# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2024-2025, 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/>.
"""
Created on Tue May 14 2024
Authors: savvinos.aristeidou@iusspavia.it
Module exports :class:`AristeidouEtAl2023`
:class:`AristeidouEtAl2023RotD100`
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import SDi
from openquake.hazardlib.gsim.campbell_bozorgnia_2014 import _get_z2pt5_ref
CONSTS = {
"available_strength_ratios": np.array([1.5, 2, 3, 4, 6]),
"mr": 6,
"rh1": 15,
"rh2": 150,
}
def _get_style_of_faulting(rake):
"""
Get fault type dummy variables
Fault type (Strike-slip, Normal, Reverse, Reverse-Oblique, Normal-oblique)
is derived from rake angle.
SOF encoding Rake Angles
_______________________________________________________
Strike-slip | 0 | -180 < rake < -150
| | -30 < rake < 30
| | 150 < rake < 180
| |
Normal | 1 | -120 < rake < -60
| |
Reverse | 2 | 60 < rake < 120
| |
Reverse-Oblique | 3 | 30 < rake < 60
| | 120 < rake < 150
| |
Normal-oblique | 4 | -150 < rake < -120
| | -60 < rake < -30
| |
Note that the 'Unspecified' case is not considered here as
rake is always given.
"""
sof = np.full_like(rake, 0)
sof[((rake >= -180) & (rake <= -150)) | ((rake > -30) &
(rake <= 30)) | ((rake > 150) & (rake <= 180))] = 0
sof[(rake > -120) & (rake <= -60)] = 1
sof[(rake > 60) & (rake <= 120)] = 2
sof[((rake > 30) & (rake <= 60)) | ((rake > 120) &
(rake <= 150))] = 3
sof[((rake > -150) & (rake <= -120)) | ((rake > -60) &
(rake <= -30))] = 4
return sof
[docs]def check_bounds(array, value):
"""
Checks whether a value is smaller than the minimum number inside the array
or bigger than the maximum number inside the array.
Returns True if it is inside bounds
"""
min_val = min(array)
max_val = max(array)
return not ((value < min_val) or (value > max_val))
def _get_magnitude_term(C, ctx):
"""
Returns the magnitude scaling term defined in equation (4), p. 1610
"""
f_m = C["b1"] * (ctx.mag - CONSTS["mr"]) + C["b2"] \
* (ctx.mag - CONSTS["mr"]) ** 2
return f_m
def _get_distance_term(C, ctx):
"""
Returns the distance scaling term given by equation (5), p. 1611
"""
r = np.sqrt(ctx.rrup ** 2 + C["c3"] ** 2)
f_d = np.zeros(ctx.sids.shape)
f_d[(r <= CONSTS["rh1"])] = (
(C["c11"] + C["c21"] * (ctx.mag - CONSTS["mr"]))
* np.log(r / CONSTS["rh2"]))[(r <= CONSTS["rh1"])]
f_d[(r > CONSTS["rh1"]) & (r <= CONSTS["rh2"])] = (
(C["c12"] + C["c22"] * (ctx.mag - CONSTS["mr"]))
* np.log(r / CONSTS["rh2"]))[(r > CONSTS["rh1"]) & (r <= CONSTS["rh2"])]
f_d[(r > CONSTS["rh2"])] = (
(C["c13"] + C["c23"] * (ctx.mag - CONSTS["mr"]))
* np.log(r / CONSTS["rh2"]))[(r > CONSTS["rh2"])]
return f_d
def _get_style_of_faulting_term(C, ctx, mechanism):
"""
Returns the style-of-faulting scaling term defined in equation (7), p. 1611
"""
fn = np.ones(ctx.sids.shape) * ((mechanism == 1) | (mechanism == 4))
ft = np.ones(ctx.sids.shape) * ((mechanism == 2) | (mechanism == 3))
f_sof = C["f1"] * fn + C["f2"] * ft
return f_sof
def _get_site_amplification_term(C, ctx):
"""
Returns the site amplification term defined in equation (8), p. 1611
"""
vs30 = ctx.vs30
f_s = np.zeros(ctx.sids.shape)
f_s[vs30 < 400] = (C["s1"] * np.log(vs30))[vs30 < 400]
f_s[(vs30 >= 400) & (vs30 < 650)] = (
C["s2"] * np.log(vs30))[(vs30 >= 400) & (vs30 < 650)]
f_s[(vs30 >= 650) & (vs30 < 1000)] = (
C["s3"] * np.log(vs30))[(vs30 >= 650) & (vs30 < 1000)]
f_s[vs30 >= 1000] = (C["s4"] * np.log(vs30))[vs30 >= 1000]
return f_s
def _get_basin_term(C, ctx, region=None):
"""
Returns the basin response term defined in equation (9), p. 1611
"""
z2pt5 = ctx.z2pt5.copy()
# Use non-Japan CB14 vs30 to z2pt5 relationship for none-measured values
mask = z2pt5 == -999
z2pt5[mask] = _get_z2pt5_ref(False, ctx.vs30[mask])
f_basin = np.zeros(ctx.sids.shape)
f_basin[(z2pt5 <= 1)] = (C["d1"] * (z2pt5 - 1))[z2pt5 <= 1]
f_basin[(z2pt5 > 1) & (z2pt5 <= 3)] = 0
f_basin[z2pt5 > 3] = (
C["d2"] * (1 - np.exp(-0.25*(z2pt5 - 3))))[z2pt5 > 3]
return f_basin
def _get_strength_ratio_interpolation(coeffs, imt, hor_comp_def):
"""
Returns the interpolated coefficients array for the intermediate
strength ratio
"""
prev_available_r = max(
v for v in CONSTS["available_strength_ratios"]
if v <= imt.strength_ratio)
next_available_r = min(
v for v in CONSTS["available_strength_ratios"]
if v > imt.strength_ratio)
prev_array = np.array(coeffs[
f"R={prev_available_r:g}, {hor_comp_def}"][
SDi(imt.period, prev_available_r)].tolist())
next_array = np.array(coeffs[
f"R={next_available_r:g}, {hor_comp_def}"][
SDi(imt.period, next_available_r)].tolist())
# Calculate the logarithmic interpolation factor
interpolation_factor = \
(np.log(imt.strength_ratio) - np.log(prev_available_r)) \
/ (np.log(next_available_r) - np.log(prev_available_r))
# Perform linear interpolation
interpolated_array = prev_array + \
(next_array - prev_array) * interpolation_factor
return interpolated_array
[docs]class AristeidouEtAl2023(GMPE):
"""
Implements a ground motion model developed by Savvinos Aristeidou,
Karim Tarbali, and Gerard J. O'Reilly, published as "A ground motion
model for orientation-independent inelastic spectral displacements
from shallow crustal earthquakes" (2023, Earthquake Spectra, Volume
39, Number 3, pages 1601 - 1624).
"""
#: Supported tectonic region type is active shallow crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types is inelastic spectral
#: acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {SDi}
#: Supported intensity measure components are orientation-
#: independent median horizontal
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: Supported standard deviation types are inter-event, intra-event
#: and total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameters are Vs30, and depth (km) to the 2.5 km/s
#: shear wave velocity layer (z2pt5)
REQUIRES_SITES_PARAMETERS = {'vs30', 'z2pt5'}
#: Required rupture parameters are magnitude, and rake
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake'}
#: Required distance measures are Rrup
REQUIRES_DISTANCES = {'rrup'}
hor_comp_def = "RotD50"
[docs] def compute(self, ctx: np.recarray, 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):
strength_ratio_inside_bounds = check_bounds(
CONSTS["available_strength_ratios"], imt.strength_ratio)
if imt.strength_ratio in CONSTS["available_strength_ratios"]:
C = self.COEFFS[
f"R={imt.strength_ratio:g}, {self.hor_comp_def}"][imt]
elif imt.strength_ratio not in CONSTS["available_strength_ratios"] \
and strength_ratio_inside_bounds:
interpolated_array = _get_strength_ratio_interpolation(
self.COEFFS, imt, self.hor_comp_def)
coeff_names = self.COEFFS[
f"R=1.5, {self.hor_comp_def}"
][imt].dtype.names
C = dict(zip(coeff_names, interpolated_array))
else:
raise ValueError(
f"Strength ratio of {imt.strength_ratio} out of bounds:"
f" {min(CONSTS['available_strength_ratios'])} - "
f"{max(CONSTS['available_strength_ratios'])}")
mechanism = _get_style_of_faulting(ctx.rake)
# Magnitude function:
f_m = _get_magnitude_term(C, ctx)
# Distance function:
f_d = _get_distance_term(C, ctx)
# Style-of-faulting function:
f_sof = _get_style_of_faulting_term(C, ctx, mechanism)
# Site amplification function:
f_s = _get_site_amplification_term(C, ctx)
# Basin-effects correction function:
f_basin = _get_basin_term(C, ctx)
# log of the functional form considered
mean[m] = np.squeeze(C["a"] + f_m + f_d + f_sof + f_s + f_basin)
sig[m] = C["σ"]
tau[m] = C["τ"]
phi[m] = C["φ"]
COEFFS = {
"R=1.5, RotD50": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,1.5) -1.758849087 1.381262180 -0.140146031 -1.398100655 0.361526612 -1.191855753 0.279898229 -2.117781082 -0.130635956 -0.110768886 0.225237477 -0.760093882 -0.757635293 -0.764738799 -0.757807959 0.434248806 0.512515224 -14.85085583 0.798745211 0.265555928 0.841732656
SDi(0.06,1.5) -1.603799818 1.348551228 -0.145063886 -1.158580911 0.344574506 -1.130981115 0.244527474 -2.321292224 0.161704967 -0.051153370 0.243531959 -0.720881079 -0.720940544 -0.722592777 -0.717302743 0.422207803 0.503374323 9.570548758 0.792294290 0.260266733 0.833947849
SDi(0.10,1.5) -1.574686474 1.368524866 -0.182937648 -1.641341044 0.406546518 -1.478841573 0.383113100 -2.632188960 0.074015150 -0.120473877 0.132413494 -0.629679981 -0.630559198 -0.635699057 -0.625933797 0.199151554 0.478394983 -14.78851441 0.712990921 0.229036204 0.748874914
SDi(0.20,1.5) -1.140285168 1.302588586 -0.272226070 -1.464360324 0.293102467 -1.522684442 0.305656360 -3.003215688 0.100660926 -0.236006185 0.005214049 -0.461113726 -0.466010239 -0.492358962 -0.512894703 0.098010197 0.397326831 12.42063332 0.615802242 0.205523409 0.649193556
SDi(0.30,1.5) -0.031438895 1.237523220 -0.148234620 -1.402180632 0.272929812 -1.391779812 0.221740335 -2.867981670 0.051665138 -0.204981118 0.167353097 -0.524922201 -0.530311095 -0.555078108 -0.563010927 0.207990552 0.334699421 10.73169742 0.608802026 0.198545391 0.640359415
SDi(0.50,1.5) 1.411521067 1.306762124 -0.190397169 -1.302645851 0.224830929 -1.279292060 0.185429778 -2.375068806 -0.047653455 -0.204596187 0.136774567 -0.618336662 -0.622706474 -0.640201151 -0.624228872 0.424243685 0.382268683 -10.04499085 0.612440807 0.204815454 0.645781010
SDi(0.75,1.5) 2.556200545 1.413181380 -0.236128044 -1.220194145 0.211300956 -1.176226161 0.180845094 -2.055955453 -0.063852806 -0.286259001 0.040854373 -0.708783854 -0.709352716 -0.715606603 -0.686591400 0.593184504 0.317620201 8.698950058 0.621967142 0.248257990 0.669682876
SDi(1.00,1.5) 2.974178276 1.496415852 -0.285067904 -1.134041626 0.174409811 -1.116058731 0.171593783 -1.880757195 -0.118671297 -0.287662804 0.074717695 -0.719813096 -0.726202156 -0.726508232 -0.687408595 0.699558221 0.406245401 7.552540994 0.626424028 0.221789485 0.664528132
SDi(1.50,1.5) 3.413913510 1.583684476 -0.324385686 -1.021830173 0.112856487 -1.005633426 0.116729551 -1.519885379 -0.014434998 -0.246904534 0.104520919 -0.717524312 -0.728818218 -0.718707900 -0.687252652 0.844941176 0.396457276 6.454938294 0.626357803 0.223506379 0.665040750
SDi(2.00,1.5) 3.647006004 1.683038675 -0.354886441 -0.992435334 0.087460079 -0.981644112 0.083034144 -1.332378913 0.051667444 -0.280003892 0.092896069 -0.722690155 -0.736509802 -0.719389394 -0.670094795 0.902655446 0.490155482 6.820444963 0.623536407 0.206688429 0.656900112
SDi(3.00,1.5) 4.054609165 1.889546075 -0.429713632 -1.037466618 0.074905503 -1.033147473 0.061239070 -1.105494574 -0.015507275 -0.337484492 0.033000350 -0.760238842 -0.770163885 -0.746076057 -0.691706581 0.923741399 0.417828867 8.349350311 0.611820161 0.223146521 0.651243640
SDi(4.00,1.5) 4.237981573 2.077832823 -0.439627726 -1.027176064 0.058419457 -1.079259311 0.098124872 -1.147095752 0.007074746 -0.421166679 -0.112579073 -0.769928210 -0.778685547 -0.746909213 -0.682370120 0.887790527 0.519053791 9.876059651 0.600012696 0.211932375 0.636341549
SDi(5.00,1.5) 4.225517745 2.174180934 -0.433792674 -1.003636314 0.066002403 -1.053923323 0.105470598 -1.106498927 -0.004875363 -0.578062061 -0.168960060 -0.744394076 -0.752495502 -0.717696455 -0.647488306 0.869751099 0.544963930 -9.079453231 0.600423691 0.234705539 0.644666812
"""),
"R=2, RotD50": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,2) -1.161601188 1.305947649 -0.171136257 -1.126220540 0.257293139 -1.155225673 0.223525560 -2.299900574 -0.124574656 -0.237036007 0.195959978 -0.661664774 -0.664738127 -0.687319622 -0.689471131 0.406006194 0.486967237 9.748876882 0.700325954 0.250277287 0.743703679
SDi(0.06,2) -0.205215058 1.330746163 -0.127451079 -1.017740139 0.240851185 -1.010704350 0.203773129 -1.926477144 -0.057422687 -0.051251953 0.286174244 -0.769257203 -0.768713691 -0.783722659 -0.784497468 0.543695066 0.529157825 8.261251597 0.783080979 0.292813889 0.836035761
SDi(0.10,2) -0.163820415 1.365990680 -0.113253918 -1.103941369 0.321671124 -1.090185747 0.255889928 -2.011599664 0.033190618 -0.036480469 0.263705021 -0.730628424 -0.731582145 -0.737662785 -0.720530619 0.491874182 0.498188602 8.061370457 0.790046586 0.281534038 0.838710334
SDi(0.20,2) -0.155942704 1.364030090 -0.232648737 -1.718293468 0.180536230 -1.475075669 0.332723054 -2.424115090 0.094194964 -0.169600986 0.063441829 -0.598049393 -0.599840227 -0.616095719 -0.623345418 0.249720866 0.502539390 -14.99853764 0.637619763 0.227669498 0.677046794
SDi(0.30,2) 0.500359282 1.301805750 -0.173343935 -1.685546582 0.200696657 -1.461807820 0.269322886 -2.485493503 0.051686632 -0.188445202 0.150563978 -0.604204609 -0.606421632 -0.623691688 -0.615914495 0.297108044 0.435350515 -14.99984050 0.598068083 0.201633985 0.631143165
SDi(0.50,2) 1.615670551 1.329014935 -0.226056799 -1.273753571 0.231200278 -1.253068618 0.194714594 -2.284205271 0.005986116 -0.262672699 0.059256751 -0.640149903 -0.644689093 -0.657699720 -0.637524846 0.469086042 0.355121017 -9.534212489 0.593588905 0.215400036 0.631462559
SDi(0.75,2) 2.528622600 1.428449359 -0.241064333 -1.199036119 0.206379826 -1.164249548 0.175177290 -1.991629972 -0.032052816 -0.275580263 0.040298529 -0.704902569 -0.706743232 -0.711934809 -0.677405734 0.612913084 0.344393110 8.154463607 0.604444501 0.246929652 0.652937522
SDi(1.00,2) 2.895577011 1.503559299 -0.285045465 -1.137939660 0.169346874 -1.114100229 0.167964955 -1.830413088 -0.046258749 -0.290615198 0.065575632 -0.707884732 -0.715721861 -0.715083001 -0.672980471 0.717402835 0.432017270 7.787718408 0.609055214 0.222688518 0.648489344
SDi(1.50,2) 3.411184207 1.587365753 -0.315607830 -1.024855619 0.106920477 -1.010884518 0.117365039 -1.502284509 0.019251771 -0.266072729 0.096243535 -0.723239129 -0.733765797 -0.722747307 -0.687436080 0.843005488 0.421938537 6.599477642 0.613110615 0.219472357 0.651208678
SDi(2.00,2) 3.651301537 1.676598386 -0.346155917 -0.992984015 0.082375967 -0.987555675 0.076190570 -1.327627850 0.071682297 -0.292961848 0.086897180 -0.729259983 -0.742203008 -0.724662111 -0.675011962 0.892028111 0.482021416 6.838351748 0.609401324 0.206477520 0.643430602
SDi(3.00,2) 3.966392278 1.889865612 -0.415337221 -1.030959806 0.076928045 -1.029325957 0.069161303 -1.100806835 0.029070700 -0.346807353 0.031834222 -0.750606407 -0.760279284 -0.736748579 -0.685150998 0.906507259 0.423534691 8.215911736 0.597571118 0.216953575 0.635735869
SDi(4.00,2) 4.156305898 2.069392981 -0.423983376 -1.031541923 0.067493720 -1.064424928 0.108449051 -1.125962891 0.014979388 -0.426098679 -0.085482339 -0.763831049 -0.771409589 -0.739844813 -0.678719580 0.864330762 0.510802186 -9.630688294 0.587031017 0.215758335 0.625425515
SDi(5.00,2) 4.083450833 2.176724488 -0.445047396 -0.526177683 0.196549513 -1.142568024 0.096016193 -1.043174754 0.028286232 -0.599651663 -0.205865413 -0.726571398 -0.734717384 -0.701323118 -0.631501583 0.851920676 0.636365339 -14.99983765 0.588109208 0.228729382 0.631022639
"""),
"R=3, RotD50": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,3) -1.121047821 1.226042008 -0.169108204 -1.268441440 0.261301839 -1.301120027 0.227365693 -2.672738653 -0.037004291 -0.229260796 0.175030804 -0.564158722 -0.570829167 -0.603500481 -0.617698463 0.253308858 0.435027959 9.814472014 0.672616368 0.218753315 0.707294699
SDi(0.06,3) 0.363125555 1.271065883 -0.175717455 -1.121054576 0.216232724 -1.104621938 0.186771874 -2.065027882 -0.137477738 -0.200949974 0.171519297 -0.720613186 -0.723431271 -0.751459918 -0.753645130 0.486694338 0.509246943 8.782551933 0.755968740 0.274319295 0.804201351
SDi(0.10,3) 1.145137992 1.330643501 -0.104426984 -1.001210240 0.228938531 -0.977664848 0.181659423 -1.629083691 -0.089018334 -0.062616945 0.215189670 -0.809648535 -0.807815685 -0.818074269 -0.797082898 0.645194464 0.506199067 6.085498866 0.836099347 0.333547816 0.900175685
SDi(0.20,3) 1.097773914 1.385645348 -0.165258723 -1.205287704 0.287531678 -1.185465371 0.270850768 -1.930512057 0.157869426 -0.078492416 0.242060162 -0.738537206 -0.739758716 -0.744378685 -0.718510998 0.486651886 0.445303656 8.299330094 0.723960431 0.276203096 0.774859249
SDi(0.30,3) 1.343147575 1.364144069 -0.197581168 -1.256373795 0.256409170 -1.241362478 0.253393166 -2.119656921 0.142500176 -0.162350480 0.163049440 -0.696914355 -0.698112992 -0.704484433 -0.678904794 0.470161155 0.413802102 8.986648675 0.639352111 0.238931753 0.682539013
SDi(0.50,3) 1.924532557 1.397846121 -0.238326054 -1.226804384 0.213557630 -1.204187809 0.209759956 -2.047888077 0.081376361 -0.251985002 0.057003983 -0.673876950 -0.678466578 -0.685221828 -0.647054289 0.563755776 0.388249618 8.781873478 0.596773863 0.240699403 0.643486787
SDi(0.75,3) 2.536960767 1.464878579 -0.248297099 -1.163536265 0.177694547 -1.141005950 0.175777781 -1.869341772 0.015452605 -0.256036597 0.051867343 -0.697508906 -0.702094773 -0.703331022 -0.660200217 0.671009150 0.353752582 7.737689700 0.595063966 0.243759180 0.643054944
SDi(1.00,3) 2.882907557 1.533063877 -0.288987135 -1.129032632 0.159321346 -1.102524546 0.157916805 -1.690565462 0.045305742 -0.305840876 0.038751973 -0.700186326 -0.709655158 -0.705633098 -0.663825702 0.740466514 0.456684699 7.788155802 0.596578991 0.214425988 0.633944001
SDi(1.50,3) 3.455261515 1.646909009 -0.339706277 -1.034132828 0.104115529 -1.023269746 0.113659154 -1.509195586 0.122602460 -0.349591335 -0.008014411 -0.728003109 -0.737067670 -0.724029483 -0.678031209 0.863960164 0.428981406 6.838823370 0.601239058 0.215607941 0.638729355
SDi(2.00,3) 3.660032865 1.698404304 -0.333718040 -0.994681490 0.081041793 -0.990642597 0.079357640 -1.336124895 0.095210136 -0.317759777 0.069705041 -0.734328059 -0.744812359 -0.725976347 -0.679388622 0.881744443 0.463265283 6.896465146 0.593879035 0.207233599 0.628997673
SDi(3.00,3) 3.845520600 1.921136562 -0.397345242 -1.026731789 0.081742862 -1.014311977 0.084000135 -1.135161518 0.092001394 -0.360397840 0.011792960 -0.730761855 -0.741254933 -0.715109299 -0.663555449 0.861666919 0.426057457 8.091893124 0.587554364 0.218733872 0.626948672
SDi(4.00,3) 4.049707138 2.076226892 -0.415940397 -1.004773335 0.085832059 -1.023219512 0.117682843 -1.110759137 0.064804687 -0.466739743 -0.084523798 -0.746658148 -0.752139669 -0.719771996 -0.660512762 0.826517193 0.490587158 8.141507650 0.578835826 0.221210627 0.619665277
SDi(5.00,3) 3.907003589 2.151924460 -0.430013692 -0.986751446 0.059943466 -1.030235329 0.115055676 -1.105008448 0.109001849 -0.595467157 -0.154363325 -0.697965166 -0.705027217 -0.672932274 -0.602223668 0.826488404 0.615097807 8.959895138 0.570213226 0.230049374 0.614870586
"""),
"R=4, RotD50": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,4) -1.112158527 1.210747431 -0.190663896 -1.344226784 0.268681429 -1.373080488 0.238891226 -2.870563449 0.016022485 -0.232996315 0.132756403 -0.524157706 -0.531268260 -0.565736699 -0.582650915 0.190617148 0.420344221 10.53258818 0.671806235 0.209217761 0.703630364
SDi(0.06,4) 0.464409387 1.223549463 -0.144835632 -1.196754523 0.210473578 -1.172770057 0.172803304 -2.182477817 -0.157287102 -0.197352934 0.236773894 -0.689971034 -0.693692191 -0.724616093 -0.728958334 0.431383249 0.494063705 -9.416592196 0.746775577 0.251406980 0.787958903
SDi(0.10,4) 1.651313409 1.334143263 -0.109752022 -1.053841951 0.203227770 -0.992631757 0.170319125 -1.568576155 -0.151982692 -0.075908023 0.256878535 -0.829756047 -0.827940917 -0.840090824 -0.819597147 0.667162926 0.527855200 7.142439298 0.840897685 0.331528749 0.903891712
SDi(0.20,4) 1.785689049 1.434758532 -0.143431971 -1.115707532 0.254688500 -1.108112318 0.280756364 -1.641936847 0.066434249 -0.072902615 0.255288268 -0.804681598 -0.806216972 -0.805683385 -0.761815924 0.603426827 0.450419956 6.620075259 0.774604992 0.311450857 0.834873961
SDi(0.30,4) 1.862285367 1.418896965 -0.190634940 -1.181370279 0.235127560 -1.176676496 0.271181772 -1.842198756 0.149305468 -0.125937474 0.176058684 -0.750107364 -0.752363533 -0.752194754 -0.712190774 0.585116938 0.436508199 7.737934483 0.684011545 0.266480269 0.734086866
SDi(0.50,4) 2.126194849 1.454679205 -0.248470288 -1.174757673 0.200660855 -1.166299798 0.221906777 -1.849511317 0.145181267 -0.255531581 0.051978775 -0.688281476 -0.693753291 -0.694858433 -0.649058069 0.647077686 0.406684024 7.738051465 0.617376611 0.262328912 0.670798284
SDi(0.75,4) 2.625277043 1.490845018 -0.253439265 -1.130328209 0.162823978 -1.120737187 0.170966626 -1.750299102 0.085129102 -0.253602827 0.064895939 -0.702676795 -0.708858681 -0.706155582 -0.657459339 0.710460416 0.418845731 7.179800422 0.602562281 0.251214319 0.652832242
SDi(1.00,4) 2.851827314 1.545772721 -0.281711603 -1.104067433 0.140277086 -1.082250532 0.144224699 -1.561987133 0.131750415 -0.291135699 0.079928506 -0.689304021 -0.699226883 -0.692301572 -0.648096459 0.758607057 0.494511648 7.552644808 0.599082258 0.212455421 0.635638937
SDi(1.50,4) 3.444448295 1.624929724 -0.311256114 -1.025011521 0.095244547 -1.005784881 0.098356152 -1.429049471 0.160030266 -0.298506167 0.079506113 -0.729150842 -0.737682169 -0.723348527 -0.673580782 0.828599840 0.447292251 6.897395403 0.599200401 0.216138386 0.636990520
SDi(2.00,4) 3.631338713 1.736343959 -0.327990607 -0.990889916 0.080481670 -0.988886664 0.083232341 -1.326497463 0.123730883 -0.321196961 0.047695239 -0.730316917 -0.739145327 -0.718908141 -0.670066718 0.840810986 0.483191512 6.765820950 0.593532692 0.213486828 0.630759608
SDi(3.00,4) 3.813694329 1.980985852 -0.403302114 -1.023770824 0.093059645 -1.009538060 0.100235130 -1.146573091 0.123741997 -0.403343364 -0.062187186 -0.720825695 -0.729769659 -0.703347211 -0.654423636 0.823338550 0.446026895 7.737816198 0.586330468 0.226610812 0.628598344
SDi(4.00,4) 3.891877162 2.096055083 -0.411513367 -1.005984506 0.088872010 -1.013218668 0.116001663 -1.086615597 0.115194071 -0.482124762 -0.075533044 -0.720575294 -0.725903129 -0.693620054 -0.635340264 0.808594634 0.502754630 8.204528434 0.575012567 0.227404951 0.618346556
SDi(5.00,4) 3.794876570 2.171914279 -0.429636002 -0.985949523 0.060352589 -1.025650534 0.131118533 -1.086031048 0.162698562 -0.608535091 -0.182149528 -0.678715289 -0.684656131 -0.654029203 -0.586156938 0.799983062 0.658604999 -8.959863927 0.563677216 0.232236220 0.609643884
"""),
"R=6, RotD50": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,6) -1.098088322 1.221496883 -0.238636341 -1.409301310 0.261478924 -1.452287672 0.256888350 -3.029107828 0.061404583 -0.264578633 0.065187959 -0.482597677 -0.489808477 -0.527722324 -0.549114676 0.127687853 0.414503186 11.64081642 0.678945650 0.205109394 0.709251055
SDi(0.06,6) 0.538247575 1.193628190 -0.150060574 -1.254035693 0.218379081 -1.224714953 0.161882219 -2.362137528 -0.118528488 -0.219869890 0.215368351 -0.648258350 -0.653291273 -0.685189297 -0.687282112 0.381303412 0.452393335 -9.534110762 0.737975678 0.230958042 0.773272086
SDi(0.10,6) 2.077056780 1.317391548 -0.133181349 -1.115167424 0.191924409 -1.041129684 0.161214452 -1.601964512 -0.195497671 -0.190339879 0.151245127 -0.827306040 -0.826001925 -0.838757312 -0.817308434 0.686583324 0.515490300 7.803450663 0.831990580 0.322249193 0.892217948
SDi(0.20,6) 2.537236466 1.502481523 -0.137545337 -1.058325290 0.236114559 -1.048235109 0.277481695 -1.386675146 -0.007776229 -0.122704148 0.228729555 -0.864034208 -0.866533638 -0.860915114 -0.808610545 0.718315414 0.481332136 5.281996784 0.812965546 0.336700512 0.879931937
SDi(0.30,6) 2.397653057 1.504630322 -0.192318638 -1.112126260 0.219363040 -1.105515509 0.276265148 -1.507987923 0.141215011 -0.127891437 0.159120680 -0.787481936 -0.793093185 -0.785269060 -0.737024173 0.731010359 0.440822377 6.527794215 0.733181734 0.296580963 0.790895520
SDi(0.50,6) 2.455815000 1.520933149 -0.243436589 -1.118894905 0.187075254 -1.119107820 0.216605373 -1.601526919 0.234022154 -0.229620155 0.065246820 -0.715255535 -0.722571417 -0.716048109 -0.663460389 0.752251922 0.409358173 6.780598314 0.653739510 0.284192722 0.712839989
SDi(0.75,6) 2.812238715 1.543309501 -0.268181233 -1.104055680 0.131906920 -1.094641696 0.150193365 -1.528522274 0.165332450 -0.261325867 0.057638329 -0.715070508 -0.723082724 -0.713504804 -0.659527020 0.781911458 0.491151109 7.146029257 0.625339268 0.265048473 0.679190616
SDi(1.00,6) 2.921628796 1.592939911 -0.283495613 -1.073130294 0.115580226 -1.063409385 0.125246271 -1.387616942 0.260957345 -0.303650372 0.057341032 -0.689077412 -0.699314065 -0.686411155 -0.639540985 0.787078941 0.518494619 7.088496234 0.614496668 0.224953076 0.654377599
SDi(1.50,6) 3.383913284 1.689509487 -0.304513410 -1.017198497 0.091289356 -1.000978958 0.095007899 -1.368254314 0.225761021 -0.303045578 0.055422734 -0.715100481 -0.723941843 -0.707627124 -0.649599812 0.803712229 0.521883812 6.599929371 0.608309042 0.226390888 0.649070663
SDi(2.00,6) 3.521185398 1.796723123 -0.317253938 -0.988074823 0.072681000 -0.979615617 0.086828425 -1.306862285 0.198471750 -0.341042837 0.025470633 -0.710279874 -0.718715655 -0.696244803 -0.640278828 0.776004032 0.538084717 6.475916722 0.602311222 0.225983986 0.643309856
SDi(3.00,6) 3.692763523 2.052536185 -0.404142016 -1.023831318 0.095271382 -1.009186698 0.116127302 -1.115326995 0.173649585 -0.416968765 -0.092264698 -0.699249749 -0.708057318 -0.680003069 -0.630278879 0.781640587 0.461670885 7.624990768 0.582941606 0.234827394 0.628462267
SDi(4.00,6) 3.653436765 2.132812898 -0.398551678 -1.014490313 0.102078556 -1.009585188 0.137766215 -1.042914709 0.147002649 -0.476916771 -0.081980857 -0.683348961 -0.689763024 -0.657275006 -0.602795611 0.768035229 0.508717113 8.091966505 0.566920011 0.241078820 0.616049751
SDi(5.00,6) 3.552790400 2.250745163 -0.436353534 -0.995000174 0.079362374 -1.029460175 0.169025489 -1.064155964 0.225974707 -0.646949492 -0.246883684 -0.636825951 -0.643241205 -0.615085602 -0.554096429 0.761545928 0.675096531 8.959875079 0.559125372 0.244441068 0.610223416
"""),
}
[docs]class AristeidouEtAl2023RotD100(AristeidouEtAl2023):
"""
Implements the Aristeidou, Tarbali, and O'Reilly (2023) GMM for
the RotD100 horizontal component definition
"""
#: Supported intensity measure components are orientation-
#: independent maximum horizontal
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD100
hor_comp_def = "RotD100"
COEFFS = {
"R=1.5, RotD100": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,1.5) -1.351111422 1.307219253 -0.139469557 -1.147938415 0.290601842 -1.165449312 0.264451688 -2.139283827 -0.166209815 -0.196499773 0.227608029 -0.656525058 -0.659422459 -0.678793702 -0.682383352 0.397436489 0.471029665 9.701920576 0.733811791 0.258094180 0.777876822
SDi(0.06,1.5) -0.673425494 1.388085210 -0.159440971 -1.092259522 0.300693428 -1.093935632 0.295111797 -2.017869321 -0.003919270 -0.188440131 0.134116838 -0.712425106 -0.713470711 -0.723111513 -0.717627189 0.539332693 0.549028905 8.380203715 0.811600918 0.282975529 0.859518005
SDi(0.10,1.5) -0.689424186 1.389646664 -0.169406397 -1.239848510 0.380927856 -1.242120832 0.331305826 -2.270214373 0.101598198 -0.171684048 0.111764828 -0.656287469 -0.658402115 -0.666434155 -0.644152502 0.365767207 0.535745454 9.026614398 0.790831205 0.249075694 0.829127672
SDi(0.20,1.5) -0.536249041 1.332943202 -0.259056571 -1.428687263 0.304753100 -1.480497752 0.323879092 -2.740176537 0.128297046 -0.220669108 0.038047615 -0.509581566 -0.512315098 -0.534238255 -0.547529796 0.173529835 0.411869748 11.74528116 0.639393740 0.208177486 0.672430086
SDi(0.30,1.5) 0.423306706 1.284189822 -0.161129003 -1.724500338 0.163741309 -1.503587674 0.270751302 -2.651152122 0.046935069 -0.217682788 0.150773725 -0.561746007 -0.564077644 -0.584740601 -0.587438557 0.238908602 0.430802682 -14.99983844 0.612644725 0.195150021 0.642975186
SDi(0.50,1.5) 1.705308399 1.318502336 -0.233003088 -1.296845887 0.234479931 -1.281361908 0.195849339 -2.354696170 -0.041957609 -0.284340263 0.056360870 -0.616749300 -0.621729935 -0.636814273 -0.621799375 0.433329683 0.347095774 9.436414919 0.610786699 0.212500087 0.646696744
SDi(0.75,1.5) 2.781242117 1.424020040 -0.240408306 -1.214349381 0.213681570 -1.186023142 0.182970413 -2.041406503 -0.053536040 -0.292278832 0.032313084 -0.706497894 -0.706375148 -0.713636562 -0.683312754 0.591093771 0.320684142 8.154475067 0.621543420 0.248224354 0.669276888
SDi(1.00,1.5) 3.162824284 1.506278722 -0.286892814 -1.136019489 0.176753783 -1.126825557 0.173124105 -1.859489396 -0.104225446 -0.293410614 0.064811405 -0.711250410 -0.717666168 -0.718158606 -0.674059418 0.692966392 0.397984681 7.179848799 0.623233125 0.224539601 0.662448157
SDi(1.50,1.5) 3.633112081 1.602893237 -0.322787093 -1.034521593 0.119421364 -1.019258438 0.127890046 -1.511337142 -0.020908785 -0.254662507 0.101649772 -0.716758779 -0.727984125 -0.716272768 -0.683389199 0.820851055 0.445987789 6.370211370 0.626061912 0.225730207 0.665513069
SDi(2.00,1.5) 3.853554858 1.695600902 -0.356593455 -1.000445188 0.090191394 -0.992410042 0.091996214 -1.330998148 0.060010622 -0.299332629 0.070924259 -0.716811612 -0.730918920 -0.713325505 -0.661080818 0.882867426 0.481879411 6.619947623 0.624055441 0.204946944 0.656847351
SDi(3.00,1.5) 4.166971263 1.902043214 -0.418693027 -1.048516923 0.086735476 -1.038192521 0.076312297 -1.079376917 -0.010366920 -0.348373234 0.029784605 -0.739345398 -0.749326418 -0.727311819 -0.673813225 0.906988986 0.403455515 8.092159636 0.614626070 0.221696054 0.653386827
SDi(4.00,1.5) 4.365221313 2.074075657 -0.432806344 -0.543085307 0.137631567 -1.165859308 0.094219096 -1.077278316 0.042899473 -0.417233173 -0.103491149 -0.755665532 -0.765037996 -0.734253091 -0.675721181 0.854278086 0.571235841 -14.99983982 0.601100733 0.219238627 0.639834093
SDi(5.00,1.5) 4.338203907 2.144239937 -0.417486091 -0.460566696 0.159822942 -1.152215986 0.090858912 -1.032637544 0.018191787 -0.570283234 -0.127758107 -0.732559253 -0.739857702 -0.706386227 -0.635737429 0.851708384 0.609916876 -14.99984062 0.603234202 0.239597614 0.649075126
"""),
"R=2, RotD100": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,2) -1.209409742 1.260940155 -0.153900084 -1.249184220 0.284319058 -1.273787840 0.257783797 -2.442510716 -0.121321084 -0.247243500 0.194471680 -0.566463059 -0.575547334 -0.605041321 -0.619245346 0.300728814 0.498034610 10.430362220 0.708552569 0.230967521 0.745246763
SDi(0.06,2) 0.028022440 1.313650895 -0.159414301 -1.102082902 0.247865535 -1.094053398 0.240978071 -1.965122624 -0.127308785 -0.196300615 0.172170848 -0.699044498 -0.703515833 -0.726491463 -0.731340137 0.502533411 0.532714439 8.440297282 0.806442360 0.279323934 0.853446624
SDi(0.10,2) 0.362570807 1.366390916 -0.116611386 -1.074693766 0.294262100 -1.082761069 0.272409925 -1.875769690 -0.003457658 -0.166586530 0.156189129 -0.714552663 -0.716251065 -0.726731227 -0.699170065 0.575428708 0.541788638 6.640535006 0.845463790 0.301775070 0.897706641
SDi(0.20,2) 0.436552854 1.336165296 -0.182945956 -1.318549907 0.320764097 -1.311840411 0.287930327 -2.287754106 0.133770757 -0.132421574 0.183084699 -0.629988175 -0.630703401 -0.642848531 -0.630583595 0.354451930 0.421316913 9.334013389 0.691470344 0.232834962 0.729618637
SDi(0.30,2) 0.956073097 1.343252840 -0.241761254 -1.331853679 0.273384754 -1.338262416 0.262152082 -2.421139754 0.135225418 -0.262133053 0.070741897 -0.608667625 -0.611563593 -0.626700093 -0.613521027 0.341682759 0.401549883 -9.654707733 0.623274485 0.208828783 0.657328338
SDi(0.50,2) 1.955389523 1.353429668 -0.232765353 -1.274893928 0.229176056 -1.255579143 0.206691715 -2.220408146 0.036321506 -0.275542401 0.053191136 -0.647393016 -0.651691144 -0.662427886 -0.634299704 0.483137648 0.344681961 9.066008656 0.602104961 0.224070398 0.642446828
SDi(0.75,2) 2.798297498 1.445693981 -0.252126290 -1.207364907 0.203726747 -1.179639175 0.179911501 -1.975038323 0.001105500 -0.291123908 0.025671291 -0.701575460 -0.702497308 -0.706008775 -0.668040016 0.625219576 0.355141808 8.154381791 0.608700409 0.244701522 0.656044986
SDi(1.00,2) 3.057569913 1.526886059 -0.289427112 -1.145979939 0.172130469 -1.127124648 0.179141909 -1.768554947 -0.054507564 -0.303177782 0.051772266 -0.688047583 -0.696791859 -0.696862676 -0.647466931 0.708238975 0.449972017 7.535522111 0.608382697 0.225974964 0.648994754
SDi(1.50,2) 3.596869507 1.611674715 -0.316769697 -1.034480583 0.108537266 -1.016557503 0.121636962 -1.479367553 0.017435873 -0.274712878 0.086906965 -0.709344602 -0.720383847 -0.709135876 -0.667345716 0.819722734 0.490139690 6.455076114 0.616694784 0.224083012 0.656144537
SDi(2.00,2) 3.863009564 1.696376018 -0.343516403 -1.000301803 0.084044283 -0.992824657 0.084524744 -1.343774482 0.090419540 -0.302907196 0.064048233 -0.716975170 -0.729748119 -0.711868391 -0.664933691 0.877981585 0.475337906 6.839400005 0.611421077 0.206008235 0.645193867
SDi(3.00,2) 4.096376573 1.906453977 -0.415081299 -1.036409200 0.082846951 -1.028604348 0.076878564 -1.113357237 0.081761759 -0.370894300 0.006930362 -0.721757495 -0.732390860 -0.709735834 -0.657330974 0.891368980 0.400746532 8.091244772 0.604487672 0.217488755 0.642422528
SDi(4.00,2) 4.351540398 2.068172133 -0.419782004 -1.005281973 0.080728082 -1.032988199 0.106440543 -1.140627178 0.040676072 -0.431036560 -0.058545107 -0.748161219 -0.756434691 -0.724186612 -0.666928470 0.834384310 0.485148961 8.092353226 0.591749141 0.221909388 0.631989574
SDi(5.00,2) 4.245508512 2.165154353 -0.445902383 -0.414834344 0.114573633 -1.135607355 0.083648064 -1.050860644 0.097981496 -0.613303675 -0.194654074 -0.706121658 -0.714657804 -0.683386948 -0.611538134 0.828583862 0.646969331 -14.999838630 0.590695492 0.232162280 0.634681407
"""),
"R=3, RotD100": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,3) -1.114207571 1.217421836 -0.168291035 -1.350807411 0.287785364 -1.382437171 0.257121092 -2.798889455 -0.034806285 -0.241510271 0.158409817 -0.507854250 -0.516996006 -0.551608365 -0.575182148 0.192038646 0.413651879 10.283646610 0.689860917 0.210591515 0.721288341
SDi(0.06,3) 0.445885363 1.249141796 -0.180153562 -1.198520891 0.229598505 -1.190217321 0.206692447 -2.150724687 -0.175260988 -0.237638948 0.162667032 -0.668341565 -0.674895173 -0.705225461 -0.712255473 0.422646104 0.497483106 -8.959845609 0.773000365 0.258531477 0.815087780
SDi(0.10,3) 1.429631690 1.319195302 -0.113954090 -1.112801812 0.231415631 -1.055154695 0.202153992 -1.697660817 -0.082823682 -0.196473427 0.154316541 -0.778457959 -0.778418528 -0.791202984 -0.771827116 0.671656949 0.556189613 7.788159402 0.868497082 0.323954208 0.926948494
SDi(0.20,3) 1.539681443 1.417629675 -0.158048489 -1.173768905 0.280010468 -1.181196540 0.303723110 -1.804044136 0.080546527 -0.099554859 0.199569629 -0.742975942 -0.744332859 -0.747653587 -0.707386549 0.537634291 0.452535150 6.620262910 0.774512359 0.293187963 0.828147678
SDi(0.30,3) 1.794061103 1.401436716 -0.213512853 -1.247232527 0.260695713 -1.244308887 0.281288942 -1.976408893 0.121654923 -0.202041122 0.123535921 -0.707835112 -0.709989121 -0.714345659 -0.677081728 0.521008251 0.424297350 8.060394265 0.685024410 0.249965771 0.729205958
SDi(0.50,3) 2.180913400 1.423651681 -0.233223089 -1.228915159 0.220562700 -1.209270545 0.220650495 -1.983220012 0.124233142 -0.219838660 0.089721402 -0.664094215 -0.669716684 -0.674896932 -0.632188220 0.578752535 0.433886393 8.276472421 0.623754067 0.246318081 0.670627865
SDi(0.75,3) 2.799352438 1.491872669 -0.254936583 -1.176032358 0.178412823 -1.156243670 0.188605351 -1.814966131 0.047613782 -0.260071331 0.057144293 -0.688711713 -0.693748311 -0.692788471 -0.642404232 0.676995872 0.392083020 7.704790901 0.613026351 0.243345986 0.659559381
SDi(1.00,3) 3.070191594 1.549723834 -0.299807990 -1.120196229 0.151890613 -1.108140557 0.149958180 -1.647443909 0.085625135 -0.333970792 0.018619385 -0.676529375 -0.686167696 -0.681742055 -0.632609240 0.732744546 0.523631545 7.252678335 0.608584881 0.221770134 0.647732622
SDi(1.50,3) 3.643361832 1.636958269 -0.323440628 -1.029224684 0.093266214 -1.011065660 0.108110281 -1.454729533 0.115426546 -0.315125546 0.037495141 -0.709351909 -0.718407120 -0.707445683 -0.654974013 0.816716484 0.416340665 6.599874251 0.610889709 0.220829287 0.649578179
SDi(2.00,3) 3.861237964 1.712334490 -0.332539212 -0.995892146 0.068490014 -0.996414821 0.079180313 -1.329502268 0.135461097 -0.324203033 0.056347801 -0.714350639 -0.724609381 -0.706171286 -0.666758913 0.856168666 0.457081200 7.013043028 0.605404792 0.213280234 0.641874926
SDi(3.00,3) 4.101730375 1.958320782 -0.406123234 -1.016723838 0.084111680 -1.011053840 0.097895677 -1.160280349 0.125822703 -0.373806505 -0.018839979 -0.716889599 -0.726387113 -0.701900503 -0.650123055 0.837129877 0.410742191 7.737962075 0.599580790 0.225236187 0.640490799
SDi(4.00,3) 4.181084731 2.074105488 -0.416786616 -0.980598678 0.077612990 -1.002147829 0.112868807 -1.148381022 0.142719197 -0.485777320 -0.090060945 -0.709581511 -0.717589226 -0.686700618 -0.627182271 0.808776373 0.477734812 7.535187843 0.589560763 0.231388970 0.633342521
SDi(5.00,3) 4.071747426 2.172288868 -0.447190664 -0.455302800 0.086663975 -1.122549760 0.092235417 -1.044228545 0.195190972 -0.623202345 -0.203149671 -0.672067210 -0.679734386 -0.651532448 -0.581089908 0.795332038 0.672335392 -14.999838890 0.580584365 0.241641848 0.628863250
"""),
"R=4, RotD100": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,4) -1.062622628 1.212082438 -0.171441908 -1.420119648 0.269796697 -1.460145005 0.274886515 -2.936638884 -0.003209747 -0.236832633 0.139250908 -0.487628632 -0.495541828 -0.531595086 -0.556491289 0.145240864 0.383149235 11.640828070 0.692392588 0.203150888 0.721580058
SDi(0.06,4) 0.599424283 1.229112885 -0.148926355 -1.673975803 0.135277660 -1.372328202 0.225433927 -2.191856011 -0.211656824 -0.223795055 0.189269068 -0.661403828 -0.666446946 -0.697295300 -0.700827120 0.376048565 0.545540107 -14.998533040 0.767959505 0.235874017 0.803366886
SDi(0.10,4) 1.888139613 1.311832092 -0.122410860 -1.112486509 0.215106411 -1.056658222 0.188510159 -1.651872051 -0.150361364 -0.198891371 0.156051026 -0.799530840 -0.798832369 -0.811250694 -0.794768950 0.667066680 0.525183441 7.143082964 0.865399166 0.322017011 0.923369196
SDi(0.20,4) 2.091007131 1.453553616 -0.133471796 -1.126789618 0.260531544 -1.126738206 0.304759366 -1.577230418 0.033094337 -0.092826891 0.254933173 -0.789856458 -0.792680953 -0.792165427 -0.740111514 0.633333783 0.456451375 5.933273820 0.813844638 0.317479692 0.873576814
SDi(0.30,4) 2.260693279 1.462335857 -0.209559954 -1.189197656 0.253851696 -1.193109104 0.292330842 -1.732083654 0.131249126 -0.204638149 0.113251799 -0.750518159 -0.754033405 -0.751352657 -0.705982616 0.628060753 0.445898338 6.839305625 0.722848359 0.278283634 0.774565382
SDi(0.50,4) 2.408765977 1.487976511 -0.239508200 -1.198088338 0.208859064 -1.188412759 0.238405322 -1.800017066 0.168510770 -0.237365679 0.084224205 -0.683021132 -0.688584623 -0.687419583 -0.636262152 0.667949333 0.450997581 7.704889746 0.648311828 0.264671723 0.70025663
SDi(0.75,4) 2.917912283 1.518299614 -0.267941055 -1.140758712 0.160595273 -1.129143882 0.175844171 -1.707618507 0.105757267 -0.274489261 0.050823550 -0.693102212 -0.699738519 -0.694706589 -0.637632085 0.723191310 0.450566581 7.099842060 0.629062606 0.251528622 0.677485358
SDi(1.00,4) 3.123849342 1.585713877 -0.310145837 -1.098634351 0.135079922 -1.089516958 0.138298940 -1.539194938 0.199061382 -0.352894941 -0.007687716 -0.674151170 -0.683500980 -0.674050897 -0.629685436 0.748851600 0.540785078 7.142976085 0.617961926 0.224606106 0.65751414
SDi(1.50,4) 3.592801336 1.663322278 -0.319790093 -1.029557489 0.087010367 -1.007890027 0.098524506 -1.406366757 0.172898705 -0.322598429 0.019727684 -0.695803789 -0.705809868 -0.693950709 -0.642225632 0.797190955 0.445739479 6.599930009 0.615775022 0.221227807 0.654309269
SDi(2.00,4) 3.903132822 1.751842311 -0.323864097 -0.993031575 0.061161060 -0.989313154 0.079616469 -1.332073370 0.170202410 -0.324154686 0.043367833 -0.719679925 -0.727740242 -0.706195574 -0.653914311 0.816613981 0.471693363 7.012651680 0.610149799 0.219621347 0.648472292
SDi(3.00,4) 4.085477184 1.991870741 -0.403708963 -0.996945298 0.076802484 -1.003609316 0.105473127 -1.156417182 0.144744383 -0.365777365 -0.020990647 -0.712501263 -0.721265129 -0.692907970 -0.644917090 0.804710131 0.421605282 7.252795375 0.596083956 0.234721929 0.640632864
SDi(4.00,4) 4.074820530 2.132080582 -0.428538989 -0.976668042 0.079135508 -0.998915491 0.122694678 -1.115121063 0.184665877 -0.519001766 -0.166137595 -0.683791522 -0.690982376 -0.660497520 -0.606641320 0.791035706 0.492442741 7.535117546 0.585368727 0.242053350 0.633440108
SDi(5.00,4) 4.024458766 2.254437376 -0.459771294 -0.960529450 0.075710334 -0.999979640 0.130899533 -1.072280040 0.176193137 -0.666944645 -0.288125796 -0.650077783 -0.656665795 -0.628752886 -0.564272862 0.777307664 0.622541495 7.448434511 0.571748509 0.255277046 0.626149126
"""),
"R=6, RotD100": CoeffsTable(sa_damping=5, table="""\
IMT a b1 b2 c11 c21 c12 c22 c13 c23 f1 f2 s1 s2 s3 s4 d1 d2 c3 φ τ σ
SDi(0.04,6) -0.956858093 1.231164367 -0.262394810 -1.437291107 0.251295877 -1.509097771 0.278618719 -3.071853524 0.055824040 -0.300635569 0.034265712 -0.460124739 -0.466853496 -0.505738697 -0.531388789 0.085273674 0.401118898 12.059623100 0.699104346 0.198422817 0.726717621
SDi(0.06,6) 0.667788910 1.187917027 -0.156630646 -1.298900472 0.233240664 -1.275223432 0.176401514 -2.432053371 -0.143491865 -0.239138284 0.187105437 -0.619316624 -0.624483540 -0.657779500 -0.660378264 0.344188713 0.419773751 -9.534322152 0.756905846 0.223364102 0.789175508
SDi(0.10,6) 2.264751667 1.331828883 -0.121392522 -1.143038456 0.201433068 -1.089655019 0.180728159 -1.664799175 -0.226398759 -0.168256596 0.221533247 -0.806853104 -0.807253049 -0.820564396 -0.801354376 0.659179017 0.474570195 7.617894975 0.848383466 0.303315970 0.900974519
SDi(0.20,6) 2.900320814 1.511529609 -0.146540442 -1.092176288 0.237133066 -1.070762854 0.289039074 -1.394361687 -0.033633512 -0.127869148 0.225906152 -0.861241722 -0.863531076 -0.855814654 -0.799202343 0.740968874 0.475684969 5.538667752 0.834436182 0.332662407 0.898302855
SDi(0.30,6) 2.807580070 1.530498865 -0.200342708 -1.139466744 0.229650371 -1.128792206 0.286313187 -1.456206311 0.122729283 -0.158485621 0.155889004 -0.796027812 -0.801175364 -0.790682394 -0.736067428 0.757618491 0.445548508 6.253862851 0.762587295 0.304596628 0.821168977
SDi(0.50,6) 2.806697408 1.547589138 -0.251839837 -1.134297079 0.183067565 -1.135394068 0.225112950 -1.578546581 0.264572096 -0.258180400 0.056005655 -0.715571203 -0.722071624 -0.712757297 -0.664000410 0.764279525 0.439122457 6.599822016 0.681053965 0.281702398 0.737014752
SDi(0.75,6) 3.206062450 1.590837295 -0.305298536 -1.114989741 0.128387264 -1.111181882 0.155101936 -1.528983833 0.219391461 -0.365050719 -0.026750099 -0.715278771 -0.721526675 -0.709259764 -0.655006188 0.789777332 0.507684627 7.179973937 0.650403789 0.267494481 0.703262672
SDi(1.00,6) 3.094884948 1.604063336 -0.297922818 -1.065387147 0.098647312 -1.053866935 0.103067130 -1.362736221 0.333233973 -0.315421456 0.044844673 -0.657518436 -0.669209532 -0.654001755 -0.613395575 0.777763568 0.515950236 6.599879779 0.640533465 0.228572736 0.680094563
SDi(1.50,6) 3.568603918 1.713199107 -0.302381235 -1.018381669 0.076197921 -1.002409648 0.086025591 -1.335649086 0.241263965 -0.320784524 0.021598521 -0.687692831 -0.698085085 -0.680997689 -0.625213664 0.779280271 0.516026029 6.599919712 0.631986510 0.231340113 0.672997174
SDi(2.00,6) 3.720817806 1.815999598 -0.314946782 -0.981623859 0.058020067 -0.976375616 0.079691726 -1.323562383 0.217647763 -0.330966912 0.021255781 -0.685410163 -0.693605530 -0.672276898 -0.614721405 0.757843535 0.530135105 6.640862950 0.622519198 0.234106332 0.665083398
SDi(3.00,6) 3.876822457 2.041579483 -0.393548151 -0.995662330 0.078264562 -1.002684250 0.118470663 -1.146421533 0.206251466 -0.385012934 -0.018162893 -0.679196309 -0.688386265 -0.659334014 -0.612929199 0.760624053 0.460474245 7.156635392 0.592808658 0.244117730 0.641104961
SDi(4.00,6) 3.795882627 2.144390862 -0.400323556 -0.997359931 0.095202789 -0.999730558 0.135844551 -1.052460806 0.174357633 -0.481562283 -0.068278754 -0.651236841 -0.657408571 -0.627668579 -0.572707598 0.762843120 0.549996307 7.952844123 0.580286767 0.255165290 0.633910133
SDi(5.00,6) 3.712725281 2.216112748 -0.420853399 -0.988383938 0.085135938 -0.993127103 0.142839033 -1.037146134 0.206070417 -0.595262466 -0.153657654 -0.614595842 -0.620549126 -0.595830220 -0.536629223 0.742789263 0.646521768 8.200021033 0.565963432 0.263362667 0.624239137
"""),
}
