# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2026 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:`NovakovicEtAl2018`
"""
import os
import pathlib
import numpy as np
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib.gsim.boore_2014 import BooreEtAl2014
from openquake.hazardlib.gsim.yenier_atkinson_2015 import (
get_fs_SeyhanStewart2014)
TFP = pathlib.Path(__file__).parent.absolute()
def _magnitude_scaling(C, mag):
""" Magnitude scaling as described in eq. 4 """
fm = np.zeros_like(mag)
dff = (mag - C['Mh'])
idx = mag <= C['Mh']
fm[idx] = C['e0'] + C['e1'] * dff[idx] + C['e2'] * dff[idx]**2
idx = mag > C['Mh']
fm[idx] = C['e0'] + C['e3'] * dff[idx]
return fm
def _stress_param_scaling(C, d_sigma, mag):
""" Stress scaling as defined in eq. 6 """
fs = np.zeros_like(mag)
idx = d_sigma <= 100
fs[idx] = (C['s0'] + C['s1'] * mag[idx] + C['s2'] * mag[idx]**2 +
C['s3'] * mag[idx]**3 + C['s4'] * mag[idx]**4)
idx = d_sigma > 100
fs[idx] = (C['s5'] + C['s6'] * mag[idx] + C['s7'] * mag[idx]**2 +
C['s8'] * mag[idx]**3 + C['s9'] * mag[idx]**4)
return fs*np.log(d_sigma/100)
def _source_scaling(C, d_sigma, mag, hypo_depth):
""" Source scaling as per eq. 3 """
if d_sigma is None:
# Implements eq. 11 in Novokovic et al. 2018
t1 = 0.097*(hypo_depth-10)
t2 = 1.329*(mag-5.1)
d_sigma = np.exp(5.65+np.minimum(0, t1)+np.minimum(0, t2))
elif not hasattr(d_sigma, "__len__"):
d_sigma = np.zeros_like(mag) * d_sigma
return _magnitude_scaling(C, mag) + _stress_param_scaling(C, d_sigma, mag)
def _geometric_spreading(C, rrup, mag):
# Effective depth
heff = 10**(-0.405+0.235*mag)
r = (rrup**2 + heff**2)**0.5
rref = (1+heff**2)**0.5
# Transition distances [km]. See right column page 5
rt1 = 45
rt2 = 200
# Compute the spreading function
fz = np.zeros_like(rrup)
idx = r <= rt1
fz[idx] = r[idx]**-1.3
idx = (r > rt1) & (r <= rt2)
fz[idx] = rt1**-1.3 * (r[idx]/rt1)**-0.05
idx = (r > rt2)
fz[idx] = rt1**-1.3 * (rt2/rt1)**-0.05 * (r[idx]/rt2)**-0.5
return np.log(fz) + (C['b3'] + C['b4'] * mag) * np.log(r/rref)
def _anelastic_attenuation_term(gamma, rrup):
""" Compute anelastic attenuation """
return gamma * rrup
[docs]def get_gm_rock(C, ctx, d_sigma, REA):
""" Compute ground-motion on bedrock """
gamma = REA['gamma']
calibration_factor = REA['C']
gm = (_source_scaling(C, d_sigma, ctx.mag, ctx.hypo_depth) +
_geometric_spreading(C, ctx.rrup, ctx.mag) +
_anelastic_attenuation_term(gamma, ctx.rrup) +
calibration_factor
)
return gm
[docs]class NovakovicEtAl2018(GMPE):
"""
Implements the model of Novakovic et al. (2018) as described in:
- Novakovic et al. (2018) "Empirically Calibrated Ground-Motion
Prediction Equation for Oklahoma" - doi: 10.1785/0120170331
Note that the default parameters used are for OK i.e. when the region_fle
is left empty, the default file used is
`novakovic_2018/novakovic_2018_reg_adj_oklahoma.txt`
:param d_sigma:
The stress-drop [bar]
:param region_fle:
A .txt file (with the same formats of a coefficient table) containing
the regional adjustments
NOTE: 5 sigma values for PGA, PGV, SA(0.02), SA(0.0495), SA(0.0655) from
erratum table A3 (between event and within event values Z)
NOTE: Changed T=0.9901 to T=1 in
novakovic_2018/novakovic_2018_reg_adj_oklahoma.txt to avoid an
interpolation that caused a discrepancy only for SA(1.0) of about
1.83% - now the tests pass at max discrep of 0.01%
"""
#: This is ground-motion model for induced seismicity earthquakes by
#: wastewater injection
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.INDUCED
#: Supported intensity measure types are spectral acceleration, peak
#: ground velocity and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is geometric-mean
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
#: Supported standard deviation types are inter-event, intra-event
#: and total. This information must be provided in the regional adjustment
#: file
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT}
#: Required site parameter is Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameter is magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'}
#: Required distance measures is Rrup
REQUIRES_DISTANCES = {'rrup'}
def __init__(self, d_sigma=None, region_fle=None, site_term=True,
**kwargs):
super().__init__(**kwargs)
self.d_sigma = d_sigma
self.site_term = site_term
# Read the file and create the coefficient table for the regional
# adjustment
if region_fle is None:
region_fle = os.path.join(
TFP, 'novakovic_2018',
'novakovic_2018_reg_adj_oklahoma.txt')
with open(region_fle, 'r') as fle:
data = fle.read()
self.REA = CoeffsTable(sa_damping=5, table=data)
# Boore et al. coefficients, used in the site model.
self.BEA14 = BooreEtAl2014.COEFFS
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
""" Compute mean """
# Compute PGA on rock. This is used for computing the soil term.
imt = PGA()
C = self.COEFFS[imt]
CR = self.REA[imt]
pga_rock = np.exp(get_gm_rock(C, ctx, self.d_sigma, CR))
# Compute ground-motion on soil.
for m, imt in enumerate(imts):
# Get the mean
C = self.COEFFS[imt]
CR = self.REA[imt]
mean[m] = get_gm_rock(C, ctx, self.d_sigma, CR)
# Site term
if self.site_term:
TMP = self.BEA14[imt]
mean[m] += get_fs_SeyhanStewart2014(TMP, imt, pga_rock,
ctx.vs30)
# Standard deviations
tau[m] = np.ones_like(tau[m]) * CR['between_event']
phi[m] = np.ones_like(tau[m]) * CR['within_event']
sig[m] = (tau[m]**2 + phi[m]**2)**0.5
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT Mh e0 e1 e2 e3 b3 b4 s0 s1 s2 s3 s4 s5 s6 s7 s8 s9
PGA 5.85 2.2156 0.6859 -0.1393 0.7656 -0.6187 0.0603 -2.1315 1.937 -0.504 0.0582 -0.0024982 -1.4442 1.2353 -0.2851 0.0302 -0.0012
PGV 5.9 5.9604 1.03 -0.1651 1.0789 -0.5785 0.0574 -2.2458 1.9508 -0.5181 0.0614 -0.0027251 -1.7584 1.3793 -0.3256 0.035 -0.0014
0.0199999996 5.9006 2.3793 0.6997 -0.1067 0.7489 -0.6376 0.0625 -1.1697 1.2816 -0.3364 0.0394 -0.0017102453 -1.2719 1.2532 -0.3167 0.0362 -0.0015
0.0219635405 5.9431 2.4579 0.693 -0.1015 0.7457 -0.6346 0.0618 -1.3148 1.4061 -0.3734 0.044 -0.0019214568 -1.3553 1.3063 -0.327 0.0368 -0.0016
0.0273298714 6.0306 2.6519 0.6779 -0.0941 0.7403 -0.6166 0.0587 -1.3383 1.4345 -0.3818 0.045 -0.0019621246 -1.8281 1.6476 -0.4136 0.0462 -0.0019
0.032959789 6.0191 2.7818 0.6747 -0.0967 0.7387 -0.585 0.0537 -0.991 1.1522 -0.2983 0.0344 -0.0014775553 -2.5924 2.2044 -0.5609 0.0632 -0.0026
0.0423190892 5.6497 2.6877 0.707 -0.123 0.7426 -0.5387 0.0468 -0.8906 1.0319 -0.2551 0.0283 -0.0011791884 -3.5399 2.8211 -0.7093 0.0789 -0.0033
0.0494804569 5.3764 2.5728 0.7181 -0.1604 0.7536 -0.5115 0.043 -0.9678 0.9945 -0.2209 0.0217 -0.0007889064 -4.1732 3.2534 -0.8208 0.0917 -0.0038
0.0655307993 5.625 2.889 0.7003 -0.1696 0.7602 -0.4634 0.0361 -2.3368 2.0173 -0.5053 0.0563 -0.0023391122 -3.8552 2.8013 -0.6513 0.0673 -0.0026
0.0815660655 5.2451 2.612 0.7566 -0.2428 0.7864 -0.4174 0.0302 -3.6821 2.9469 -0.7444 0.0832 -0.0034585228 -3.0859 2.1292 -0.4532 0.0429 -0.0015
0.098328419 5.4332 2.7636 0.7155 -0.2604 0.7935 -0.3807 0.0252 -4.0209 3.0878 -0.761 0.0833 -0.0033984683 -2.5045 1.6147 -0.3024 0.0246 -0.0007
0.1262626201 5.3609 2.6555 0.7327 -0.3243 0.8098 -0.3575 0.0225 -4.157 3.09 -0.745 0.0801 -0.0032210921 -1.4994 0.7291 -0.042 -0.0072 0.0007
0.1569858789 5.2587 2.4809 0.8026 -0.3823 0.8382 -0.3289 0.0194 -3.9816 2.8425 -0.6577 0.0683 -0.0026638928 -0.3022 -0.2533 0.2336 -0.0398 0.0021
0.1953125 5.4307 2.5414 0.818 -0.3859 0.8423 -0.2908 0.0143 -2.8318 1.8381 -0.3622 0.0321 -0.0010772438 0.7143 -1.0055 0.4204 -0.0591 0.0028
0.2512562871 5.6059 2.5206 0.8664 -0.3771 0.8783 -0.2423 0.0091 -1.733 0.9565 -0.1244 0.0052 0.0000218818 1.7886 -1.7704 0.6066 -0.0782 0.0035
0.3030303121 5.8482 2.6187 0.8513 -0.3634 0.8798 -0.2146 0.0059 -0.2401 -0.1858 0.1799 -0.0293 0.0014404841 2.1854 -1.9496 0.6164 -0.075 0.0032
0.3322259188 5.9569 2.6486 0.8482 -0.3573 0.8836 -0.2049 0.0051 0.5148 -0.7513 0.3278 -0.0457 0.0021057417 2.3083 -1.9797 0.6052 -0.0716 0.003
0.375939846 6.0872 2.6658 0.8495 -0.3503 0.8924 -0.1966 0.0049 1.5292 -1.4975 0.5194 -0.0666 0.0029394061 2.385 -1.9513 0.5719 -0.0649 0.0026
0.4694835544 6.2216 2.5819 0.8752 -0.348 0.9119 -0.2037 0.0075 3.3782 -2.86 0.8753 -0.1067 0.0045977338 1.3014 -0.8769 0.2053 -0.014 0.0001
0.5 6.2509 2.5469 0.8848 -0.3483 0.9178 -0.2078 0.0085 3.9137 -3.2548 0.9791 -0.1185 0.0050909007 0.8735 -0.4705 0.0707 0.0044 -0.0008
0.5847952962 6.4552 2.5866 0.8799 -0.3295 0.9223 -0.2195 0.0116 3.7737 -3.015 0.874 -0.1018 0.0042109804 -0.0375 0.3569 -0.1908 0.0384 -0.0024
0.7246376872 6.7311 2.6414 0.8936 -0.3015 0.9068 -0.2413 0.0166 2.9309 -2.1566 0.5764 -0.06 0.0021569513 -1.4537 1.5845 -0.5622 0.0848 -0.0044
0.9009009004 6.6235 2.2857 1.1469 -0.2652 0.9442 -0.277 0.0238 1.6778 -1.0035 0.2079 -0.0115 -0.0000997096 -3.4097 3.1906 -1.0274 0.1412 -0.0068
1.0 6.4642 2.0102 1.3242 -0.2472 0.9798 -0.2957 0.0273 1.116 -0.5002 0.0514 0.0085 -0.0010035093 -4.3861 3.9802 -1.2537 0.1685 -0.008
1.1235954762 6.5833 1.9969 1.3605 -0.2279 0.9907 -0.3209 0.0321 -0.5218 0.8676 -0.3544 0.0593 -0.0032785707 -4.9268 4.3684 -1.3471 0.1772 -0.0083
1.3888888359 6.73 1.8972 1.4604 -0.1919 1.0225 -0.3618 0.0399 -3.4682 3.2873 -1.0605 0.1461 -0.0071120951 -5.5938 4.8102 -1.439 0.1833 -0.0083
1.7543859482 6.71 1.5588 1.6329 -0.1544 1.108 -0.4042 0.0478 -5.7412 5.0899 -1.5655 0.2054 -0.0095954046 -5.9214 4.9748 -1.4514 0.1799 -0.0079
1.9607843161 6.6563 1.2828 1.7362 -0.134 1.1836 -0.4321 0.053 -6.5491 5.697 -1.7236 0.2222 -0.0102122375 -6.0007 4.984 -1.4353 0.1753 -0.0076
2.7027027607 6.695 0.7877 1.852 -0.1018 1.3351 -0.4919 0.0638 -7.9988 6.7253 -1.9714 0.2457 -0.0109460534 -4.5705 3.6687 -1.0001 0.1144 -0.0046
3.3333332539 6.7271 0.4494 1.9171 -0.084 1.4521 -0.5278 0.0702 -7.6498 6.3092 -1.8048 0.2188 -0.0094611053 -3.5814 2.7948 -0.7224 0.0771 -0.0028
4.1666669846 6.8479 0.2606 1.941 -0.0723 1.5209 -0.5568 0.0751 -6.9827 5.6453 -1.5705 0.1843 -0.0076800415 -2.3926 1.7661 -0.4021 0.0348 -0.0008
5.2631578445 6.8927 -0.0689 1.9793 -0.061 1.5919 -0.5823 0.0793 -6.1625 4.8839 -1.3179 0.149 -0.0059499122 -1.2368 0.7939 -0.1084 -0.0028 0.0009
""")
