Source code for openquake.hazardlib.gsim.campbell_bozorgnia_2003

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"""
Module exports :class:`CampbellBozorgnia2003NSHMP2007`.
"""
from __future__ import division

import numpy as np

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


[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 = set([ 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 = set([ const.StdDev.TOTAL ]) #: No sites parameters are required. Mean value is computed for #: 'firm rock'. REQUIRES_SITES_PARAMETERS = set(()) #: Required rupture parameters are magnitude, rake and dip (eq. 1 and #: following, page 319). REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'rake', 'dip')) #: Required distance measure are RRup and Rjb (eq. 1 and following, #: page 319). REQUIRES_DISTANCES = set(('rrup', 'rjb'))
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types): """ See :meth:`superclass method <.base.GroundShakingIntensityModel.get_mean_and_stddevs>` for spec of input and result values. """ assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES for stddev_type in stddev_types) C = self.COEFFS[imt] mean = self._get_mean( C, rup.mag, rup.rake, rup.dip, dists.rrup, dists.rjb ) stddevs = self._get_stddevs(C, rup.mag, stddev_types, dists.rrup.size) return mean, stddevs
def _get_mean(self, C, mag, rake, dip, rrup, rjb): """ Return mean value (eq. 1, page 319). """ f1 = self._compute_magnitude_scaling(C, mag) f2 = self._compute_distance_scaling(C, mag, rrup) f3 = self._compute_faulting_mechanism(C, rake, dip) f4 = self._compute_far_source_soil_effect(C) f5 = self._compute_hanging_wall_effect(C, rjb, rrup, dip, mag) mean = ( C['c1'] + f1 + C['c4'] * np.log(np.sqrt(f2)) + f3 + f4 + f5 ) return mean def _get_stddevs(self, C, mag, stddev_types, num_sites): """ Return standard deviation as defined in eq.11 page 319. """ std = C['c16'] + np.zeros(num_sites) if mag < 7.4: std -= 0.07 * mag else: std -= 0.518 # only the 'total' standard deviation is supported, therefore the # std is always the same for all types stddevs = [std for _ in stddev_types] return stddevs def _compute_magnitude_scaling(self, 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(self, 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(self, 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 = float((dip > 45) and (22.5 <= rake <= 157.5)) # flag for thrust faulting fth = float((dip <= 45) and (22.5 <= rake <= 157.5)) return C['c10'] * frv + C['c11'] * fth def _compute_far_source_soil_effect(self, 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(self, 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) if dip <= 70.: hw = (5. - rjb) / 5. # eq. 9 f_m = 1 if mag > 6.5 else mag - 5.5 # # 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 #: 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 """)