# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2020 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:`NGAEastUSGSGMPE`
"""
import os
import numpy as np
from scipy.interpolate import interp1d
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
from openquake.hazardlib.gsim.base import CoeffsTable, gsim_aliases
from openquake.hazardlib.gsim.nga_east import ITPL, NGAEastGMPE
# Coefficients for EPRI sigma model taken from Table 5.5 of Goulet et al.
# (2017)
COEFFS_USGS_SIGMA_EPRI = CoeffsTable(sa_damping=5, table="""\
imt tau_M5 phi_M5 tau_M6 phi_M6 tau_M7 phi_M7
pga 0.4320 0.6269 0.3779 0.5168 0.3525 0.5039
0.010 0.4320 0.6269 0.3779 0.5168 0.3525 0.5039
0.020 0.4710 0.6682 0.4385 0.5588 0.4138 0.5462
0.030 0.4710 0.6682 0.4385 0.5588 0.4138 0.5462
0.050 0.4710 0.6682 0.4385 0.5588 0.4138 0.5462
0.075 0.4710 0.6682 0.4385 0.5588 0.4138 0.5462
0.100 0.4710 0.6682 0.4385 0.5588 0.4138 0.5462
0.150 0.4433 0.6693 0.4130 0.5631 0.3886 0.5506
0.200 0.4216 0.6691 0.3822 0.5689 0.3579 0.5566
0.250 0.4150 0.6646 0.3669 0.5717 0.3427 0.5597
0.300 0.4106 0.6623 0.3543 0.5846 0.3302 0.5727
0.400 0.4088 0.6562 0.3416 0.5997 0.3176 0.5882
0.500 0.4175 0.6526 0.3456 0.6125 0.3217 0.6015
0.750 0.4439 0.6375 0.3732 0.6271 0.3494 0.6187
1.000 0.4620 0.6219 0.3887 0.6283 0.3650 0.6227
1.500 0.4774 0.5957 0.4055 0.6198 0.3819 0.6187
2.000 0.4809 0.5860 0.4098 0.6167 0.3863 0.6167
3.000 0.4862 0.5813 0.4186 0.6098 0.3952 0.6098
4.000 0.4904 0.5726 0.4144 0.6003 0.3910 0.6003
5.000 0.4899 0.5651 0.4182 0.5986 0.3949 0.5986
7.500 0.4803 0.5502 0.4067 0.5982 0.3835 0.5982
10.00 0.4666 0.5389 0.3993 0.5885 0.3761 0.5885
""")
COEFFS_USGS_SIGMA_PANEL = CoeffsTable(sa_damping=5, table="""\
imt t1 t2 t3 t4 ss_a ss_b s2s1 s2s2
pga 0.4436 0.4169 0.3736 0.3415 0.5423 0.3439 0.533 0.566
0.010 0.4436 0.4169 0.3736 0.3415 0.5423 0.3439 0.533 0.566
0.020 0.4436 0.4169 0.3736 0.3415 0.5410 0.3438 0.537 0.577
0.030 0.4436 0.4169 0.3736 0.3415 0.5397 0.3437 0.542 0.598
0.050 0.4436 0.4169 0.3736 0.3415 0.5371 0.3435 0.583 0.653
0.075 0.4436 0.4169 0.3736 0.3415 0.5339 0.3433 0.619 0.633
0.100 0.4436 0.4169 0.3736 0.3415 0.5308 0.3431 0.623 0.590
0.150 0.4436 0.4169 0.3736 0.3415 0.5247 0.3466 0.603 0.532
0.200 0.4436 0.4169 0.3736 0.3415 0.5189 0.3585 0.578 0.461
0.250 0.4436 0.4169 0.3736 0.3415 0.5132 0.3694 0.554 0.396
0.300 0.4436 0.4169 0.3736 0.3415 0.5077 0.3808 0.527 0.373
0.400 0.4436 0.4169 0.3736 0.3415 0.4973 0.4004 0.491 0.339
0.500 0.4436 0.4169 0.3736 0.3415 0.4875 0.4109 0.472 0.305
0.750 0.4436 0.4169 0.3736 0.3415 0.4658 0.4218 0.432 0.273
1.000 0.4436 0.4169 0.3736 0.3415 0.4475 0.4201 0.431 0.257
1.500 0.4436 0.4169 0.3736 0.3415 0.4188 0.4097 0.424 0.247
2.000 0.4436 0.4169 0.3736 0.3415 0.3984 0.3986 0.423 0.239
3.000 0.4436 0.4169 0.3736 0.3415 0.3733 0.3734 0.418 0.230
4.000 0.4436 0.4169 0.3736 0.3415 0.3604 0.3604 0.412 0.221
5.000 0.4436 0.4169 0.3736 0.3415 0.3538 0.3537 0.404 0.214
7.500 0.4436 0.4169 0.3736 0.3415 0.3482 0.3481 0.378 0.201
10.00 0.4436 0.4169 0.3736 0.3415 0.3472 0.3471 0.319 0.193
""")
[docs]def get_epri_tau_phi(imt, mag):
"""
Returns the inter-event (tau) and intra_event standard deviation (phi)
according to the updated EPRI (2013) model"""
C = COEFFS_USGS_SIGMA_EPRI[imt]
if mag <= 5.0:
tau = C["tau_M5"]
phi = C["phi_M5"]
elif mag <= 6.0:
tau = ITPL(mag, C["tau_M6"], C["tau_M5"], 5.0, 1.0)
phi = ITPL(mag, C["phi_M6"], C["phi_M5"], 5.0, 1.0)
elif mag <= 7.0:
tau = ITPL(mag, C["tau_M7"], C["tau_M6"], 6.0, 1.0)
phi = ITPL(mag, C["phi_M7"], C["phi_M6"], 6.0, 1.0)
else:
tau = C["tau_M7"]
phi = C["phi_M7"]
return tau, phi
[docs]def get_panel_tau_phi(imt, mag):
"""
Returns the inter-event (tau) and intra_event standard deviation (phi)
according to the USGS Sigma Panel recommendations
"""
C = COEFFS_USGS_SIGMA_PANEL[imt]
# Get tau
if mag <= 4.5:
tau = C["t1"]
elif mag <= 5.0:
tau = ITPL(mag, C["t2"], C["t1"], 4.5, 0.5)
elif mag <= 5.5:
tau = ITPL(mag, C["t3"], C["t2"], 5.0, 0.5)
elif mag <= 6.5:
tau = ITPL(mag, C["t4"], C["t3"], 5.5, 1.0)
else:
tau = C["t4"]
# Get phi
if mag <= 5.0:
phi = C["ss_a"]
elif mag <= 6.5:
phi = ITPL(mag, C["ss_b"], C["ss_a"], 5.0, 1.5)
else:
phi = C["ss_b"]
return tau, phi
[docs]def get_stewart_2019_phis2s(imt, vs30):
"""
Returns the phis2s model of Stewart et al. (2019)
"""
v_1 = 1200.
v_2 = 1500.
C = COEFFS_USGS_SIGMA_PANEL[imt]
phis2s = C["s2s1"] + np.zeros(vs30.shape)
idx = vs30 > v_2
phis2s[idx] = C["s2s2"]
idx = np.logical_and(vs30 > v_1, vs30 <= v_2)
if np.any(idx):
phis2s[idx] = C["s2s1"] - ((C["s2s1"] - C["s2s2"]) / (v_2 - v_1)) *\
(vs30[idx] - v_1)
return phis2s
[docs]class NGAEastUSGSGMPE(NGAEastGMPE):
"""
For the "core" NGA East set the table is provided in the code in a
subdirectory fixed to the path of the present file. The GMPE table option
is therefore no longer needed
"""
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set((const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT))
gmpe_table = ""
PATH = os.path.join(os.path.dirname(__file__), "usgs_nga_east_tables")
def __init__(self, **kwargs):
self.sigma_model = kwargs.get("sigma_model", "COLLAPSED")
self.epistemic_site = kwargs.get("epistemic_site", True)
if self.sigma_model not in ("EPRI", "PANEL", "COLLAPSED"):
raise ValueError("USGS CEUS Sigma Model %s not supported"
% self.sigma_model)
if self.sigma_model == "COLLAPSED":
# In the case of the collapsed model only the total standard
# deviation can be defined
self.DEFINED_FOR_STANDARD_DEVIATION_TYPES =\
set((const.StdDev.TOTAL,))
super().__init__(**kwargs)
def _setup_standard_deviations(self, fle):
# Not needed here
pass
[docs] def get_mean_and_stddevs(self, sctx, rctx, dctx, imt, stddev_types):
"""
Returns the mean and standard deviations
"""
# Get the PGA on the reference rock condition
if PGA in self.DEFINED_FOR_INTENSITY_MEASURE_TYPES:
rock_imt = PGA()
else:
rock_imt = SA(0.01)
pga_r = self.get_hard_rock_mean(rctx, dctx, rock_imt, stddev_types)
# Get the desired spectral acceleration on rock
if not str(imt) == "PGA":
# Calculate the ground motion at required spectral period for
# the reference rock
imean = self.get_hard_rock_mean(rctx, dctx, imt, stddev_types)
else:
# Avoid re-calculating PGA if that was already done!
imean = np.copy(pga_r)
# Get the coefficients for the IMT
C_LIN = self.LINEAR_COEFFS[imt]
C_F760 = self.F760[imt]
C_NL = self.NONLINEAR_COEFFS[imt]
site_amp = self.get_site_amplification(imt, np.exp(pga_r), sctx)
# Get collapsed amplification model for -sigma, 0, +sigma with weights
# of 0.185, 0.63, 0.185 respectively
if self.epistemic_site:
f_rk = np.log((np.exp(pga_r) + C_NL["f3"]) / C_NL["f3"])
site_amp_sigma = self.get_site_amplification_sigma(
sctx, f_rk, C_LIN, C_F760, C_NL)
mean = np.log(
0.185 * (np.exp(imean + (site_amp - site_amp_sigma))) +
0.63 * (np.exp(imean + site_amp)) +
0.185 * (np.exp(imean + (site_amp + site_amp_sigma))))
else:
mean = imean + site_amp
# Get standard deviation model
nsites = getattr(dctx, self.distance_type).shape
stddevs = self.get_stddevs(rctx.mag, sctx.vs30, imt,
stddev_types, nsites)
return mean, stddevs
def _get_mean(self, data, dctx, dists):
"""
Returns the mean intensity measure level from the tables applying
log-log interpolation of the IML with distance (contrast with the
linear interpolation applied in usual GMPE tables)
:param data:
The intensity measure level vector for the given magnitude and IMT
:param key:
The distance type
:param distances:
The distance vector for the given magnitude and IMT
"""
# For values outside of the interpolation range use -999. to ensure
# value is identifiable and outside of potential real values
# For extremely short distance (rrup = 0) use an arbitrarily small
# distance measure (1.0E-5 used by US NSHMP code)
dists[dists < 1.0E-5] = 1.0E-5
interpolator_mean = interp1d(np.log10(dists), np.log(data),
bounds_error=False,
fill_value=-999.)
mean = np.exp(interpolator_mean(np.log10(getattr(dctx,
self.distance_type))))
# For those distances less than or equal to the shortest distance
# extrapolate the shortest distance value
mean[getattr(dctx, self.distance_type) <= dists[0]] = data[0]
# For those distances significantly greater than the furthest distance
# set to 1E-20.
mean[getattr(dctx, self.distance_type) > (dists[-1] + 1.0E-3)] = 1E-20
# If any distance is between the final distance and a margin of 0.001
# km then assign to smallest distance
mean[mean < -1.] = data[-1]
return mean
[docs] def get_stddevs(self, mag, vs30, imt, stddev_types, num_sites):
"""
Returns the standard deviations according to the choice of aleatory
uncertainty model. Note that for compatibility with the US NSHMP
code a weighted sum of the two aleatory uncertainty models is used,
with the EPRI model assigned a weight of 0.8 and the PANEL model 0.2.
"""
if self.sigma_model in ("EPRI", "COLLAPSED"):
# EPRI recommended aleatory uncertainty model
tau_epri, phi_epri = get_epri_tau_phi(imt, mag)
tau_epri += np.zeros(num_sites)
phi_epri += np.zeros(num_sites)
if self.sigma_model in ("PANEL", "COLLAPSED"):
# Panel recommended model
tau_panel, phi0_panel = get_panel_tau_phi(imt, mag)
tau_panel += np.zeros(num_sites)
phis2s = get_stewart_2019_phis2s(imt, vs30)
phi_panel = np.sqrt(phi0_panel ** 2. + phis2s ** 2.)
if self.sigma_model == "EPRI":
tau = tau_epri
phi = phi_epri
sigma = np.sqrt(tau ** 2. + phi ** 2.)
elif self.sigma_model == "PANEL":
tau = tau_panel
phi = phi_panel
sigma = np.sqrt(tau ** 2. + phi ** 2.)
else:
# Get the weighted sum of the two models
sigma_epri = np.sqrt(tau_epri ** 2. + phi_epri ** 2.)
sigma_panel = np.sqrt(tau_panel ** 2. + phi_panel ** 2.)
sigma = 0.8 * sigma_epri + 0.2 * sigma_panel
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(sigma)
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(phi)
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(tau)
return stddevs
lines = '''\
NGAEastUSGSSeedSP15 SP15
NGAEastUSGSSeed1CCSP 1CCSP
NGAEastUSGSSeed2CVSP 2CVSP
NGAEastUSGSSeed1CVSP 1CVSP
NGAEastUSGSSeed2CCSP 2CCSP
NGAEastUSGSSeedGraizer Graizer
NGAEastUSGSSeedB_ab95 B_ab95
NGAEastUSGSSeedB_bca10d B_bca10d
NGAEastUSGSSeedB_sgd02 B_sgd02
NGAEastUSGSSeedB_a04 B_a04
NGAEastUSGSSeedB_bs11 B_bs11
NGAEastUSGSSeedB_ab14 B_ab14
NGAEastUSGSSeedHA15 HA15
NGAEastUSGSSeedPEER_EX PEER_EX
NGAEastUSGSSeedPEER_GP PEER_GP
NGAEastUSGSSeedGraizer16 Graizer16
NGAEastUSGSSeedGraizer17 Graizer17
NGAEastUSGSSeedFrankel Frankel
NGAEastUSGSSeedYA15 YA15
NGAEastUSGSSeedPZCT15_M1SS PZCT15_M1SS
NGAEastUSGSSeedPZCT15_M2ES PZCT15_M2ES
NGAEastUSGSSammons1 usgs_1
NGAEastUSGSSammons2 usgs_2
NGAEastUSGSSammons3 usgs_3
NGAEastUSGSSammons4 usgs_4
NGAEastUSGSSammons5 usgs_5
NGAEastUSGSSammons6 usgs_6
NGAEastUSGSSammons7 usgs_7
NGAEastUSGSSammons8 usgs_8
NGAEastUSGSSammons9 usgs_9
NGAEastUSGSSammons10 usgs_10
NGAEastUSGSSammons11 usgs_11
NGAEastUSGSSammons12 usgs_12
NGAEastUSGSSammons13 usgs_13
NGAEastUSGSSammons14 usgs_14
NGAEastUSGSSammons15 usgs_15
NGAEastUSGSSammons16 usgs_16
NGAEastUSGSSammons17 usgs_17'''.splitlines()
for line in lines:
alias, key = line.split()
gsim_aliases[alias] = (f'[NGAEastUSGSGMPE]\n'
f'gmpe_table="nga_east_{key}.hdf5"')