Source code for openquake.hazardlib.gsim.bindi_2011

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
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"""
Module exports :class:`BindiEtAl2011`.
"""
from __future__ import division

import numpy as np

from scipy.constants import g

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


[docs]class BindiEtAl2011(GMPE): """ Implements GMPE developed by D.Bindi, F.Pacor, L.Luzi, R.Puglia, M.Massa, G. Ameri, R. Paolucci and published as "Ground motion prediction equations derived from the Italian strong motion data", Bull Earthquake Eng, DOI 10.1007/s10518-011-9313-z. SA are given up to 2 s. The regressions are developed considering the geometrical mean of the as-recorded horizontal components """ #: Supported tectonic region type is 'active shallow crust' because the #: equations have been derived from data from Italian database ITACA, as #: explained in the 'Introduction'. DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Set of :mod:`intensity measure types <openquake.hazardlib.imt>` #: this GSIM can calculate. A set should contain classes from module #: :mod:`openquake.hazardlib.imt`. DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([ PGA, PGV, SA ]) #: Supported intensity measure component is the geometric mean of two #: horizontal components DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types are inter-event, intra-event #: and total, page 1904 DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([ const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT ]) #: Required site parameter is only Vs30 REQUIRES_SITES_PARAMETERS = set(('vs30', )) #: Required rupture parameters are magnitude and rake (eq. 1). REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag')) #: Required distance measure is RRup (eq. 1). REQUIRES_DISTANCES = set(('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. """ # extracting dictionary of coefficients specific to required # intensity measure type. C = self.COEFFS[imt] imean = (self._compute_magnitude(rup, C) + self._compute_distance(rup, dists, C) + self._get_site_amplification(sites, C) + self._get_mechanism(rup, C)) istddevs = self._get_stddevs(C, stddev_types, num_sites=len(sites.vs30)) # Convert units to g, # but only for PGA and SA (not PGV): if isinstance(imt, (PGA, SA)): mean = np.log((10.0 ** (imean - 2.0)) / g) else: # PGV: mean = np.log(10.0 ** imean) # Return stddevs in terms of natural log scaling stddevs = np.log(10.0 ** np.array(istddevs)) #mean_LogNaturale = np.log((10 ** mean) * 1e-2 / g) return mean, stddevs
def _get_stddevs(self, C, stddev_types, num_sites): """ Return standard deviations as defined in table 1. """ 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['SigmaTot'] + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTRA_EVENT: stddevs.append(C['SigmaW'] + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTER_EVENT: stddevs.append(C['SigmaB'] + np.zeros(num_sites)) return stddevs def _compute_distance(self, rup, dists, C): """ Compute the second term of the equation 1 described on paragraph 3: ``c1 + c2 * (M-Mref) * log(sqrt(Rjb ** 2 + h ** 2)/Rref) - c3*(sqrt(Rjb ** 2 + h ** 2)-Rref)`` """ mref = 5.0 rref = 1.0 rval = np.sqrt(dists.rjb ** 2 + C['h'] ** 2) return (C['c1'] + C['c2'] * (rup.mag - mref)) *\ np.log10(rval / rref) - C['c3'] * (rval - rref) def _compute_magnitude(self, rup, C): """ Compute the third term of the equation 1: e1 + b1 * (M-Mh) + b2 * (M-Mh)**2 for M<=Mh e1 + b3 * (M-Mh) otherwise """ m_h = 6.75 b_3 = 0.0 if rup.mag <= m_h: return C["e1"] + (C['b1'] * (rup.mag - m_h)) +\ (C['b2'] * (rup.mag - m_h) ** 2) else: return C["e1"] + (b_3 * (rup.mag - m_h)) def _get_site_amplification(self, sites, C): """ Compute the fourth term of the equation 1 described on paragraph : The functional form Fs in Eq. (1) represents the site amplification and it is given by FS = sj Cj , for j = 1,...,5, where sj are the coefficients to be determined through the regression analysis, while Cj are dummy variables used to denote the five different EC8 site classes """ ssa, ssb, ssc, ssd, sse = self._get_site_type_dummy_variables(sites) return (C['sA'] * ssa) + (C['sB'] * ssb) + (C['sC'] * ssc) + \ (C['sD'] * ssd) + (C['sE'] * sse) def _get_site_type_dummy_variables(self, sites): """ Get site type dummy variables, five different EC8 site classes he recording sites are classified into 5 classes, based on the shear wave velocity intervals in the uppermost 30 m, Vs30, according to the EC8 (CEN 2003): class A: Vs30 > 800 m/s class B: Vs30 = 360 − 800 m/s class C: Vs30 = 180 - 360 m/s class D: Vs30 < 180 m/s class E: 5 to 20 m of C- or D-type alluvium underlain by stiffer material with Vs30 > 800 m/s. """ ssa = np.zeros(len(sites.vs30)) ssb = np.zeros(len(sites.vs30)) ssc = np.zeros(len(sites.vs30)) ssd = np.zeros(len(sites.vs30)) sse = np.zeros(len(sites.vs30)) # Class E Vs30 = 0 m/s. We fixed this value to define class E idx = (np.fabs(sites.vs30) < 1E-10) sse[idx] = 1.0 # Class D; Vs30 < 180 m/s. idx = (sites.vs30 >= 1E-10) & (sites.vs30 < 180.0) ssd[idx] = 1.0 # SClass C; 180 m/s <= Vs30 <= 360 m/s. idx = (sites.vs30 >= 180.0) & (sites.vs30 < 360.0) ssc[idx] = 1.0 # Class B; 360 m/s <= Vs30 <= 800 m/s. idx = (sites.vs30 >= 360.0) & (sites.vs30 < 800) ssb[idx] = 1.0 # Class A; Vs30 > 800 m/s. idx = (sites.vs30 >= 800.0) ssa[idx] = 1.0 return ssa, ssb, ssc, ssd, sse def _get_mechanism(self, rup, C): """ Compute the fifth term of the equation 1 described on paragraph : Get fault type dummy variables, see Table 1 """ U, SS, NS, RS = self._get_fault_type_dummy_variables(rup) return C['f1'] * NS + C['f2'] * RS + C['f3'] * SS def _get_fault_type_dummy_variables(self, rup): """ Fault type (Strike-slip, Normal, Thrust/reverse) is derived from rake angle. Rakes angles within 30 of horizontal are strike-slip, angles from 30 to 150 are reverse, and angles from -30 to -150 are normal. Note that the 'Unspecified' case is not considered, because rake is always given. """ U, SS, NS, RS = 0, 0, 0, 0 if np.abs(rup.rake) <= 30.0 or (180.0 - np.abs(rup.rake)) <= 30.0: # strike-slip SS = 1 elif rup.rake > 30.0 and rup.rake < 150.0: # reverse RS = 1 else: # normal NS = 1 return U, SS, NS, RS #: Coefficients from SA from Table 1 #: Coefficients from PGA e PGV from Table 5 COEFFS = CoeffsTable(sa_damping=5, table=""" IMT e1 c1 c2 h c3 b1 b2 sA sB sC sD sE f1 f2 f3 f4 SigmaB SigmaW SigmaTot pgv 2.305 -1.5170 0.3260 7.879 0.000000 0.2360 -0.00686 0.0 0.2050 0.269 0.321 0.428 -0.0308 0.0754 -0.0446 0.0 0.194 0.270 0.332 pga 3.672 -1.9400 0.4130 10.322 0.000134 -0.2620 -0.07070 0.0 0.1620 0.240 0.105 0.570 -0.0503 0.1050 -0.0544 0.0 0.172 0.290 0.337 0.04 3.725 -1.9760 0.4220 9.445 0.000270 -0.3150 -0.07870 0.0 0.1610 0.240 0.060 0.614 -0.0442 0.1060 -0.0615 0.0 0.154 0.307 0.343 0.07 3.906 -2.0500 0.4460 9.810 0.000758 -0.3750 -0.07730 0.0 0.1540 0.235 0.057 0.536 -0.0454 0.1030 -0.0576 0.0 0.152 0.324 0.358 0.10 3.796 -1.7940 0.4150 9.500 0.002550 -0.2900 -0.06510 0.0 0.1780 0.247 0.037 0.599 -0.0656 0.1110 -0.0451 0.0 0.154 0.328 0.363 0.15 3.799 -1.5210 0.3200 9.163 0.003720 -0.0987 -0.05740 0.0 0.1740 0.240 0.148 0.740 -0.0755 0.1230 -0.0477 0.0 0.179 0.318 0.365 0.20 3.750 -1.3790 0.2800 8.502 0.003840 0.0094 -0.05170 0.0 0.1560 0.234 0.115 0.556 -0.0733 0.1060 -0.0328 0.0 0.209 0.320 0.382 0.25 3.699 -1.3400 0.2540 7.912 0.003260 0.0860 -0.04570 0.0 0.1820 0.245 0.154 0.414 -0.0568 0.1100 -0.0534 0.0 0.212 0.308 0.374 0.30 3.753 -1.4140 0.2550 8.215 0.002190 0.1240 -0.04350 0.0 0.2010 0.244 0.213 0.301 -0.0564 0.0877 -0.0313 0.0 0.218 0.290 0.363 0.35 3.600 -1.3200 0.2530 7.507 0.002320 0.1540 -0.04370 0.0 0.2200 0.257 0.243 0.235 -0.0523 0.0905 -0.0382 0.0 0.221 0.283 0.359 0.40 3.549 -1.2620 0.2330 6.760 0.002190 0.2250 -0.04060 0.0 0.2290 0.255 0.226 0.202 -0.0565 0.0927 -0.0363 0.0 0.210 0.279 0.349 0.45 3.550 -1.2610 0.2230 6.775 0.001760 0.2920 -0.03060 0.0 0.2260 0.271 0.237 0.181 -0.0597 0.0886 -0.0289 0.0 0.204 0.284 0.350 0.50 3.526 -1.1810 0.1840 5.992 0.001860 0.3840 -0.02500 0.0 0.2180 0.280 0.263 0.168 -0.0599 0.0850 -0.0252 0.0 0.203 0.283 0.349 0.60 3.561 -1.2300 0.1780 6.382 0.001140 0.4360 -0.02270 0.0 0.2190 0.296 0.355 0.142 -0.0559 0.0790 -0.0231 0.0 0.203 0.283 0.348 0.70 3.485 -1.1720 0.1540 5.574 0.000942 0.5290 -0.01850 0.0 0.2100 0.303 0.496 0.134 -0.0461 0.0896 -0.0435 0.0 0.212 0.283 0.354 0.80 3.325 -1.1150 0.1630 4.998 0.000909 0.5450 -0.02150 0.0 0.2100 0.304 0.621 0.150 -0.0457 0.0795 -0.0338 0.0 0.213 0.284 0.355 0.90 3.318 -1.1370 0.1540 5.231 0.000483 0.5630 -0.02630 0.0 0.2120 0.315 0.680 0.154 -0.0351 0.0715 -0.0364 0.0 0.214 0.286 0.357 1.00 3.264 -1.1140 0.1400 5.002 0.000254 0.5990 -0.02700 0.0 0.2210 0.332 0.707 0.152 -0.0298 0.0660 -0.0362 0.0 0.222 0.283 0.360 1.25 2.896 -0.9860 0.1730 4.340 0.000783 0.5790 -0.03360 0.0 0.2440 0.365 0.717 0.183 -0.0207 0.0614 -0.0407 0.0 0.227 0.290 0.368 1.50 2.675 -0.9600 0.1920 4.117 0.000802 0.5750 -0.03530 0.0 0.2510 0.375 0.667 0.203 -0.0140 0.0505 -0.0365 0.0 0.218 0.303 0.373 1.75 2.584 -1.0060 0.2050 4.505 0.000427 0.5740 -0.03710 0.0 0.2520 0.357 0.593 0.220 0.00154 0.0370 -0.0385 0.0 0.219 0.305 0.376 2.00 2.537 -1.0090 0.1930 4.373 0.000164 0.5970 -0.03670 0.0 0.2450 0.352 0.540 0.226 0.00512 0.0350 -0.0401 0.0 0.211 0.308 0.373 """)