# -*- coding: utf-8 -*-
# The Hazard Library
# Copyright (C) 2013-2014, GEM Foundation
#
# This program 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.
#
# This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports
:class:`EdwardsFah2013Alpine10MPa`,
:class:`EdwardsFah2013Alpine20MPa`,
:class:`EdwardsFah2013Alpine30MPa`,
:class:`EdwardsFah2013Alpine50MPa`,
:class:`EdwardsFah2013Alpine60MPa`,
:class:`EdwardsFah2013Alpine75MPa`,
:class:`EdwardsFah2013Alpine90MPa`,
:class:`EdwardsFah2013Alpine120MPa`.
"""
from __future__ import division
import numpy as np
from scipy.constants import g
from openquake.hazardlib.gsim.base import GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGV, PGA, SA
from openquake.hazardlib.gsim.edwards_fah_2013a_coeffs import (
COEFFS_ALPINE_60Bars,
COEFFS_ALPINE_10Bars,
COEFFS_ALPINE_20Bars,
COEFFS_ALPINE_30Bars,
COEFFS_ALPINE_50Bars,
COEFFS_ALPINE_75Bars,
COEFFS_ALPINE_90Bars,
COEFFS_ALPINE_120Bars
)
from openquake.hazardlib.gsim.utils_swiss_gmpe import (
_compute_phi_ss,
_compute_C1_term
)
[docs]class EdwardsFah2013Alpine10MPa(GMPE):
"""
This function implements the GMPE developed by Ben Edwars and Donath Fah
and published as "A Stochastic Ground-Motion Model for Switzerland"
Bulletin of the Seismological Society of America,
Vol. 103, No. 1, pp. 78–98, February 2013.
The GMPE was parametrized by Carlo Cauzzi to be implemented in OpenQuake.
This class implements the equations for 'Alpine' and 'Foreland - two
tectonic regionalizations defined for the Switzerland -
therefore this GMPE is region specific".
@ implemented by laurentiu.danciu@sed.ethz.zh
"""
#: Supported tectonic region type is ALPINE which
#: is a sub-region of Active Shallow Crust.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration, see tables 3 and 4, pages 227 and 228.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGV,
PGA,
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 type is total,
#: Carlo Cauzzi - Personal Communication
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: Required site parameter is only Vs30 (used to distinguish rock
#: and deep soil).
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters: magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'rake'))
#: Required distance measure is Rrup
REQUIRES_DISTANCES = set(('rrup', ))
#: Vs30 value representing typical rock conditions in Switzerland.
#: confirmed by the Swiss GMPE group
ROCK_VS30 = 1105
[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.
"""
COEFFS = self.COEFFS[imt]
R = self._compute_term_r(COEFFS, rup.mag, dists.rrup)
mean = 10 ** (self._compute_mean(COEFFS, rup.mag, R))
# Convert units to g,
# but only for PGA and SA (not PGV):
if isinstance(imt, (PGA, SA)):
mean = np.log(mean / (g*100.))
else:
# PGV:
mean = np.log(mean)
c1_rrup = _compute_C1_term(COEFFS, dists.rrup)
log_phi_ss = 1.00
stddevs = self._get_stddevs(
COEFFS, stddev_types, sites.vs30.shape[0], rup.mag, c1_rrup,
log_phi_ss, COEFFS['mean_phi_ss']
)
return mean, stddevs
def _get_stddevs(self, C, stddev_types, num_sites, mag, c1_rrup,
log_phi_ss, mean_phi_ss):
"""
Return standard deviations
"""
phi_ss = _compute_phi_ss(C, mag, c1_rrup, log_phi_ss, mean_phi_ss)
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(
C['tau'] * C['tau'] +
phi_ss * phi_ss) +
np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(phi_ss + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['tau'] + np.zeros(num_sites))
return stddevs
def _compute_term_r(self, C, mag, rrup):
"""
Compute distance term
d = log10(max(R,rmin));
"""
if mag > self.M1:
rrup_min = 0.55
elif mag > self.M2:
rrup_min = -2.80 * mag + 14.55
else:
rrup_min = -0.295 * mag + 2.65
R = np.maximum(rrup, rrup_min)
return np.log10(R)
def _compute_term_1(self, C, mag):
"""
Compute term 1
a1 + a2.*M + a3.*M.^2 + a4.*M.^3 + a5.*M.^4 + a6.*M.^5 + a7.*M.^6
"""
return (
C['a1'] + C['a2'] * mag + C['a3'] *
np.power(mag, 2) + C['a4'] * np.power(mag, 3)
+ C['a5'] * np.power(mag, 4) + C['a6'] *
np.power(mag, 5) + C['a7'] * np.power(mag, 6)
)
def _compute_term_2(self, C, mag, R):
"""
(a8 + a9.*M + a10.*M.*M + a11.*M.*M.*M).*d(r)
"""
return (
(C['a8'] + C['a9'] * mag + C['a10'] * np.power(mag, 2) +
C['a11'] * np.power(mag, 3)) * R
)
def _compute_term_3(self, C, mag, R):
"""
(a12 + a13.*M + a14.*M.*M + a15.*M.*M.*M).*(d(r).^2)
"""
return (
(C['a12'] + C['a13'] * mag + C['a14'] * np.power(mag, 2) +
C['a15'] * np.power(mag, 3)) * np.power(R, 2)
)
def _compute_term_4(self, C, mag, R):
"""
(a16 + a17.*M + a18.*M.*M + a19.*M.*M.*M).*(d(r).^3)
"""
return (
(C['a16'] + C['a17'] * mag + C['a18'] * np.power(mag, 2) +
C['a19'] * np.power(mag, 3)) * np.power(R, 3)
)
def _compute_term_5(self, C, mag, R):
"""
(a20 + a21.*M + a22.*M.*M + a23.*M.*M.*M).*(d(r).^4)
"""
return (
(C['a20'] + C['a21'] * mag + C['a22'] * np.power(mag, 2) +
C['a23'] * np.power(mag, 3)) * np.power(R, 4)
)
def _compute_mean(self, C, mag, term_dist_r):
"""
compute mean
"""
return (self._compute_term_1(C, mag) +
self._compute_term_2(C, mag, term_dist_r) +
self._compute_term_3(C, mag, term_dist_r) +
self._compute_term_4(C, mag, term_dist_r) +
self._compute_term_5(C, mag, term_dist_r))
#: Fixed magnitude terms
M1 = 5.00
M2 = 4.70
COEFFS = COEFFS_ALPINE_10Bars
[docs]class EdwardsFah2013Alpine20MPa(EdwardsFah2013Alpine10MPa):
"""
This class extends :class:`EdwardsFah2013Alpine10MPa`
and implements the 20Bars Model :class:`EdwardsFah2013Alpine20MPa`
"""
COEFFS = COEFFS_ALPINE_20Bars
[docs]class EdwardsFah2013Alpine30MPa(EdwardsFah2013Alpine10MPa):
"""
This class extends :class:`EdwardsFah2013Alpine10MPa`
and implements the 30Bars Model :class:`EdwardsFah2013Alpine30MPa`
"""
COEFFS = COEFFS_ALPINE_30Bars
[docs]class EdwardsFah2013Alpine50MPa(EdwardsFah2013Alpine10MPa):
"""
This class extends :class:`EdwardsFah2013Alpine10MPa`
and implements the 50Bars Model :class:`EdwardsFah2013Alpine50MPa`
"""
COEFFS = COEFFS_ALPINE_50Bars
[docs]class EdwardsFah2013Alpine60MPa(EdwardsFah2013Alpine10MPa):
"""
This class extends :class:`EdwardsFah2013Alpine10MPa`
and implements the 60Bars Model :class:`EdwardsFah2013Alpine60MPa`
"""
COEFFS = COEFFS_ALPINE_60Bars
[docs]class EdwardsFah2013Alpine75MPa(EdwardsFah2013Alpine10MPa):
"""
This class extends :class:`EdwardsFah2013Alpine10MPa`
and implements the 75Bars Model :class:`EdwardsFah2013Alpine75MPa`
"""
COEFFS = COEFFS_ALPINE_75Bars
[docs]class EdwardsFah2013Alpine90MPa(EdwardsFah2013Alpine10MPa):
"""
This class extends :class:`EdwardsFah2013Alpine10MPa`
and implements the 90Bars Model :class:`EdwardsFah2013Alpine90MPa`
"""
COEFFS = COEFFS_ALPINE_90Bars
[docs]class EdwardsFah2013Alpine120MPa(EdwardsFah2013Alpine10MPa):
"""
This class extends :class:`EdwardsFah2013Alpine10MPa`
and implements the 120Bars Model :class:`EdwardsFah2013Alpine120MPa`
"""
COEFFS = COEFFS_ALPINE_120Bars