# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2021 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.
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# 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:`SkarlatoudisEtAlSSlab2013`.
"""
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
def _compute_distance(ctx, C):
"""
equation 3 pag 1960:
``c31 * logR + c32 * (R-Rref)``
"""
rref = 1.0
c31 = -1.7
return (c31 * np.log10(ctx.rhypo) + C['c32'] * (ctx.rhypo - rref))
def _compute_magnitude(ctx, C):
"""
equation 3 pag 1960:
c1 + c2(M-5.5)
"""
m_h = 5.5
return C['c1'] + (C['c2'] * (ctx.mag - m_h))
def _get_site_amplification(ctx, C):
"""
Compute the fourth term of the equation 3:
The functional form Fs in Eq. (1) represents the site amplification and
it is given by FS = c61*S + c62*SS , where c61 and c62 are the
coefficients to be determined through the regression analysis,
while S and SS are dummy variables used to denote NEHRP site category
C and D respectively
Coefficents for categories A and B are set to zero
"""
S, SS = _get_site_type_dummy_variables(ctx)
return (C['c61'] * S) + (C['c62'] * SS)
def _get_site_type_dummy_variables(ctx):
"""
Get site type dummy variables, three different site classes,
based on the shear wave velocity intervals in the uppermost 30 m, Vs30,
according to the NEHRP:
class A-B: Vs30 > 760 m/s
class C: Vs30 = 360 − 760 m/s
class D: Vs30 < 360 m/s
"""
S = np.zeros(len(ctx.vs30))
SS = np.zeros(len(ctx.vs30))
# Class C; 180 m/s <= Vs30 <= 360 m/s.
idx = (ctx.vs30 < 360.0)
SS[idx] = 1.0
# Class B; 360 m/s <= Vs30 <= 760 m/s. (NEHRP)
idx = (ctx.vs30 >= 360.0) & (ctx.vs30 < 760)
S[idx] = 1.0
return S, SS
def _compute_forearc_backarc_term(C, ctx):
"""
Compute back-arc term of Equation 3
"""
# flag 1 (R < 335 & R >= 205)
flag1 = np.zeros(len(ctx.rhypo))
ind1 = np.logical_and((ctx.rhypo < 335), (ctx.rhypo >= 205))
flag1[ind1] = 1.0
# flag 2 (R >= 335)
flag2 = np.zeros(len(ctx.rhypo))
ind2 = (ctx.rhypo >= 335)
flag2[ind2] = 1.0
# flag 3 (R < 240 & R >= 140)
flag3 = np.zeros(len(ctx.rhypo))
ind3 = np.logical_and((ctx.rhypo < 240), (ctx.rhypo >= 140))
flag3[ind3] = 1.0
# flag 4 (R >= 240)
flag4 = np.zeros(len(ctx.rhypo))
ind4 = (ctx.rhypo >= 240)
flag4[ind4] = 1.0
A = flag1 * ((205 - ctx.rhypo)/150) + flag2
B = flag3 * ((140 - ctx.rhypo)/100) + flag4
if (ctx.hypo_depth < 80):
FHR = A
else:
FHR = B
H0 = 100
# Heaviside function
if (ctx.hypo_depth >= H0):
H = 1
else:
H = 0
# ARC = 0 for back-arc - ARC = 1 for forearc
ARC = np.zeros(len(ctx.backarc))
idxarc = (ctx.backarc == 1)
ARC[idxarc] = 1.0
return ((C['c41'] * (1 - ARC) * H) + (C['c42'] * (1 - ARC) * H * FHR) +
(C['c51'] * ARC * H) + (C['c52'] * ARC * H * FHR))
[docs]class SkarlatoudisEtAlSSlab2013(GMPE):
"""
Implements GMPEs developed by A.A.Skarlatoudis, C.B.Papazachos,
B.N.Margaris, C.Ventouzi, I.Kalogeras and EGELADOS group published as
"Ground-Motion Prediction Equations of Intermediate-Depth Earthquakes in
the Hellenic Arc, Southern Aegean Subduction Area“,
Bull Seism Soc Am, DOI 10.1785/0120120265
SA are given up to 4 s.
The regressions are developed considering the RotD50 (Boore, 2010) of the
as-recorded horizontal components
"""
#: Supported tectonic region type is ‘subduction intraslab’ because the
#: equations have been derived from data from Hellenic Arc events, as
#: explained in the 'Introduction'.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB
#: 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 = {PGA, PGV, SA}
#: Supported intensity measure component is the RotD50 of two
#: horizontal components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: Supported standard deviation types are inter-event, intra-event
#: and total, page 1961
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameter is Vs30 and backarc flag
REQUIRES_SITES_PARAMETERS = {'vs30', 'backarc'}
#: Required rupture parameters are magnitude and hypocentral depth
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'}
#: Required distance measure is Rhypo.
REQUIRES_DISTANCES = {'rhypo'}
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imean = (_compute_magnitude(ctx, C) +
_compute_distance(ctx, C) +
_get_site_amplification(ctx, C) +
_compute_forearc_backarc_term(C, ctx))
stp = np.array([C['epsilon'], C['tau'], C['sigma']])
# Convert units to g,
# but only for PGA and SA (not PGV)
if imt.string.startswith(("SA", "PGA")):
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
else:
# PGV
mean[m] = np.log(10.0 ** imean)
# Return stddevs in terms of natural log scaling
sig[m], tau[m], phi[m] = np.log(10.0 ** stp)
# mean_LogNaturale = np.log((10 ** mean) * 1e-2 / g)
#: Coefficients from SA from Table 1
#: Coefficients from PGA e PGV from Table 5
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c1 c2 c32 c41 c42 c51 c52 c61 c62 sigma tau epsilon
pga 4.229 0.877 -0.00206 -0.481 -0.152 0.425 0.303 0.267 0.491 0.352 0.112 0.369
pgv 2.965 1.069 -0.00178 -0.264 0.018 0.390 0.333 0.408 0.599 0.315 0.144 0.346
0.010 4.235 0.876 -0.00206 -0.482 -0.153 0.425 0.304 0.265 0.488 0.353 0.111 0.370
0.025 4.119 0.877 -0.00202 -0.490 -0.140 0.415 0.326 0.301 0.511 0.352 0.103 0.367
0.050 4.320 0.863 -0.00212 -0.483 -0.178 0.410 0.286 0.245 0.475 0.376 0.095 0.388
0.100 4.565 0.867 -0.00244 -0.515 -0.185 0.452 0.371 0.234 0.442 0.404 0.066 0.410
0.200 4.613 0.842 -0.00199 -0.596 -0.221 0.396 0.291 0.289 0.469 0.379 0.154 0.409
0.400 4.463 0.926 -0.00190 -0.427 -0.110 0.459 0.295 0.298 0.516 0.322 0.141 0.351
1.000 3.952 1.102 -0.00178 -0.199 0.112 0.316 0.442 0.371 0.512 0.305 0.201 0.365
2.000 3.281 1.260 -0.00106 -0.136 0.055 0.196 0.352 0.408 0.578 0.277 0.203 0.343
4.000 2.588 1.384 -0.00039 -0.179 -0.046 0.113 0.189 0.264 0.475 0.278 0.176 0.329
""")