Source code for openquake.hazardlib.gsim.cauzzi_2014

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2019 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.

"""
Module exports :class:`CauzziEtAl2014`,
               :class:`CauzziEtAl2014NoSOF`,
               :class:`CauzziEtAl2014FixedVs30`,
               :class:`CauzziEtAl2014FixedVs30NoSOF`,
               :class:`CauzziEtAl2014Eurocode8`,
               :class:`CauzziEtAl2014Eurocode8NoSOF`,
"""
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g

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


[docs]class CauzziEtAl2014(GMPE): """ Implements GMPE developed by Carlo Cauzzi et al (2014) and published as C.Cauzzi, E. Faccioli, M. Vanini and A. Bianchini (2014) "Updated predictive equations for broadband (0.0 - 10.0 s) horizontal response spectra and peak ground motions, based on a global dataset of digital acceleration records", Bulletin of Earthquake Engineering, In Press Spectral acceleration (SA) values are obtained from displacement response spectrum (DSR) values (as provided by the original equations) using the following formula :: SA = DSR * (2 * π / T) ** 2 """ #: Supported tectonic region type is active shallow crust, DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST #: Supported intensity measure types are spectral acceleration, peak #: ground acceleration and peak ground velocity. #: The original paper provides coefficients for PGA and PGV, while SA #: is obtained from displacement response spectrum values. #: Coefficients for PGA are taken from the SA (0.01 s) spectral #: acceleration, as indicated in Page 11 (at the time of writing) #: of Cauzzi et al. (2014) DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([ PGA, PGV, SA ]) #: Supported intensity measure component is the geometric mean of two #: horizontal components #: :attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`, DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types are inter-event, intra-event and #: total DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([ const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT, const.StdDev.TOTAL ]) #: Required site parameter is only Vs30 REQUIRES_SITES_PARAMETERS = set(('vs30', )) #: Required rupture parameters are magnitude and rake REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag')) #: Required distance measure is Rrup, 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 C = self.COEFFS[imt] mean = self._compute_mean(C, rup, dists, sites, imt) stddevs = self._get_stddevs(C, stddev_types, sites.vs30.shape[0]) return mean, stddevs
def _compute_mean(self, C, rup, dists, sites, imt): """ Returns the mean ground motion acceleration and velocity """ mean = (self._get_magnitude_scaling_term(C, rup.mag) + self._get_distance_scaling_term(C, rup.mag, dists.rrup) + self._get_style_of_faulting_term(C, rup.rake) + self._get_site_amplification_term(C, sites.vs30)) # convert from cm/s**2 to g for SA and from cm/s**2 to g for PGA (PGV # is already in cm/s) and also convert from base 10 to base e. if imt.name == "PGA": mean = np.log((10 ** mean) * ((2 * np.pi / 0.01) ** 2) * 1e-2 / g) elif imt.name == "SA": mean = np.log((10 ** mean) * ((2 * np.pi / imt.period) ** 2) * 1e-2 / g) else: mean = np.log(10 ** mean) return mean def _get_magnitude_scaling_term(self, C, mag): """ Returns the magnitude term """ return C["c1"] + (C["m1"] * mag) + (C["m2"] * (mag ** 2.)) def _get_distance_scaling_term(self, C, mag, rrup): """ Returns the distance scaling parameter """ return (C["r1"] + C["r2"] * mag) * np.log10(rrup + C["r3"]) def _get_style_of_faulting_term(self, C, rake): """ Returns the style of faulting term. Cauzzi et al. determind SOF from the plunge of the B-, T- and P-axes. For consistency with existing GMPEs the Wells & Coppersmith model is preferred """ if rake > -150.0 and rake <= -30.0: return C['fN'] elif rake > 30.0 and rake <= 150.0: return C['fR'] else: return C['fSS'] def _get_site_amplification_term(self, C, vs30): """ Returns the site amplification scaling term assuming period dependent reference vs30 """ return C["bV"] * np.log10(vs30 / C["VA"]) def _get_stddevs(self, C, stddev_types, num_sites): """ Return total standard deviation. """ 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.log(10.0 ** C['sM']) + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTRA_EVENT: stddevs.append(np.log(10.0 ** C['f']) + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTER_EVENT: stddevs.append(np.log(10.0 ** C["tM"]) + np.zeros(num_sites)) return stddevs #: Coefficient table constructed from the electronic suplements of the #: original paper. COEFFS = CoeffsTable(sa_damping=5, table="""\ imt c1 m1 m2 r1 r2 r3 sB sC sD bV bV800 VA fN fR fSS f t s tM sM pgv 0.4422159946365680 0.5482239378818140 -0.0319470258028777 -2.8457788432226700 0.2406737047414070 6.51696666287798000 0.1919277313361110 0.3706196443240230 0.4978018189249720 -0.6909580227999990 -0.7596804404000000 883.9565406477700000 -0.1433313027208760 0.0184633160924233 0.0049897699311183 0.2398935826956730 0.2213004346208430 0.3263783286033860 0.2149404298227920 0.3220998664588330 pga -2.1961743955816300 0.5237450060972680 -0.0609447663010394 -3.8019035608295600 0.3550808121411740 11.6415555876916000 0.2106985279596590 0.2825106921224770 0.2828846140789600 -0.3100704816000000 -0.7024376883999990 2319.1859784562300000 -0.0241122431339601 0.0724633666482452 -0.0563165754085399 0.2589229720745850 0.2214506097241730 0.3407073201666570 0.2162221044760760 0.3373323345485870 0.0100 -2.1961743955816300 0.5237450060972680 -0.0609447663010394 -3.8019035608295600 0.3550808121411740 11.6415555876916000 0.2106985279596590 0.2825106921224770 0.2828846140789600 -0.3100704816000000 -0.7024376883999990 2319.1859784562300000 -0.0241122431339601 0.0724633666482452 -0.0563165754085399 0.2589229720745850 0.2214506097241730 0.3407073201666570 0.2162221044760760 0.3373323345485870 0.0200 -1.8195694621090300 0.6453679917780000 -0.0718828302259198 -3.8644883929436800 0.3593203519694770 12.1350058517031000 0.1992376827391620 0.2657559899035650 0.2597832779404480 -0.2838417797000000 -0.6697416278000000 2528.8050326671200000 -0.0272261357768130 0.0770853044555010 -0.0589959439154124 0.2592700212170700 0.2266408762153660 0.3443646768667910 0.2208310066257620 0.3405690493706790 0.0300 -1.2943572408433100 0.6982707545157320 -0.0795637931948720 -4.0443482492067200 0.3765163250150630 13.3154555674385000 0.1781152657707780 0.2315977870956060 0.2152815315755380 -0.2288226422000000 -0.6191416576999990 3228.4186287294800000 -0.0333340581611655 0.0835931466396944 -0.0620510202333671 0.2610359421517940 0.2329378875769420 0.3498568601069340 0.2262184621898820 0.3454193910750090 0.0400 -0.6931089735055480 0.7088746113257160 -0.0846090922165347 -4.2569567103123300 0.3973949524463510 14.9701297686778000 0.1812772493016900 0.2182921854255120 0.1831111109272540 -0.1573206416000000 -0.6076234879999990 8228.7311143995100000 -0.0383834128731151 0.0898513499539263 -0.0655039981465477 0.2655226521597100 0.2370812514738440 0.3559631983932190 0.2293557959689310 0.3508651592199890 0.0500 -0.1738965355678180 0.7038280147755070 -0.0875507720994941 -4.4155335972196800 0.4140306595178590 15.9634085011888000 0.1678531023791990 0.1863342553869610 0.1392855607298930 -0.1000000000000000 -0.5639501998999990 30552.3271673005000000 -0.0389955855635790 0.0960304396771990 -0.0706779148995298 0.2702569776994650 0.2423624069839720 0.3630129065395790 0.2337736891265200 0.3573359367920780 0.0600 0.2069820440679000 0.6906315133559440 -0.0888413835088005 -4.4921203206778700 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[docs]class CauzziEtAl2014NoSOF(CauzziEtAl2014): """ Returns the Cauzzi et al (GMPE) for the case when no style-of-faulting is input. This modifies both the expected ground motion as well as the inter-event (and thus total) standard deviations. """ #: Required rupture parameters are magnitude REQUIRES_RUPTURE_PARAMETERS = set(('mag',)) def _compute_mean(self, C, rup, dists, sites, imt): """ Returns the mean ground motion acceleration and velocity """ mean = (self._get_magnitude_scaling_term(C, rup.mag) + self._get_distance_scaling_term(C, rup.mag, dists.rrup) + self._get_site_amplification_term(C, sites.vs30)) # convert from cm/s**2 to g for SA and from m/s**2 to g for PGA (PGV # is already in cm/s) and also convert from base 10 to base e. if imt.name == "PGA": mean = np.log((10 ** mean) * ((2 * np.pi / 0.01) ** 2) * 1e-2 / g) elif imt.name == "SA": mean = np.log((10 ** mean) * ((2 * np.pi / imt.period) ** 2) * 1e-2 / g) else: mean = np.log(10 ** mean) return mean def _get_stddevs(self, C, stddev_types, num_sites): """ Returns the standard deviation terms assuming no style-of-faulting is known """ 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.log(10.0 ** C['s']) + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTRA_EVENT: stddevs.append(np.log(10.0 ** C['f']) + np.zeros(num_sites)) elif stddev_type == const.StdDev.INTER_EVENT: stddevs.append(np.log(10.0 ** C["t"]) + np.zeros(num_sites)) return stddevs
[docs]class CauzziEtAl2014FixedVs30(CauzziEtAl2014): """ Implements the Cauzzi et al (2014) model for the case in which the reference Vs30 in the site amplification term is fixed at 800 m/s """ def _get_site_amplification_term(self, C, vs30): """ Returns the site amplification scaling term assuming period dependent reference vs30 """ return C["bV800"] * np.log10(vs30 / 800.)
[docs]class CauzziEtAl2014FixedVs30NoSOF(CauzziEtAl2014NoSOF): """ Implements the Cauzzi et al (2014) model for the case in which the reference Vs30 in the site amplification term is fixed at 800 m/s """ def _get_site_amplification_term(self, C, vs30): """ Returns the site amplification scaling term assuming the reference Vs30 is fixed at 800 m/s """ return C["bV800"] * np.log10(vs30 / 800.)
[docs]class CauzziEtAl2014Eurocode8(CauzziEtAl2014): """ Implmements the Cauzzi et al. (2014) GMPE for the case in which the Eurocode 8 site classification is preferred """ def _get_site_amplification_term(self, C, vs30): """ Returns the site amplification term on the basis of Eurocode 8 site class """ s_b, s_c, s_d = self._get_site_dummy_variables(vs30) return (C["sB"] * s_b) + (C["sC"] * s_c) + (C["sD"] * s_d) def _get_site_dummy_variables(self, vs30): """ Returns the Eurocode 8 site class dummy variable """ s_b = np.zeros_like(vs30) s_c = np.zeros_like(vs30) s_d = np.zeros_like(vs30) s_b[np.logical_and(vs30 >= 360., vs30 < 800.)] = 1.0 s_c[np.logical_and(vs30 >= 180., vs30 < 360.)] = 1.0 s_d[vs30 < 180] = 1.0 return s_b, s_c, s_d
[docs]class CauzziEtAl2014Eurocode8NoSOF(CauzziEtAl2014NoSOF): """ Implmements the Cauzzi et al. (2014) GMPE for the case in which the Eurocode 8 site classification is preferred and style of faulting is not specified. """ def _get_site_amplification_term(self, C, vs30): """ Returns the site amplification term on the basis of Eurocode 8 site class """ s_b, s_c, s_d = self._get_site_dummy_variables(vs30) return (C["sB"] * s_b) + (C["sC"] * s_c) + (C["sD"] * s_d) def _get_site_dummy_variables(self, vs30): """ Returns the Eurocode 8 site class dummy variable """ s_b = np.zeros_like(vs30) s_c = np.zeros_like(vs30) s_d = np.zeros_like(vs30) s_b[np.logical_and(vs30 >= 360., vs30 < 800.)] = 1.0 s_c[np.logical_and(vs30 >= 180., vs30 < 360.)] = 1.0 s_d[vs30 < 180.] = 1.0 return s_b, s_c, s_d