, ctx.mag, ctx.rake, ctx.dip, ctx.rrup, ctx.rjb) sig[m] = C['c16'] - np.where(ctx.mag < 7.4, 0.07 * ctx.mag, 0.518)
#: Coefficient table (table 4, page 321. Coefficients for horizontal #: component and for corrected PGA) COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 c16 pga -4.033 0.812 0.036 -1.061 0.041 -0.005 -0.018 0.766 0.034 0.343 0.351 -0.123 -0.138 -0.289 0.370 0.920 0.10 -2.661 0.812 0.060 -1.308 0.166 -0.009 -0.068 0.621 0.046 0.224 0.313 -0.146 -0.253 -0.299 0.370 0.958 0.20 -2.771 0.812 0.030 -1.153 0.098 -0.014 -0.038 0.704 0.026 0.296 0.342 -0.148 -0.183 -0.330 0.370 0.981 0.30 -2.999 0.812 0.007 -1.080 0.059 -0.007 -0.022 0.752 0.007 0.359 0.385 -0.162 -0.157 -0.453 0.370 0.984 0.50 -3.556 0.812 -0.035 -0.964 0.023 -0.002 -0.004 0.842 -0.036 0.406 0.479 -0.122 -0.130 -0.528 0.370 0.990 1.0 -3.867 0.812 -0.101 -0.964 0.019 0 0 0.842 -0.105 0.329 0.338 -0.073 -0.072 -0.607 0.281 1.021 2.0 -4.311 0.812 -0.180 -0.964 0.019 0 0 0.842 -0.187 0.060 0.064 -0.124 -0.116 -0.649 0.160 1.021 """)