Source code for openquake.hazardlib.gsim.abrahamson_2015

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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# Copyright (C) 2015-2016 GEM Foundation
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"""
Module exports :class:`AbrahamsonEtAl2015`
               :class:`AbrahamsonEtAl2015SInter`
               :class:`AbrahamsonEtAl2015SInterHigh`
               :class:`AbrahamsonEtAl2015SInterLow`
               :class:`AbrahamsonEtAl2015SSlab`
               :class:`AbrahamsonEtAl2015SSlabHigh`
               :class:`AbrahamsonEtAl2015SSlabLow`

"""

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 AbrahamsonEtAl2015SInter(GMPE): """ Implements the Subduction GMPE developed by Norman Abrahamson, Nicholas Gregor and Kofi Addo, otherwise known as the "BC Hydro" Model, published as "BC Hydro Ground Motion Prediction Equations For Subduction Earthquakes (2015, Earthquake Spectra, in press), for subduction interface events. From observations of very large events it was found that the magnitude scaling term can be adjusted as part of the epistemic uncertainty model. The adjustment comes in the form of the parameter DeltaC1, which is period dependent for interface events. To capture the epistemic uncertainty in DeltaC1, three models are proposed: a 'central', 'upper' and 'lower' model. The current class implements the 'central' model, whilst additional classes will implement the 'upper' and 'lower' alternatives. """ #: Supported tectonic region type is subduction interface DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE #: Supported intensity measure types are spectral acceleration, #: and peak ground acceleration DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([ PGA, SA ]) #: Supported intensity measure component is the geometric mean component DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types are inter-event, intra-event #: and total, see table 3, pages 12 - 13 DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([ const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT ]) #: Site amplification is dependent upon Vs30 #: For the Abrahamson et al (2013) GMPE a new term is introduced to #: determine whether a site is on the forearc with respect to the #: subduction interface, or on the backarc. This boolean is a vector #: containing True for a backarc site or False for a forearc or #: unknown site. REQUIRES_SITES_PARAMETERS = set(('vs30', 'backarc')) #: Required rupture parameters are magnitude for the interface model REQUIRES_RUPTURE_PARAMETERS = set(('mag',)) #: Required distance measure is closest distance to rupture, for #: interface events REQUIRES_DISTANCES = set(('rrup',))
[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. """ # extract dictionaries of coefficients specific to required # intensity measure type and for PGA C = self.COEFFS[imt] dc1 = self._get_delta_c1(imt) C_PGA = self.COEFFS[PGA()] dc1_pga = self._get_delta_c1(PGA()) # compute median pga on rock (vs30=1000), needed for site response # term calculation pga1000 = np.exp( self._compute_pga_rock(C_PGA, dc1_pga, sites, rup, dists)) mean = (self._compute_magnitude_term(C, dc1, rup.mag) + self._compute_distance_term(C, rup.mag, dists) + self._compute_focal_depth_term(C, rup) + self._compute_forearc_backarc_term(C, sites, dists) + self._compute_site_response_term(C, sites, pga1000)) stddevs = self._get_stddevs(C, stddev_types, len(sites.vs30)) return mean, stddevs
def _get_delta_c1(self, imt): """ Returns the magnitude scaling parameter deltaC1 for capturing scaling for large events. """ return self.COEFFS_MAG_SCALE[imt]["dc1"] def _compute_pga_rock(self, C, dc1, sites, rup, dists): """ Compute and return mean imt value for rock conditions (vs30 = 1000 m/s) """ mean = (self._compute_magnitude_term(C, dc1, rup.mag) + self._compute_distance_term(C, rup.mag, dists) + self._compute_focal_depth_term(C, rup) + self._compute_forearc_backarc_term(C, sites, dists)) # Apply linear site term site_response = ((C['theta12'] + C['b'] * self.CONSTS['n']) * np.log(1000. / C['vlin'])) return mean + site_response def _compute_magnitude_term(self, C, dc1, mag): """ Computes the magnitude scaling term given by equation (2) """ base = C['theta1'] + (self.CONSTS['theta4'] * dc1) dmag = self.CONSTS["C1"] + dc1 if mag > dmag: f_mag = (self.CONSTS['theta5'] * (mag - dmag)) +\ C['theta13'] * ((10. - mag) ** 2.) else: f_mag = (self.CONSTS['theta4'] * (mag - dmag)) +\ C['theta13'] * ((10. - mag) ** 2.) return base + f_mag def _compute_distance_term(self, C, mag, dists): """ Computes the distance scaling term, as contained within equation (1) """ return (C['theta2'] + self.CONSTS['theta3'] * (mag - 7.8)) *\ np.log(dists.rrup + self.CONSTS['c4'] * np.exp((mag - 6.) * self.CONSTS['theta9'])) + (C['theta6'] * dists.rrup) def _compute_focal_depth_term(self, C, rup): """ Computes the hypocentral depth scaling term - as indicated by equation (3) For interface events F_EVENT = 0.. so no depth scaling is returned """ return 0. def _compute_forearc_backarc_term(self, C, sites, dists): """ Computes the forearc/backarc scaling term given by equation (4) """ f_faba = np.zeros_like(dists.rrup) # Term only applies to backarc sites (F_FABA = 0. for forearc) max_dist = dists.rrup[sites.backarc] max_dist[max_dist < 100.0] = 100.0 f_faba[sites.backarc] = C['theta15'] + \ (C['theta16'] * np.log(max_dist / 40.0)) return f_faba def _compute_site_response_term(self, C, sites, pga1000): """ Compute and return site response model term This GMPE adopts the same site response scaling model of Walling et al (2008) as implemented in the Abrahamson & Silva (2008) GMPE. The functional form is retained here. """ vs_star = sites.vs30.copy() vs_star[vs_star > 1000.0] = 1000. arg = vs_star / C["vlin"] site_resp_term = C["theta12"] * np.log(arg) # Get linear scaling term idx = sites.vs30 >= C["vlin"] site_resp_term[idx] += (C["b"] * self.CONSTS["n"] * np.log(arg[idx])) # Get nonlinear scaling term idx = np.logical_not(idx) site_resp_term[idx] += ( -C["b"] * np.log(pga1000[idx] + self.CONSTS["c"]) + C["b"] * np.log(pga1000[idx] + self.CONSTS["c"] * (arg[idx] ** self.CONSTS["n"]))) return site_resp_term def _get_stddevs(self, C, stddev_types, num_sites): """ Return standard deviations as defined in Table 3 """ stddevs = [] for stddev_type in stddev_types: assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES if stddev_type == const.StdDev.TOTAL: stddevs.append(C['sigma'] + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTER_EVENT: stddevs.append(C['tau'] + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTRA_EVENT: stddevs.append(C['phi'] + np.zeros(num_sites)) return stddevs # Period-dependent coefficients (Table 3) COEFFS = CoeffsTable(sa_damping=5, table="""\ imt vlin b theta1 theta2 theta6 theta7 theta8 theta10 theta11 theta12 theta13 theta14 theta15 theta16 phi tau sigma sigma_ss pga 865.1000 -1.1860 4.2203 -1.3500 -0.0012 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000 0.0200 865.1000 -1.1860 4.2203 -1.3500 -0.0012 1.0988 -1.4200 3.1200 0.0130 0.9800 -0.0135 -0.4000 0.9969 -1.0000 0.6000 0.4300 0.7400 0.6000 0.0500 1053.5000 -1.3460 4.5371 -1.4000 -0.0012 1.2536 -1.6500 3.3700 0.0130 1.2880 -0.0138 -0.4000 1.1030 -1.1800 0.6000 0.4300 0.7400 0.6000 0.0750 1085.7000 -1.4710 5.0733 -1.4500 -0.0012 1.4175 -1.8000 3.3700 0.0130 1.4830 -0.0142 -0.4000 1.2732 -1.3600 0.6000 0.4300 0.7400 0.6000 0.1000 1032.5000 -1.6240 5.2892 -1.4500 -0.0012 1.3997 -1.8000 3.3300 0.0130 1.6130 -0.0145 -0.4000 1.3042 -1.3600 0.6000 0.4300 0.7400 0.6000 0.1500 877.6000 -1.9310 5.4563 -1.4500 -0.0014 1.3582 -1.6900 3.2500 0.0130 1.8820 -0.0153 -0.4000 1.2600 -1.3000 0.6000 0.4300 0.7400 0.6000 0.2000 748.2000 -2.1880 5.2684 -1.4000 -0.0018 1.1648 -1.4900 3.0300 0.0129 2.0760 -0.0162 -0.3500 1.2230 -1.2500 0.6000 0.4300 0.7400 0.6000 0.2500 654.3000 -2.3810 5.0594 -1.3500 -0.0023 0.9940 -1.3000 2.8000 0.0129 2.2480 -0.0172 -0.3100 1.1600 -1.1700 0.6000 0.4300 0.7400 0.6000 0.3000 587.1000 -2.5180 4.7945 -1.2800 -0.0027 0.8821 -1.1800 2.5900 0.0128 2.3480 -0.0183 -0.2800 1.0500 -1.0600 0.6000 0.4300 0.7400 0.6000 0.4000 503.0000 -2.6570 4.4644 -1.1800 -0.0035 0.7046 -0.9800 2.2000 0.0127 2.4270 -0.0206 -0.2300 0.8000 -0.7800 0.6000 0.4300 0.7400 0.6000 0.5000 456.6000 -2.6690 4.0181 -1.0800 -0.0044 0.5799 -0.8200 1.9200 0.0125 2.3990 -0.0231 -0.1900 0.6620 -0.6200 0.6000 0.4300 0.7400 0.6000 0.6000 430.3000 -2.5990 3.6055 -0.9900 -0.0050 0.5021 -0.7000 1.7000 0.0124 2.2730 -0.0256 -0.1600 0.5800 -0.5000 0.6000 0.4300 0.7400 0.6000 0.7500 410.5000 -2.4010 3.2174 -0.9100 -0.0058 0.3687 -0.5400 1.4200 0.0120 1.9930 -0.0296 -0.1200 0.4800 -0.3400 0.6000 0.4300 0.7400 0.6000 1.0000 400.0000 -1.9550 2.7981 -0.8500 -0.0062 0.1746 -0.3400 1.1000 0.0114 1.4700 -0.0363 -0.0700 0.3300 -0.1400 0.6000 0.4300 0.7400 0.6000 1.5000 400.0000 -1.0250 2.0123 -0.7700 -0.0064 -0.0820 -0.0500 0.7000 0.0100 0.4080 -0.0493 0.0000 0.3100 0.0000 0.6000 0.4300 0.7400 0.6000 2.0000 400.0000 -0.2990 1.4128 -0.7100 -0.0064 -0.2821 0.1200 0.7000 0.0085 -0.4010 -0.0610 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 2.5000 400.0000 0.0000 0.9976 -0.6700 -0.0064 -0.4108 0.2500 0.7000 0.0069 -0.7230 -0.0711 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 3.0000 400.0000 0.0000 0.6443 -0.6400 -0.0064 -0.4466 0.3000 0.7000 0.0054 -0.6730 -0.0798 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 4.0000 400.0000 0.0000 0.0657 -0.5800 -0.0064 -0.4344 0.3000 0.7000 0.0027 -0.6270 -0.0935 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 5.0000 400.0000 0.0000 -0.4624 -0.5400 -0.0064 -0.4368 0.3000 0.7000 0.0005 -0.5960 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 6.0000 400.0000 0.0000 -0.9809 -0.5000 -0.0064 -0.4586 0.3000 0.7000 -0.0013 -0.5660 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 7.5000 400.0000 0.0000 -1.6017 -0.4600 -0.0064 -0.4433 0.3000 0.7000 -0.0033 -0.5280 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 10.0000 400.0000 0.0000 -2.2937 -0.4000 -0.0064 -0.4828 0.3000 0.7000 -0.0060 -0.5040 -0.0980 0.0000 0.3000 0.0000 0.6000 0.4300 0.7400 0.6000 """) COEFFS_MAG_SCALE = CoeffsTable(sa_damping=5, table=""" IMT dc1 pga 0.2 0.02 0.2 0.30 0.2 0.50 0.1 1.00 0.0 2.00 -0.1 3.00 -0.2 10.0 -0.2 """) CONSTS = { # Period-Independent Coefficients (Table 2) 'n': 1.18, 'c': 1.88, 'theta3': 0.1, 'theta4': 0.9, 'theta5': 0.0, 'theta9': 0.4, 'c4': 10.0, 'C1': 7.8 }
[docs]class AbrahamsonEtAl2015SInterHigh(AbrahamsonEtAl2015SInter): """ Defines the Abrahamson et al. (2013) scaling relation assuming the upper values of the magnitude scaling for large slab earthquakes, as defined in table 4 """ COEFFS_MAG_SCALE = CoeffsTable(sa_damping=5, table=""" IMT dc1 pga 0.4 0.02 0.4 0.30 0.4 0.50 0.3 1.00 0.2 2.00 0.1 3.00 0.0 10.0 0.0 """)
[docs]class AbrahamsonEtAl2015SInterLow(AbrahamsonEtAl2015SInter): """ Defines the Abrahamson et al. (2013) scaling relation assuming the lower values of the magnitude scaling for large slab earthquakes, as defined in table 4 """ COEFFS_MAG_SCALE = CoeffsTable(sa_damping=5, table=""" IMT dc1 pga 0.0 0.02 0.0 0.30 0.0 0.50 -0.1 1.00 -0.2 2.00 -0.3 3.00 -0.4 10.0 -0.4 """)
[docs]class AbrahamsonEtAl2015SSlab(AbrahamsonEtAl2015SInter): """ Implements the Subduction GMPE developed by Norman Abrahamson, Nicholas Gregor and Kofi Addo, otherwise known as the "BC Hydro" Model, published as "BC Hydro Ground Motion Prediction Equations For Subduction Earthquakes (2013, Earthquake Spectra, in press). This implements only the inslab GMPE. For inslab events the source is considered to be a point source located at the hypocentre. Therefore the hypocentral distance metric is used in place of the rupture distance, and the hypocentral depth is used to scale the ground motion by depth """ #: Supported tectonic region type is subduction in-slab DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB #: Required distance measure is hypocentral for in-slab events REQUIRES_DISTANCES = set(('rhypo',)) #: In-slab events require constraint of hypocentral depth and magnitude REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'hypo_depth')) def _get_delta_c1(self, imt): """ Returns the magnitude scaling parameter deltaC1 which is fixed at -0.3 for the central branch of the in-slab model """ return -0.3 def _compute_focal_depth_term(self, C, rup): """ Computes the hypocentral depth scaling term - as indicated by equation (3) """ if rup.hypo_depth > 120.0: z_h = 120.0 else: z_h = rup.hypo_depth return C['theta11'] * (z_h - 60.) def _compute_distance_term(self, C, mag, dists): """ Computes the distance scaling term, as contained within equation (1b) """ return ((C['theta2'] + C['theta14'] + self.CONSTS['theta3'] * (mag - 7.8)) * np.log(dists.rhypo + self.CONSTS['c4'] * np.exp((mag - 6.) * self.CONSTS['theta9'])) + (C['theta6'] * dists.rhypo)) + C["theta10"] def _compute_forearc_backarc_term(self, C, sites, dists): """ Computes the forearc/backarc scaling term given by equation (4). """ f_faba = np.zeros_like(dists.rhypo) # Term only applies to backarc sites (F_FABA = 0. for forearc) max_dist = dists.rhypo[sites.backarc] max_dist[max_dist < 85.0] = 85.0 f_faba[sites.backarc] = C['theta7'] +\ (C['theta8'] * np.log(max_dist / 40.0)) return f_faba
[docs]class AbrahamsonEtAl2015SSlabHigh(AbrahamsonEtAl2015SSlab): """ Defines the Abrahamson et al. (2013) scaling relation assuming the upper values of the magnitude scaling for large slab earthquakes, as defined in table 8 """ def _get_delta_c1(self, imt): """ Returns them agnitude scaling parameter deltaC1 which is fixed at -0.1 for the upper branch of the in-slab model """ return -0.1
[docs]class AbrahamsonEtAl2015SSlabLow(AbrahamsonEtAl2015SSlab): """ Defines the Abrahamson et al. (2013) scaling relation assuming the lower values of the magnitude scaling for large slab earthquakes, as defined in table 8 """ def _get_delta_c1(self, imt): """ Returns them agnitude scaling parameter deltaC1 which is fixed at -0.5 for the lower branch of the in-slab model """ return -0.5