# -*- coding: utf-8 -*-
# Copyright (C) 2015-2024 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:`Allen2022`
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
def _get_distance_scaling(C, rhypo):
"""
Distance scaling as a piece-wise linear geometrical attenuation
[Equations 2a and 2b, p. 1047].
Hinge distance Rx = 600 km separates two linear slopes in log10 space:
FR = c3 * log10(Rhypo) Rhypo <= Rx
FR = c3 * log10(Rx) + c4*(log10(Rhypo) - log10(Rx)) Rhypo > Rx
"""
Rx = 600.0
return np.where(
rhypo <= Rx,
C["c3"] * np.log10(rhypo),
C["c3"] * np.log10(Rx) + C["c4"] * (np.log10(rhypo) - np.log10(Rx)),
)
def _get_magnitude_scaling(C, mag):
"""
Quadratic magnitude scaling [Equation 3, p. 1048].
FM = c0 + c1*(Mw - 6)^2 + c2*(Mw - 6)
For periods < 0.3 s c1 is set to zero in the table (paper p. 1048).
"""
return C["c0"] + C["c1"] * ((mag - 6.0) ** 2) + C["c2"] * (mag - 6.0)
def _get_depth_scaling(C, hypo_depth):
"""
Cubic hypocentral-depth scaling [Equation 4, p. 1049].
FD = d0 + d1*log10(hz)^3 + d2*log10(hz)^2 + d3*log10(hz)
where hz is hypocentral depth anchored to [10, 500] km.
The paper states (p. 1049): "If h < 10 km or h > 500 km,
it is recommended to truncate hz to either 10 or 500 km."
The original OQ implementation omitted this truncation.
"""
hz = np.clip(hypo_depth, 10.0, 500.0) # BUG FIX: depth truncation
log_hz = np.log10(hz)
return C["d0"] + C["d1"] * (log_hz ** 3) + C["d2"] * (log_hz ** 2) + C["d3"] * log_hz
def _get_near_source_correction(C, rhypo):
"""
Near-source distance correction [Equations 5a and 5b, p. 1050].
FN = n0 * (log10(Rhypo) - log10(Rx)) Rhypo <= Rx
FN = 0 Rhypo > Rx
Applied to correct biases in near-source residuals that emerged
after the depth term was introduced (paper p. 1049-1050).
Uses the same hinge distance Rx = 600 km as the distance scaling.
"""
Rx = 600.0
return np.where(
rhypo <= Rx,
C["n0"] * (np.log10(rhypo) - np.log10(Rx)),
0.0,
)
def _get_site_scaling(C, vs30):
"""
Site amplification [Equation 6, p. 1050].
FS = s0 + s1 / (log10(Vs30) - log10(150))
Calibrated for 220 <= Vs30 <= 800 m/s using topographic-proxy
Vs30 estimates (Wald and Allen, 2007). The denominator is zero at
Vs30 = 150 m/s; the caller must respect the model applicability range.
"""
return C["s0"] + C["s1"] / (np.log10(vs30) - np.log10(150.0))
[docs]class Allen2022(GMPE):
"""
Implements the far-field GMM for the North Australian Craton:
Allen, T. I. (2022). A far-field ground-motion model for the North
Australian Craton from plate-margin earthquakes.
Bull. Seismol. Soc. Am. 112, 1041-1059. doi: 10.1785/0120210191
**Application range:** hypocentral distances ~500-1500 km, magnitudes up
to Mw 8.0, sites within the North Australian Craton (NAC), subduction
interface and intraslab sources in the Banda Sea region.
Note on PGA sigma [Equation 10, p. 1051]:
sigma_PGA = sqrt(tau_PGA^2 + phi_PGA^2 + lambda_PGA^2)
where lambda_PGA = 0.270 accounts for the additional uncertainty from
PGA proxy estimation using low-sample-rate data (paper p. 1050).
This term is already incorporated into the sigma value in Table 1
(footnote), so sigma is read directly from the table for all IMTs.
"""
## Supported tectonic region type is subduction intraslab.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB
## PGA, PGV, and 5%-damped PSA at 20 periods 0.1-10 s (Table 1, p. 1047).
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
# The paper uses geometric mean of horizontal components (p. 1046).
# GEOMETRIC_MEAN is not available in the current OQ const.IMC, so
# MEDIAN_HORIZONTAL is used as a substitute.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.MEDIAN_HORIZONTAL
## Total (sigma), inter-event (tau), and intra-event (phi) std devs
## [Equations 7-10, p. 1051].
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT,
}
## Vs30 (m/s) required for site scaling [Equation 6].
REQUIRES_SITES_PARAMETERS = {"vs30"}
## Moment magnitude and hypocentral depth (km) [Equations 3 and 4].
REQUIRES_RUPTURE_PARAMETERS = {"mag", "hypo_depth"}
## Hypocentral distance Rhypo (km) [Equations 2a, 2b, 5a, 5b].
REQUIRES_DISTANCES = {"rhypo"}
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
"""
Compute median ground motion (ln g or ln cm/s) and standard deviations.
mean = FR + FM + FD + FN + FS [Equation 1, median term only]
Standard deviations are read directly from Table 1.
The sigma value for PGA in Table 1 already includes the lambda_PGA term:
it was computed using Equation 10 [p. 1051], not Equation 9.
So we read it directly from the table instead of recomputing it from tau and phi.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
mean[m] = (
_get_distance_scaling(C, ctx.rhypo)
+ _get_magnitude_scaling(C, ctx.mag)
+ _get_depth_scaling(C, ctx.hypo_depth)
+ _get_near_source_correction(C, ctx.rhypo)
+ _get_site_scaling(C, ctx.vs30)
)
tau[m] = C["tau"]
phi[m] = C["phi"]
sig[m] = C["sigma"] # includes lambda_PGA for PGA [Eq. 10]
# Coefficient table — Table 1, p. 1047.
# Copied verbatim from the existing OQ implementation (allen_2022.py).
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c0 c1 c2 c3 c4 d0 d1 d2 d3 n0 s0 s1 tau phi sigma
pgv 5.1394 0.0000 1.9713 -2.6644 -7.336 5.2107 -1.8808 9.459 -13.949 -1.0181 -0.5880 0.2536 0.6361 0.4883 0.8019
pga -4.5508 0.0000 1.6129 -0.4923 -10.167 4.8787 -2.5207 12.070 -16.388 -1.3651 -1.0254 0.4008 0.7066 0.5094 0.9118
0.1 -5.3000 0.0000 1.4672 0.0000 -10.513 4.3555 -2.7260 12.699 -16.557 -2.6602 -1.0022 0.4258 0.7532 0.5038 0.9061
0.15 -5.2557 0.0000 1.4638 0.0456 -10.580 5.7681 -2.9707 14.147 -19.169 -1.2049 -0.9190 0.4239 0.7578 0.5252 0.9220
0.2 -5.1597 0.0000 1.4603 0.0284 -10.382 6.0008 -3.0078 14.372 -19.594 -1.2446 -0.8846 0.4066 0.7568 0.5343 0.9264
0.25 -5.0958 0.0000 1.4502 -0.0069 -10.080 6.0464 -3.0019 14.338 -19.567 -1.3811 -0.8669 0.3822 0.7436 0.5291 0.9127
0.3 -4.9242 0.0000 1.4988 -0.0897 -9.920 6.5203 -3.0348 14.583 -20.160 -1.4749 -0.7987 0.3619 0.7172 0.5286 0.8910
0.4 -4.2365 -0.0213 1.6047 -0.3716 -9.728 6.1641 -2.8040 13.533 -18.818 -1.5512 -0.7893 0.3403 0.7019 0.5499 0.8917
0.5 -1.6262 -0.0192 1.6542 -1.4501 -8.792 6.7588 -2.7780 13.581 -19.326 -1.0315 -0.6889 0.3084 0.7046 0.5530 0.8957
0.6 0.1424 -0.0670 1.7420 -2.2296 -7.931 5.3677 -2.4344 11.765 -16.380 -1.1632 -0.6341 0.2919 0.6765 0.5214 0.8541
0.75 1.8210 -0.1674 1.9003 -3.0099 -6.912 4.4379 -2.0824 10.083 -13.980 -1.0232 -0.7019 0.2781 0.6455 0.4849 0.8073
1.0 3.4777 -0.2088 1.9943 -3.8107 -6.044 4.8745 -1.9619 9.702 -13.938 -1.0307 -0.6230 0.2654 0.6146 0.4532 0.7636
1.25 4.7348 -0.1776 2.1150 -4.4348 -5.403 5.2371 -1.8821 9.451 -13.950 -0.8072 -0.5700 0.2509 0.6223 0.4257 0.7540
1.5 5.6353 -0.2334 2.2245 -4.8971 -4.781 5.9873 -1.9196 9.800 -14.879 -0.9129 -0.5587 0.2342 0.6233 0.4387 0.7622
2.0 6.0524 -0.3545 2.4366 -5.2236 -4.348 5.0004 -1.5450 7.960 -12.217 -0.6695 -0.4756 0.2230 0.5910 0.4394 0.7365
2.5 5.7973 -0.3619 2.4976 -5.2934 -4.005 5.0432 -1.4210 7.407 -11.637 -0.6849 -0.4486 0.2183 0.5689 0.4162 0.7049
3.0 5.4552 -0.3484 2.5378 -5.3066 -3.734 5.0210 -1.3028 6.860 -11.007 -0.6495 -0.4330 0.2095 0.5618 0.4033 0.6915
4.0 4.8483 -0.3590 2.6446 -5.2890 -3.656 5.0015 -1.1239 6.057 -10.102 -0.4710 -0.3915 0.2042 0.6152 0.3843 0.7254
5.0 4.1446 -0.3549 2.7324 -5.1969 -3.636 5.0599 -1.0292 5.628 -9.653 -0.5199 -0.4377 0.1985 0.6352 0.3917 0.7463
6.0 3.4946 -0.3247 2.7833 -5.1162 -3.547 4.6695 -0.9160 5.042 -8.744 -0.5526 -0.4253 0.1910 0.6207 0.4018 0.7394
7.5 2.8095 -0.3034 2.7654 -5.0636 -3.453 4.7249 -0.8061 4.540 -8.204 -0.5132 -0.4327 0.1820 0.5969 0.4066 0.7222
10.0 2.0278 -0.3459 2.7722 -5.0168 -3.368 5.0737 -0.7276 4.187 -7.966 -0.2645 -0.4564 0.1736 0.5880 0.4185 0.7217
""")
