Source code for openquake.hazardlib.gsim.abrahamson_2014

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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"""
Module exports :class:`AbrahamsonEtAl2014`
               :class:`AbrahamsonEtAl2014RegCHN`
               :class:`AbrahamsonEtAl2014RegJPN`
               :class:`AbrahamsonEtAl2014RegTWN`
"""
import copy
import numpy as np

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

METRES_PER_KM = 1000.0


[docs]class AbrahamsonEtAl2014(GMPE): """ Implements GMPE by Abrahamson, Silva and Kamai developed within the the PEER West 2 Project. This GMPE is described in a paper published in 2014 on Earthquake Spectra, Volume 30, Number 3 and titled 'Summary of the ASK14 Ground Motion Relation for Active Crustal Regions'. """ #: Supported tectonic region type is active shallow crust, see title! DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure types are spectral acceleration, peak #: ground velocity and peak ground acceleration, see tables 4 #: pages 1036 DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([ PGA, PGV, SA ]) #: Supported intensity measure component is orientation-independent #: average horizontal :attr:`~openquake.hazardlib.const.IMC.RotD50`, #: see page 1025. DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50 #: Supported standard deviation types are inter-event, intra-event #: and total, see paragraph "Equations for standard deviations", page #: 1046. DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([ const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT ]) #: Required site parameters are Vs30 and Z1.0, see table 2, page 1031 #: Unit of measure for Z1.0 is [m] REQUIRES_SITES_PARAMETERS = {'vs30', 'z1pt0', 'vs30measured'} #: Required rupture parameters are magnitude, rake, dip, ztor, and width #: (see table 2, page 1031) REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'dip', 'ztor', 'width'} #: Required distance measures are Rrup, Rjb, Ry0 and Rx (see Table 2, #: page 1031). REQUIRES_DISTANCES = {'rrup', 'rjb', 'rx', 'ry0'} #: Reference rock conditions as defined at page DEFINED_FOR_REFERENCE_VELOCITY = 1180
[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. """ # get the necessary set of coefficients C = self.COEFFS[imt] # compute median sa on rock (vs30=1180m/s). Used for site response # term calculation sa1180 = np.exp(self._get_sa_at_1180(C, imt, sites, rup, dists)) # get the mean value mean = (self._get_basic_term(C, rup, dists) + self._get_faulting_style_term(C, rup) + self._get_site_response_term(C, imt, sites.vs30, sa1180) + self._get_hanging_wall_term(C, dists, rup) + self._get_top_of_rupture_depth_term(C, imt, rup) + self._get_soil_depth_term(C, sites.z1pt0 / METRES_PER_KM, sites.vs30) ) mean += self._get_regional_term(C, imt, sites.vs30, dists.rrup) # get standard deviations stddevs = self._get_stddevs(C, imt, rup, sites, stddev_types, sa1180, dists) return mean, stddevs
def _get_sa_at_1180(self, C, imt, sites, rup, dists): """ Compute and return mean imt value for rock conditions (vs30 = 1100 m/s) """ # reference vs30 = 1180 m/s vs30_1180 = np.ones_like(sites.vs30) * 1180. # reference shaking intensity = 0 ref_iml = np.zeros_like(sites.vs30) # fake Z1.0 - Since negative it will be replaced by the default Z1.0 # for the corresponding region fake_z1pt0 = np.ones_like(sites.vs30) * -1 return (self._get_basic_term(C, rup, dists) + self._get_faulting_style_term(C, rup) + self._get_site_response_term(C, imt, vs30_1180, ref_iml) + self._get_hanging_wall_term(C, dists, rup) + self._get_top_of_rupture_depth_term(C, imt, rup) + self._get_soil_depth_term(C, fake_z1pt0, vs30_1180) + self._get_regional_term(C, imt, vs30_1180, dists.rrup) ) def _get_basic_term(self, C, rup, dists): """ Compute and return basic form, see page 1030. """ # Fictitious depth calculation if rup.mag > 5.: c4m = C['c4'] elif rup.mag > 4.: c4m = C['c4'] - (C['c4']-1.) * (5. - rup.mag) else: c4m = 1. R = np.sqrt(dists.rrup**2. + c4m**2.) # basic form base_term = C['a1'] * np.ones_like(dists.rrup) + C['a17'] * dists.rrup # equation 2 at page 1030 if rup.mag >= C['m1']: base_term += (C['a5'] * (rup.mag - C['m1']) + C['a8'] * (8.5 - rup.mag)**2. + (C['a2'] + C['a3'] * (rup.mag - C['m1'])) * np.log(R)) elif rup.mag >= self.CONSTS['m2']: base_term += (C['a4'] * (rup.mag - C['m1']) + C['a8'] * (8.5 - rup.mag)**2. + (C['a2'] + C['a3'] * (rup.mag - C['m1'])) * np.log(R)) else: base_term += (C['a4'] * (self.CONSTS['m2'] - C['m1']) + C['a8'] * (8.5 - self.CONSTS['m2'])**2. + C['a6'] * (rup.mag - self.CONSTS['m2']) + C['a7'] * (rup.mag - self.CONSTS['m2'])**2. + (C['a2'] + C['a3'] * (self.CONSTS['m2'] - C['m1'])) * np.log(R)) return base_term def _get_faulting_style_term(self, C, rup): """ Compute and return faulting style term, that is the sum of the second and third terms in equation 1, page 74. """ # this implements equations 5 and 6 at page 1032. f7 is the # coefficient for reverse mechanisms while f8 is the correction # factor for normal ruptures if rup.mag > 5.0: f7 = C['a11'] f8 = C['a12'] elif rup.mag >= 4: f7 = C['a11'] * (rup.mag - 4.) f8 = C['a12'] * (rup.mag - 4.) else: f7 = 0.0 f8 = 0.0 # ranges of rake values for each faulting mechanism are specified in # table 2, page 1031 return (f7 * float(rup.rake > 30 and rup.rake < 150) + f8 * float(rup.rake > -150 and rup.rake < -30)) def _get_vs30star(self, vs30, imt): """ This computes equations 8 and 9 at page 1034 """ # compute the v1 value (see eq. 9, page 1034) if imt.name == "SA": t = imt.period if t <= 0.50: v1 = 1500.0 elif t < 3.0: v1 = np.exp(-0.35 * np.log(t / 0.5) + np.log(1500.)) else: v1 = 800.0 elif imt.name == "PGA": v1 = 1500.0 else: # This covers the PGV case v1 = 1500.0 # set the vs30 star value (see eq. 8, page 1034) vs30_star = np.ones_like(vs30) * vs30 vs30_star[vs30 >= v1] = v1 return vs30_star def _get_site_response_term(self, C, imt, vs30, sa1180): """ Compute and return site response model term see page 1033 """ # vs30 star vs30_star = self._get_vs30star(vs30, imt) # compute the site term site_resp_term = np.zeros_like(vs30) gt_vlin = vs30 >= C['vlin'] lw_vlin = vs30 < C['vlin'] # compute site response term for sites with vs30 greater than vlin vs30_rat = vs30_star / C['vlin'] site_resp_term[gt_vlin] = ((C['a10'] + C['b'] * self.CONSTS['n']) * np.log(vs30_rat[gt_vlin])) # compute site response term for sites with vs30 lower than vlin site_resp_term[lw_vlin] = (C['a10'] * np.log(vs30_rat[lw_vlin]) - C['b'] * np.log(sa1180[lw_vlin] + C['c']) + C['b'] * np.log(sa1180[lw_vlin] + C['c'] * vs30_rat[lw_vlin] ** self.CONSTS['n'])) return site_resp_term def _hw_taper1(self, dists, rup): # Compute taper t1 T1 = np.ones_like(dists.rx) T1 *= 60./45. if rup.dip <= 30. else (90.-rup.dip)/45.0 return T1 def _hw_taper2(self, dists, rup): # Compute taper t2 (eq 12 at page 1039) - a2hw set to 0.2 as # indicated at page 1041 T2 = np.zeros_like(dists.rx) a2hw = 0.2 if rup.mag > 6.5: T2 += (1. + a2hw * (rup.mag - 6.5)) elif rup.mag > 5.5: T2 += (1. + a2hw * (rup.mag - 6.5) - (1. - a2hw) * (rup.mag - 6.5)**2) else: T2 *= 0. return T2 def _hw_taper3(self, dists, rup): # Compute taper t3 (eq. 13 at page 1039) - r1 and r2 specified at # page 1040 T3 = np.zeros_like(dists.rx) r1 = rup.width * np.cos(np.radians(rup.dip)) r2 = 3. * r1 # idx = dists.rx < r1 T3[idx] = (np.ones_like(dists.rx)[idx] * self.CONSTS['h1'] + self.CONSTS['h2'] * (dists.rx[idx] / r1) + self.CONSTS['h3'] * (dists.rx[idx] / r1)**2) # idx = ((dists.rx >= r1) & (dists.rx <= r2)) T3[idx] = 1. - (dists.rx[idx] - r1) / (r2 - r1) return T3 def _hw_taper4(self, dists, rup): # Compute taper t4 (eq. 14 at page 1040) T4 = np.zeros_like(dists.rx) # if rup.ztor <= 10.: T4 += (1. - rup.ztor**2. / 100.) return T4 def _hw_taper5(self, dists, rup): # Compute T5 (eq 15a at page 1040) - ry1 computed according to # suggestions provided at page 1040 T5 = np.zeros_like(dists.rx) ry1 = dists.rx * np.tan(np.radians(20.)) # idx = (dists.ry0 - ry1) <= 0.0 T5[idx] = 1. # idx = (((dists.ry0 - ry1) > 0.0) & ((dists.ry0 - ry1) < 5.0)) T5[idx] = 1. - (dists.ry0[idx] - ry1[idx]) / 5.0 return T5 def _get_hanging_wall_term(self, C, dists, rup): """ Compute and return hanging wall model term, see page 1038. """ if rup.dip == 90.0: return np.zeros_like(dists.rx) else: Fhw = np.zeros_like(dists.rx) Fhw[dists.rx > 0] = 1. # Taper 1 T1 = self._hw_taper1(dists, rup) # Taper 2 T2 = self._hw_taper2(dists, rup) # Taper 3 T3 = self._hw_taper3(dists, rup) # Taper 4 T4 = self._hw_taper4(dists, rup) # Taper 5 T5 = self._hw_taper5(dists, rup) # Finally, compute the hanging wall term return Fhw*C['a13']*T1*T2*T3*T4*T5 def _get_top_of_rupture_depth_term(self, C, imt, rup): """ Compute and return top of rupture depth term. See paragraph 'Depth-to-Top of Rupture Model', page 1042. """ if rup.ztor >= 20.0: return C['a15'] else: return C['a15'] * rup.ztor / 20.0 def _get_z1pt0ref(self, vs30): """ This computes the reference depth to the 1.0 km/s interface using equation 18 at page 1042 of Abrahamson et al. (2014) """ return (1. / 1000.) * np.exp((-7.67 / 4.)*np.log((vs30**4 + 610.**4) / (1360.**4 + 610.**4))) def _get_soil_depth_term(self, C, z1pt0, vs30): """ Compute and return soil depth term. See page 1042. """ # Get reference z1pt0 z1ref = self._get_z1pt0ref(vs30) # Get z1pt0 z10 = copy.deepcopy(z1pt0) # This is used for the calculation of the motion on reference rock idx = z1pt0 < 0 z10[idx] = z1ref[idx] factor = np.log((z10 + 0.01) / (z1ref + 0.01)) # Here we use a linear interpolation as suggested in the 'Application # guidelines' at page 1044 # Above 700 m/s the trend is flat, but we extend the Vs30 range to # 6,000 m/s (basically the upper limit for mantle shear wave velocity # on earth) to allow extrapolation without throwing an error. f2 = interpolate.interp1d( [0.0, 150, 250, 400, 700, 1000, 6000], [C['a43'], C['a43'], C['a44'], C['a45'], C['a46'], C['a46'], C['a46']], kind='linear') return f2(vs30) * factor def _get_regional_term(self, C, imt, vs30, rrup): """ In accordance with Abrahamson et al. (2014) we assume California as the default region hence here the regional term is assumed = 0. """ return 0. def _get_stddevs(self, C, imt, rup, sites, stddev_types, sa1180, dists): """ Return standard deviations as described in paragraph 'Equations for standard deviation', page 1046. """ std_intra = self._get_intra_event_std(C, rup.mag, sa1180, sites.vs30, sites.vs30measured, dists.rrup) std_inter = self._get_inter_event_std(C, rup.mag, sa1180, sites.vs30) 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(np.sqrt(std_intra ** 2 + std_inter ** 2)) elif stddev_type == const.StdDev.INTRA_EVENT: stddevs.append(std_intra) elif stddev_type == const.StdDev.INTER_EVENT: stddevs.append(std_inter) return stddevs def _get_intra_event_std(self, C, mag, sa1180, vs30, vs30measured, rrup): """ Returns Phi as described at pages 1046 and 1047 """ phi_al = self._get_phi_al_regional(C, mag, vs30measured, rrup) derAmp = self._get_derivative(C, sa1180, vs30) phi_amp = 0.4 idx = phi_al < phi_amp if np.any(idx): # In the case of small magnitudes and long periods it is possible # for phi_al to take a value less than phi_amp, which would return # a complex value. According to the GMPE authors in this case # phi_amp should be reduced such that it is fractionally smaller # than phi_al phi_amp = 0.4 * np.ones_like(phi_al) phi_amp[idx] = 0.99 * phi_al[idx] phi_b = np.sqrt(phi_al**2 - phi_amp**2) phi = np.sqrt(phi_b**2 * (1 + derAmp)**2 + phi_amp**2) return phi def _get_derivative(self, C, sa1180, vs30): """ Returns equation 30 page 1047 """ derAmp = np.zeros_like(vs30) n = self.CONSTS['n'] c = C['c'] b = C['b'] idx = vs30 < C['vlin'] derAmp[idx] = (b * sa1180[idx] * (-1./(sa1180[idx]+c) + 1./(sa1180[idx] + c*(vs30[idx]/C['vlin'])**n))) return derAmp def _get_phi_al_regional(self, C, mag, vs30measured, rrup): """ Returns intra-event (Phi) standard deviation (equation 24, page 1046) """ phi_al = np.ones((len(vs30measured))) s1 = np.ones_like(phi_al) * C['s1e'] s2 = np.ones_like(phi_al) * C['s2e'] s1[vs30measured] = C['s1m'] s2[vs30measured] = C['s2m'] if mag < 4: phi_al *= s1 elif mag <= 6: phi_al *= s1 + (s2 - s1) / 2. * (mag - 4.) else: phi_al *= s2 return phi_al def _get_inter_event_std(self, C, mag, sa1180, vs30): """ Returns inter event (tau) standard deviation (equation 25, page 1046) """ if mag < 5: tau_al = C['s3'] elif mag <= 7: tau_al = C['s3'] + (C['s4'] - C['s3']) / 2. * (mag - 5.) else: tau_al = C['s4'] tau_b = tau_al tau = tau_b * (1 + self._get_derivative(C, sa1180, vs30)) return tau #: Coefficient tables as per annex B of Abrahamson et al. (2014) COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT m1 vlin b c c4 a1 a2 a3 a4 a5 a6 a7 a8 a10 a11 a12 a13 a14 a15 a17 a43 a44 a45 a46 a25 a28 a29 a31 a36 a37 a38 a39 a40 a41 a42 s1e s2e s3 s4 s1m s2m s5 s6 pga 6.75 660 -1.47 2.4 4.5 0.587 -0.79 0.275 -0.1 -0.41 2.154 0.0 -0.015 1.735 0 -0.1 0.6 -0.3 1.1 -0.0072 0.1 0.05 0 -0.05 -0.0015 0.0025 -0.0034 -0.1503 0.265 0.337 0.188 0 0.088 -0.196 0.044 0.754 0.52 0.47 0.36 0.741 0.501 0.54 0.6300 pgv 6.75 330 -2.02 2400 4.5 5.975 -0.919 0.275 -0.1 -0.41 2.366 0.0 -0.094 2.36 0 -0.1 0.25 0.22 0.3 -0.0005 0.28 0.15 0.09 0.07 -0.0001 0.0005 -0.0037 -0.1462 0.377 0.212 0.157 0 0.095 -0.038 0.065 0.662 0.51 0.38 0.38 0.66 0.51 0.58 0.5300 0.01 6.75 660 -1.47 2.4 4.5 0.587 -0.790 0.275 -0.1 -0.41 2.154 0.0 -0.015 1.735 0 -0.1 0.6 -0.3 1.1 -0.0072 0.1 0.05 0 -0.05 -0.0015 0.0025 -0.0034 -0.1503 0.265 0.337 0.188 0 0.088 -0.196 0.044 0.754 0.52 0.47 0.36 0.741 0.501 0.54 0.6300 0.02 6.75 680 -1.46 2.4 4.5 0.598 -0.790 0.275 -0.1 -0.41 2.146 0.0 -0.015 1.718 0 -0.1 0.6 -0.3 1.1 -0.0073 0.1 0.05 0 -0.05 -0.0015 0.0024 -0.0033 -0.1479 0.255 0.328 0.184 0 0.088 -0.194 0.061 0.76 0.52 0.47 0.36 0.747 0.501 0.54 0.6300 0.03 6.75 770 -1.39 2.4 4.5 0.602 -0.790 0.275 -0.1 -0.41 2.157 0.0 -0.015 1.615 0 -0.1 0.6 -0.3 1.1 -0.0075 0.1 0.05 0 -0.05 -0.0016 0.0023 -0.0034 -0.1447 0.249 0.32 0.18 0 0.093 -0.175 0.162 0.781 0.52 0.47 0.36 0.769 0.501 0.55 0.6300 0.05 6.75 915 -1.22 2.4 4.5 0.707 -0.790 0.275 -0.1 -0.41 2.085 0.0 -0.015 1.358 0 -0.1 0.6 -0.3 1.1 -0.008 0.1 0.05 0 -0.05 -0.002 0.0027 -0.0033 -0.1326 0.202 0.289 0.167 0 0.133 -0.09 0.451 0.81 0.53 0.47 0.36 0.798 0.512 0.56 0.6500 0.075 6.75 960 -1.15 2.4 4.5 0.973 -0.790 0.275 -0.1 -0.41 2.029 0.0 -0.015 1.258 0 -0.1 0.6 -0.3 1.1 -0.0089 0.1 0.05 0 -0.05 -0.0027 0.0032 -0.0029 -0.1353 0.126 0.275 0.173 0 0.186 0.09 0.506 0.81 0.54 0.47 0.36 0.798 0.522 0.57 0.6900 0.1 6.75 910 -1.23 2.4 4.5 1.169 -0.790 0.275 -0.1 -0.41 2.041 0.0 -0.015 1.31 0 -0.1 0.6 -0.3 1.1 -0.0095 0.1 0.05 0 -0.05 -0.0033 0.0036 -0.0025 -0.1128 0.022 0.256 0.189 0 0.16 0.006 0.335 0.81 0.55 0.47 0.36 0.795 0.527 0.57 0.7000 0.15 6.75 740 -1.59 2.4 4.5 1.442 -0.790 0.275 -0.1 -0.41 2.121 0.0 -0.022 1.66 0 -0.1 0.6 -0.3 1.1 -0.0095 0.1 0.05 0 -0.05 -0.0035 0.0033 -0.0025 0.0383 -0.136 0.162 0.108 0 0.068 -0.156 -0.084 0.801 0.56 0.47 0.36 0.773 0.519 0.58 0.7000 0.2 6.75 590 -2.01 2.4 4.5 1.637 -0.790 0.275 -0.1 -0.41 2.224 0.0 -0.03 2.22 0 -0.1 0.6 -0.3 1.1 -0.0086 0.1 0.05 0 -0.03 -0.0033 0.0027 -0.0031 0.0775 -0.078 0.224 0.115 0 0.048 -0.274 -0.178 0.789 0.565 0.47 0.36 0.753 0.514 0.59 0.7000 0.25 6.75 495 -2.41 2.4 4.5 1.701 -0.790 0.275 -0.1 -0.41 2.312 0.0 -0.038 2.77 0 -0.1 0.6 -0.24 1.1 -0.0074 0.1 0.05 0 0 -0.0029 0.0024 -0.0036 0.0741 0.037 0.248 0.122 0 0.055 -0.248 -0.187 0.77 0.57 0.47 0.36 0.729 0.513 0.61 0.7000 0.3 6.75 430 -2.76 2.4 4.5 1.712 -0.790 0.275 -0.1 -0.41 2.338 0.0 -0.045 3.25 0 -0.1 0.6 -0.19 1.03 -0.0064 0.1 0.05 0.03 0.03 -0.0027 0.002 -0.0039 0.2548 -0.091 0.203 0.096 0 0.073 -0.203 -0.159 0.74 0.58 0.47 0.36 0.693 0.519 0.63 0.7000 0.4 6.75 360 -3.28 2.4 4.5 1.662 -0.790 0.275 -0.1 -0.41 2.469 0.0 -0.055 3.99 0 -0.1 0.58 -0.11 0.92 -0.0043 0.1 0.07 0.06 0.06 -0.0023 0.001 -0.0048 0.2136 0.129 0.232 0.123 0 0.143 -0.154 -0.023 0.699 0.59 0.47 0.36 0.644 0.524 0.66 0.7000 0.5 6.75 340 -3.6 2.4 4.5 1.571 -0.790 0.275 -0.1 -0.41 2.559 0.0 -0.065 4.45 0 -0.1 0.56 -0.04 0.84 -0.0032 0.1 0.1 0.1 0.09 -0.002 0.0008 -0.005 0.1542 0.31 0.252 0.134 0 0.16 -0.159 -0.029 0.676 0.6 0.47 0.36 0.616 0.532 0.69 0.7000 0.75 6.75 330 -3.8 2.4 4.5 1.299 -0.790 0.275 -0.1 -0.41 2.682 0.0 -0.095 4.75 0 -0.1 0.53 0.07 0.68 -0.0025 0.14 0.14 0.14 0.13 -0.001 0.0007 -0.0041 0.0787 0.505 0.208 0.129 0 0.158 -0.141 0.061 0.631 0.615 0.47 0.36 0.566 0.548 0.73 0.6900 1 6.75 330 -3.5 2.4 4.5 1.043 -0.790 0.275 -0.1 -0.41 2.763 0.0 -0.11 4.3 0 -0.1 0.5 0.15 0.57 -0.0025 0.17 0.17 0.17 0.14 -0.0005 0.0007 -0.0032 0.0476 0.358 0.208 0.152 0 0.145 -0.144 0.062 0.609 0.63 0.47 0.36 0.541 0.565 0.77 0.6800 1.5 6.75 330 -2.4 2.4 4.5 0.665 -0.790 0.275 -0.1 -0.41 2.836 0.0 -0.124 2.6 0 -0.1 0.42 0.27 0.42 -0.0022 0.22 0.21 0.2 0.16 -0.0004 0.0006 -0.002 -0.0163 0.131 0.108 0.118 0 0.131 -0.126 0.037 0.578 0.64 0.47 0.36 0.506 0.576 0.8 0.6600 2 6.75 330 -1 2.4 4.5 0.329 -0.790 0.275 -0.1 -0.41 2.897 0.0 -0.138 0.55 0 -0.1 0.35 0.35 0.31 -0.0019 0.26 0.25 0.22 0.16 -0.0002 0.0003 -0.0017 -0.1203 0.123 0.068 0.119 0 0.083 -0.075 -0.143 0.555 0.65 0.47 0.36 0.48 0.587 0.8 0.6200 3 6.82 330 0 2.4 4.5 -0.060 -0.790 0.275 -0.1 -0.41 2.906 0.0 -0.172 -0.95 0 -0.1 0.2 0.46 0.16 -0.0015 0.34 0.3 0.23 0.16 0 0 -0.002 -0.2719 0.109 -0.023 0.093 0 0.07 -0.021 -0.028 0.548 0.64 0.47 0.36 0.472 0.576 0.8 0.5500 4 6.92 330 0 2.4 4.5 -0.299 -0.790 0.275 -0.1 -0.41 2.889 0.0 -0.197 -0.95 0 -0.1 0 0.54 0.05 -0.001 0.41 0.32 0.23 0.14 0 0 -0.002 -0.2958 0.135 0.028 0.084 0 0.101 0.072 -0.097 0.527 0.63 0.47 0.36 0.447 0.565 0.76 0.5200 5 7 330 0 2.4 4.5 -0.562 -0.765 0.275 -0.1 -0.41 2.898 0.0 -0.218 -0.93 0 -0.1 0 0.61 -0.04 -0.001 0.51 0.32 0.22 0.13 0 0 -0.002 -0.2718 0.189 0.031 0.058 0 0.095 0.205 0.015 0.505 0.63 0.47 0.36 0.425 0.568 0.72 0.5000 6 7.06 330 0 2.4 4.5 -0.875 -0.711 0.275 -0.1 -0.41 2.896 0.0 -0.235 -0.91 0 -0.2 0 0.65 -0.11 -0.001 0.55 0.32 0.2 0.1 0 0 -0.002 -0.2517 0.215 0.024 0.065 0 0.133 0.285 0.104 0.477 0.63 0.47 0.36 0.395 0.571 0.7 0.5000 7.5 7.15 330 0 2.4 4.5 -1.303 -0.634 0.275 -0.1 -0.41 2.870 0.0 -0.255 -0.87 0 -0.2 0 0.72 -0.19 -0.001 0.49 0.28 0.17 0.09 0 0 -0.002 -0.14 0.15 -0.07 0 0 0.151 0.329 0.299 0.457 0.63 0.47 0.36 0.378 0.575 0.67 0.5000 10 7.25 330 0 2.4 4.5 -1.928 -0.529 0.275 -0.1 -0.41 2.843 0.0 -0.285 -0.8 0 -0.2 0 0.8 -0.3 -0.001 0.42 0.22 0.14 0.08 0 0 -0.002 -0.0216 0.092 -0.159 -0.05 0 0.124 0.301 0.243 0.429 0.63 0.47 0.36 0.359 0.585 0.64 0.5000 """) #: equation constants (that are IMT independent) CONSTS = { 'n': 1.5, # m2 specified at page 1032 (top) 'm2': 5.00, # h1, h2, h3 specified at page 1040 (top) 'h1': +0.25, 'h2': +1.50, 'h3': -0.75, }
[docs]class AbrahamsonEtAl2014RegTWN(AbrahamsonEtAl2014): """ Implements GMPE developed by Abrahamson, Silva and Kamai in 2014 as part of the PEER West 2 Project. The GMPE is described in a paper published in 2014 on Earthquake Spectra, Volume 30, Number 3. Regional corrections for Taiwan """ def _get_regional_term(self, C, imt, vs30, rrup): """ In accordance with Abrahamson et al. (2014) we assume as the default region California """ vs30star = self._get_vs30star(vs30, imt) return C['a31'] * np.log(vs30star/C['vlin']) + C['a25'] * rrup
[docs]class AbrahamsonEtAl2014RegCHN(AbrahamsonEtAl2014): """ Implements GMPE developed by Abrahamson, Silva and Kamai in 2014 as part of the PEER West 2 Project. The GMPE is described in a paper published in 2014 on Earthquake Spectra, Volume 30, Number 3. Regional corrections for China """ def _get_regional_term(self, C, imt, vs30, rrup): """ In accordance with Abrahamson et al. (2014) we assume as the default region California """ return C['a28'] * rrup
[docs]class AbrahamsonEtAl2014RegJPN(AbrahamsonEtAl2014): """ Implements GMPE developed by Abrahamson, Silva and Kamai in 2014 as part of the PEER West 2 Project. The GMPE is described in a paper published in 2014 on Earthquake Spectra, Volume 30, Number 3. Regional corrections for Japan """ def _get_z1pt0ref(self, vs30): """ This provides the default depth to the 1.0 km/s interface for Japan """ return 1./1000. * np.exp(-5.23/2.*np.log((vs30**2+412.**2.) / (1360.**2+412**2.))) def _get_regional_term(self, C, imt, vs30, rrup): """ Compute regional term for Japan. See page 1043 """ f3 = interpolate.interp1d( [150, 250, 350, 450, 600, 850, 1150, 2000], [C['a36'], C['a37'], C['a38'], C['a39'], C['a40'], C['a41'], C['a42'], C['a42']], kind='linear') return f3(vs30) + C['a29'] * rrup def _get_phi_al_regional(self, C, mag, vs30measured, rrup): """ Returns intra-event (Tau) standard deviation (equation 26, page 1046) """ phi_al = np.ones((len(vs30measured))) idx = rrup < 30 phi_al[idx] *= C['s5'] idx = ((rrup <= 80) & (rrup >= 30.)) phi_al[idx] *= C['s5'] + (C['s6'] - C['s5']) / 50. * (rrup[idx] - 30.) idx = rrup > 80 phi_al[idx] *= C['s6'] return phi_al