# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2025 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/>.
"""
Module exports :class:`Stafford2022`
"""
import numpy as np
from scipy import stats
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
from openquake.hazardlib.gsim.chiou_youngs_2014 import (
_get_centered_ztor,
get_hanging_wall_term,
get_geometric_spreading,
get_magnitude_scaling,
get_directivity,
_get_basin_term,
get_linear_site_term,
get_nonlinear_site_term,
)
CONSTANTS = {
"c2": 1.06,
"c4": -2.1,
"c4a": -0.5,
"crb": 50.0,
"c8a": 0.2695,
"c11": 0.0,
"phi6": 300.0,
"phi6jp": 800.0,
}
def _sigmoid1d(x, start, finish, centre, slope):
"""
Returns 1D sigmoid function allowing a smooth transition from `start` to
`finish`. The transition is centred at `centre` and changes at a rate
linked to `slope`
"""
amplitude = finish - start
y = start + amplitude / (1.0 + np.exp(-(x - centre) / slope))
return y
def _empirical_sigma(T, r, m, start=0.4, finish=0.15):
"""
Epistemic standard deviation associated with empirical constraint.
Takes period `T`, rupture distance `r` and magnitude `m`.
"""
centre_r = _sigmoid1d(T, 3.75, 5.75, 3.5, 0.5)
slope_r = _sigmoid1d(T, 0.225, 1.3, 3.5, 0.5)
centre_m = _sigmoid1d(T, 5.82, 6.4, 3.5, 0.5)
slope_m = _sigmoid1d(T, 0.42, 0.38, 2.5, 0.2)
amplitude = finish - start
s_lnr = _sigmoid1d(
np.log(np.clip(r, 10**-10, None)), 0.0, 1.0, centre_r, slope_r
)
s_m = _sigmoid1d(m, 1.0, 0.0, centre_m, slope_m)
y = start + amplitude * s_lnr * s_m
return y
def _saturation_sigma(m, r):
"""
Standard deviation of the near-source saturation model.
Takes a magnitude `m` and rupture distance `r`
"""
return _sigmoid1d(
np.log(np.clip(r, 10**-10, None)),
0.6638 - 0.2570 * (np.clip(m, -np.inf, 7.0) - 6.0),
0.0,
0.7990,
0.9835,
)
def _anelastic_correction(T):
"""
Mean anelastic attenuation correction -- a function of period `T`
"""
return np.clip(0.0024 * np.tanh(0.8 * np.log(T / 1.8)), -np.inf, 0.0)
def _anelastic_sigma(T):
"""
Standard deviation of the anelastic attenuation coefficient -- a function
of period `T`
"""
return _sigmoid1d(np.log(T), 0.00054, 0.0004, np.log(0.9), 0.2)
def _between_event(T, M):
"""
Between-event standard deviation, function of period `T` and magnitude `M`
"""
# between event
β0_0 = 0.45
β0_1 = 0.35
β1 = 0.4
β2 = 0.0
β3 = 0.2
τ0 = _sigmoid1d(np.log(T), β0_0, β1, β2, β3)
τ1 = _sigmoid1d(np.log(T), β0_1, β1, β2, β3)
τ = τ0 + (τ1 - τ0) * (np.clip(M, 5.0, 6.5) - 5.0) / 1.5
return τ
def _between_station(T):
"""
Between-station standard deviation, function of period `T`
"""
β0_S2S = 0.3171
β1_S2S = 0.3248
β2_S2S = 0.7911
β3_S2S = 0.8970
β4_S2S = 0.7170
ϕS2S = β0_S2S + β1_S2S * (T / β4_S2S) ** (β2_S2S) * np.exp(
-β3_S2S * (T / β4_S2S)
)
return ϕS2S
def _neff_model(T):
"""
neff_model(T)
Model for the effective number of observations in NZ data, function of
period `T`
"""
β0 = 190.34
β1 = 221.16
β2 = -2.4341
β3 = 0.10366
β4 = 0.10299
if T <= 0.3:
return _sigmoid1d(np.log(T), β0, β1, β2, β3)
else:
return β1 / ((T / 0.3) ** β4)
[docs]def get_adjustments(T, ctx, adjust_c1, adjust_chm, adjust_c7, adjust_cg1):
ρEhEx = 0.4
epistemic_scale_factor = 0.893
# The scale factor of 0.9 is applied based upon the discussion that it
# accounts for the reduction in epistemic uncertainty when no perfect
# correlation is assumed between rupture scenarios. See the note of Peter
# and Brendon on slack.
MEAN_ADJUSTMENT_TERMS_IF = {
"Lower": {
"delta_c1": (
-1.28155
* epistemic_scale_factor
* _empirical_sigma(T, ctx.rrup, ctx.mag)
if adjust_c1
else 0.0
),
"delta_c1hm": (
-1.28155
* epistemic_scale_factor
* ρEhEx
* _saturation_sigma(ctx.mag, ctx.rrup)
if adjust_chm
else 0.0
),
"delta_c7": (-0.02578 if adjust_c7 else 0.0),
"delta_c7b": (
_sigmoid1d(np.log(T), -0.05737, 0.05733, -1.0324, 0.04875)
if adjust_c7
else 0.0
),
"delta_cg1": (
_anelastic_correction(T)
- 1.28155 * epistemic_scale_factor * _anelastic_sigma(T)
if adjust_cg1
else 0.0
),
},
"Central": {
"delta_c1": 0.0,
"delta_c1hm": 0.0,
"delta_c7": 0.0,
"delta_c7b": (
_sigmoid1d(np.log(T), -0.0865, 0.0, -1.5364, 0.3266)
if adjust_c7
else 0.0
),
"delta_cg1": (_anelastic_correction(T) if adjust_cg1 else 0.0),
},
"Upper": {
"delta_c1": (
1.28155
* epistemic_scale_factor
* _empirical_sigma(T, ctx.rrup, ctx.mag)
if adjust_c1
else 0.0
),
"delta_c1hm": (
1.28155
* epistemic_scale_factor
* ρEhEx
* _saturation_sigma(ctx.mag, ctx.rrup)
if adjust_chm
else 0.0
),
"delta_c7": 0.0,
"delta_c7b": 0.0,
"delta_cg1": (
_anelastic_correction(T)
+ 1.28155 * epistemic_scale_factor * _anelastic_sigma(T)
if adjust_cg1
else 0.0
),
},
}
return MEAN_ADJUSTMENT_TERMS_IF
# Modified CY14 fucntions:
[docs]def get_stress_scaling(
T, C, ctx, mu_branch, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
):
"""This term includes adjustments related to stress scaling."""
delta_c1 = get_adjustments(
T, ctx, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)[mu_branch]["delta_c1"]
delta_c1hm = get_adjustments(
T, ctx, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)[mu_branch]["delta_c1hm"]
return C["c1"] + delta_c1 + delta_c1hm
[docs]def get_far_field_distance_scaling(
T, C, ctx, mu_branch, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
):
"""
Returns the far-field distance scaling term - both magnitude and
distance. It includes adjustments made for NZ through delta_cg1.
"""
delta_cg1 = get_adjustments(
T, ctx, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)[mu_branch]["delta_cg1"]
# Get the attenuation distance scaling
f_r = (CONSTANTS["c4a"] - CONSTANTS["c4"]) * np.log(
np.sqrt(ctx.rrup**2.0 + CONSTANTS["crb"] ** 2.0)
)
# Get the magnitude dependent term
f_rm = (
C["cg1"]
+ delta_cg1
+ C["cg2"] / np.cosh(np.clip(ctx.mag - C["cg3"], 0.0, None))
)
return f_r + f_rm * ctx.rrup
[docs]def get_source_scaling_terms(
T,
C,
ctx,
delta_ztor,
mu_branch,
adjust_c1,
adjust_chm,
adjust_c7,
adjust_cg1,
):
"""
Returns additional source scaling parameters related to style of
faulting, dip and top of rupture depth. It includes adjustments for NZ backbone model through
delta_c7 and delta_c7b.
"""
delta_c7 = get_adjustments(
T, ctx, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)[mu_branch]["delta_c7"]
delta_c7b = get_adjustments(
T, ctx, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)[mu_branch]["delta_c7b"]
f_src = np.zeros_like(ctx.mag)
coshm = np.cosh(2.0 * np.clip(ctx.mag - 4.5, 0.0, None))
# Style of faulting term
pos = (30 <= ctx.rake) & (ctx.rake <= 150)
neg = (-120 <= ctx.rake) & (ctx.rake <= -60)
# reverse faulting flag
f_src[pos] += C["c1a"] + (C["c1c"] / coshm[pos])
# normal faulting flag
f_src[neg] += C["c1b"] + (C["c1d"] / coshm[neg])
# Top of rupture term
f_src += (
(C["c7"] + delta_c7) + ((C["c7b"] + delta_c7b) / coshm)
) * delta_ztor
# Dip term
f_src += (CONSTANTS["c11"] + (C["c11b"] / coshm)) * np.cos(
np.radians(ctx.dip)
) ** 2
return f_src
[docs]def get_ln_y_ref(
T, C, ctx, mu_branch, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
):
"""
Returns the ground motion on the reference rock.
"""
delta_ztor = _get_centered_ztor(ctx)
return (
get_stress_scaling(
T, C, ctx, mu_branch, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)
+ get_magnitude_scaling(C, ctx.mag, delta_cm=0)
+ get_source_scaling_terms(
T,
C,
ctx,
delta_ztor,
mu_branch,
adjust_c1,
adjust_chm,
adjust_c7,
adjust_cg1,
)
+ get_hanging_wall_term(C, ctx)
+ get_geometric_spreading(C, ctx.mag, ctx.rrup)
+ get_far_field_distance_scaling(
T, C, ctx, mu_branch, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)
+ get_directivity(C, ctx)
)
def _nl_sigma(C, ctx, ln_y_ref):
vs = ctx.vs30.clip(-np.inf, 1130.0)
NL = C["phi2"] * (
(
np.exp(C["phi3"] * (vs - 360.0))
- np.exp(C["phi3"] * (1130.0 - 360.0))
)
* (np.exp(ln_y_ref) / (np.exp(ln_y_ref) + C["phi4"]))
)
return NL
[docs]def get_stddevs(T, ln_y_ref, C, ctx, sigma_branch):
"""
Returns the standard deviation model described in equation 8.16
(Peter Stafford NSHM report)
"""
tau = _between_event(T, ctx.mag)
phi_S2S = _between_station(T)
phi_SS = 0.39
NL = _nl_sigma(C, ctx, ln_y_ref)
phi = np.sqrt(
phi_S2S**2 + (1.0 + NL) ** 2 * 0.736 * phi_SS**2 + 0.264 * phi_SS**2
)
# nominal total standard deviation for the branch
sigma = np.sqrt((1.0 + NL) ** 2 * tau**2 + phi**2)
# perform the potential inflation of σ for epistemic uncertainty
neff = _neff_model(T)
nfac = (
_empirical_sigma(T, ctx.rrup, ctx.mag) / _empirical_sigma(T, 80.0, 5.0)
) ** 2
ndof = neff / nfac
if sigma_branch == "Lower":
sigma = np.sqrt(
(sigma**2 / (ndof - 1)) * stats.chi2.ppf(0.1, ndof - 1)
)
elif sigma_branch == "Central":
sigma = np.sqrt(
(sigma**2 / (ndof - 1)) * stats.chi2.ppf(0.5, ndof - 1)
)
elif sigma_branch == "Upper":
sigma = np.sqrt(
(sigma**2 / (ndof - 1)) * stats.chi2.ppf(0.9, ndof - 1)
)
else:
print("sigma branch not recognised: "
"must be one of :Lower, :Central, :Upper")
sigma = np.nan
return sigma, np.abs((1.0 + NL) * tau), phi
[docs]def get_mean_stddevs(
T,
mu_branch,
sigma_branch,
adjust_c1,
adjust_chm,
adjust_c7,
adjust_cg1,
C,
ctx,
imt
):
"""
Return mean and standard deviation values.
"""
# Get ground motion on reference rock
ln_y_ref = get_ln_y_ref(
T, C, ctx, mu_branch, adjust_c1, adjust_chm, adjust_c7, adjust_cg1
)
y_ref = np.exp(ln_y_ref)
# Get the site amplification
# Get basin depth
f_z1pt0 = _get_basin_term(C, ctx, "Stafford2022", imt)
# Get linear amplification term
f_lin = get_linear_site_term("Stafford2022", C, ctx)
# Get nonlinear amplification term
f_nl, _f_nl_scaling = get_nonlinear_site_term(C, ctx, y_ref)
# Add on the site amplification
mean = ln_y_ref + (f_lin + f_nl + f_z1pt0)
# Get standard deviations
sig, tau, phi = get_stddevs(T, ln_y_ref, C, ctx, sigma_branch)
return mean, sig, tau, phi
[docs]class Stafford2022(GMPE):
"""
Implements Backbone model developed by Peter Stafford for NZ NSHM revision.
For more details see Peter Stafford's GNS report.
The base model implementation remains the same as for Chiou and Youngs
(2014).
Chiou, B. S.-J. and Youngs, R. R. (2014), "Updated of the Chiou and Youngs
NGA Model for the Average Horizontal Component of Peak Ground Motion and
Response Spectra, Earthquake Spectra, 30(3), 1117 - 1153,
DOI: 10.1193/072813EQS219M
"""
#: Supported tectonic region type is active shallow crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.RotD50`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: Supported standard deviation types are inter-event, intra-event
#: and total, see chapter "Variance model".
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameters are Vs30, Vs30 measured flag
#: and Z1.0.
REQUIRES_SITES_PARAMETERS = {"vs30", "vs30measured", "z1pt0"}
#: Required rupture parameters are magnitude, rake,
#: dip and ztor.
REQUIRES_RUPTURE_PARAMETERS = {"dip", "rake", "mag", "ztor"}
#: Required distance measures are RRup, Rjb and Rx.
REQUIRES_DISTANCES = {"rrup", "rjb", "rx"}
#: Reference shear wave velocity
DEFINED_FOR_REFERENCE_VELOCITY = 1130
def __init__(
self,
mu_branch="Central",
sigma_branch="Central",
adjust_c1=True,
adjust_chm=True,
adjust_c7=True,
adjust_cg1=True,
):
"""
Additional parameter for epistemic central,
lower and upper bounds.
"""
self.mu_branch = mu_branch
self.sigma_branch = sigma_branch
self.adjust_c1 = adjust_c1
self.adjust_chm = adjust_chm
self.adjust_c7 = adjust_c7
self.adjust_cg1 = adjust_cg1
[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):
if repr(imt) == "PGV":
print("Invalid IMT provided. The model does not predict"
" ground motions for PGV.")
sig[m], tau[m], phi[m] = None, None, None
elif repr(imt) == "PGA":
pga_mean, pga_sig, pga_tau, pga_phi = get_mean_stddevs(
SA(0.01).period,
self.mu_branch,
self.sigma_branch,
self.adjust_c1,
self.adjust_chm,
self.adjust_c7,
self.adjust_cg1,
self.COEFFS[SA(0.01)],
ctx,
imt
)
# Peter has used T = 0.01 as the period for PGA because the
# coefficients (for 0.01s and PGA) are identical.
mean[m] = pga_mean
sig[m], tau[m], phi[m] = pga_sig, pga_tau, pga_phi
else:
T = imt.period
imt_mean, imt_sig, imt_tau, imt_phi = get_mean_stddevs(
T,
self.mu_branch,
self.sigma_branch,
self.adjust_c1,
self.adjust_chm,
self.adjust_c7,
self.adjust_cg1,
self.COEFFS[imt],
ctx,
imt
)
mean[m] = imt_mean
sig[m], tau[m], phi[m] = imt_sig, imt_tau, imt_phi
#: Coefficient tables are constructed from values in tables 1 - 5
COEFFS = CoeffsTable(
sa_damping=5,
table="""\
IMT c1 c1a c1b c1c c1d cn cm c2 c3 c4 c4a crb c5 chm c6 c7 c7b c8 c8a c8b c9 c9a c9b c11 c11b cg1 cg2 cg3 phi1 phi2 phi3 phi4 phi5 phi6 gjpit gwn phi1jp phi5jp phi6jp tau1 tau2 sig1 sig2 sig3 sig2jp
pga -1.5065 0.165 -0.255 -0.165 0.255 16.0875 4.9993 1.06 1.9636 -2.1 -0.5 50 6.4551 3.0956 0.4908 0.0352 0.0462 0. 0.2695 0.4833 0.9228 0.1202 6.8607 0. -0.4536 -0.007146 -0.006758 4.2542 -0.521 -0.1417 -0.00701 0.102151 0. 300 1.5817 0.7594 -0.6846 0.459 800. 0.4 0.26 0.4912 0.3762 0.8 0.4528
pgv 2.3549 0.165 -0.0626 -0.165 0.0626 3.3024 5.423 1.06 2.3152 -2.1 -0.5 50 5.8096 3.0514 0.4407 0.0324 0.0097 0.2154 0.2695 5. 0.3079 0.1 6.5 0 -0.3834 -0.001852 -0.007403 4.3439 -0.7936 -0.0699 -0.008444 5.41 0.0202 300. 2.2306 0.335 -0.7966 0.9488 800. 0.3894 0.2578 0.4785 0.3629 0.7504 0.3918
0.01 -1.5065 0.165 -0.255 -0.165 0.255 16.0875 4.9993 1.06 1.9636 -2.1 -0.5 50 6.4551 3.0956 0.4908 0.0352 0.0462 0. 0.2695 0.4833 0.9228 0.1202 6.8607 0. -0.4536 -0.007146 -0.006758 4.2542 -0.521 -0.1417 -0.00701 0.102151 0. 300 1.5817 0.7594 -0.6846 0.459 800. 0.4 0.26 0.4912 0.3762 0.8 0.4528
0.02 -1.4798 0.165 -0.255 -0.165 0.255 15.7118 4.9993 1.06 1.9636 -2.1 -0.5 50 6.4551 3.0963 0.4925 0.0352 0.0472 0. 0.2695 1.2144 0.9296 0.1217 6.8697 0. -0.4536 -0.007249 -0.006758 4.2386 -0.5055 -0.1364 -0.007279 0.10836 0. 300 1.574 0.7606 -0.6681 0.458 800. 0.4026 0.2637 0.4904 0.3762 0.8 0.4551
0.03 -1.2972 0.165 -0.255 -0.165 0.255 15.8819 4.9993 1.06 1.9636 -2.1 -0.5 50 6.4551 3.0974 0.4992 0.0352 0.0533 0. 0.2695 1.6421 0.9396 0.1194 6.9113 0. -0.4536 -0.007869 -0.006758 4.2519 -0.4368 -0.1403 -0.007354 0.119888 0. 300 1.5544 0.7642 -0.6314 0.462 800. 0.4063 0.2689 0.4988 0.3849 0.8 0.4571
0.04 -1.1007 0.165 -0.255 -0.165 0.255 16.4556 4.9993 1.06 1.9636 -2.1 -0.5 50 6.4551 3.0988 0.5037 0.0352 0.0596 0. 0.2695 1.9456 0.9661 0.1166 7.0271 0. -0.4536 -0.008316 -0.006758 4.296 -0.3752 -0.1591 -0.006977 0.133641 0. 300 1.5502 0.7676 -0.5855 0.453 800. 0.4095 0.2736 0.5049 0.391 0.8 0.4642
0.05 -0.9292 0.165 -0.255 -0.165 0.255 17.6453 4.9993 1.06 1.9636 -2.1 -0.5 50 6.4551 3.1011 0.5048 0.0352 0.0639 0. 0.2695 2.181 0.9794 0.1176 7.0959 0. -0.4536 -0.008743 -0.006758 4.3578 -0.3469 -0.1862 -0.006467 0.148927 0. 300 1.5391 0.7739 -0.5457 0.436 800. 0.4124 0.2777 0.5096 0.3957 0.8 0.4716
0.075 -0.658 0.165 -0.254 -0.165 0.254 20.1772 5.0031 1.06 1.9636 -2.1 -0.5 50 6.4551 3.1094 0.5048 0.0352 0.063 0. 0.2695 2.6087 1.026 0.1171 7.3298 0. -0.4536 -0.009537 -0.00619 4.5455 -0.3747 -0.2538 -0.005734 0.190596 0. 300 1.4804 0.7956 -0.4685 0.383 800. 0.4179 0.2855 0.5179 0.4043 0.8 0.5022
0.1 -0.5613 0.165 -0.253 -0.165 0.253 19.9992 5.0172 1.06 1.9636 -2.1 -0.5 50 6.8305 3.2381 0.5048 0.0352 0.0532 0. 0.2695 2.9122 1.0177 0.1146 7.2588 0. -0.4536 -0.00983 -0.005332 4.7603 -0.444 -0.2943 -0.005604 0.230662 0. 300 1.4094 0.7932 -0.4985 0.375 800. 0.4219 0.2913 0.5236 0.4104 0.8 0.523
0.12 -0.5342 0.165 -0.252 -0.165 0.252 18.7106 5.0315 1.06 1.9795 -2.1 -0.5 50 7.1333 3.3407 0.5048 0.0352 0.0452 0. 0.2695 3.1045 1.0008 0.1128 7.2372 0. -0.4536 -0.009913 -0.004732 4.8963 -0.4895 -0.3077 -0.005696 0.253169 0. 300 1.3682 0.7768 -0.5603 0.377 800. 0.4244 0.2949 0.527 0.4143 0.8 0.5278
0.15 -0.5462 0.165 -0.25 -0.165 0.25 16.6246 5.0547 1.06 2.0362 -2.1 -0.5 50 7.3621 3.43 0.5045 0.0352 0.0345 0. 0.2695 3.3399 0.9801 0.1106 7.2109 0. -0.4536 -0.009896 -0.003806 5.0644 -0.5477 -0.3113 -0.005845 0.266468 0. 300 1.3241 0.7437 -0.6451 0.379 800. 0.4275 0.2993 0.5308 0.4191 0.8 0.5304
0.17 -0.5858 0.165 -0.248 -0.165 0.248 15.3709 5.0704 1.06 2.0823 -2.1 -0.5 50 7.4365 3.4688 0.5036 0.0352 0.0283 0. 0.2695 3.4719 0.9652 0.115 7.2491 0. -0.4536 -0.009787 -0.00328 5.1371 -0.5922 -0.3062 -0.005959 0.26506 0. 300 1.3071 0.7219 -0.6981 0.38 800. 0.4292 0.3017 0.5328 0.4217 0.8 0.531
0.2 -0.6798 0.165 -0.2449 -0.165 0.2449 13.7012 5.0939 1.06 2.1521 -2.1 -0.5 50 7.4972 3.5146 0.5016 0.0352 0.0202 0. 0.2695 3.6434 0.9459 0.1208 7.2988 0. -0.444 -0.009505 -0.00269 5.188 -0.6693 -0.2927 -0.006141 0.255253 0. 300 1.2931 0.6922 -0.7653 0.384 800. 0.4313 0.3047 0.5351 0.4252 0.8 0.5312
0.25 -0.8663 0.165 -0.2382 -0.165 0.2382 11.2667 5.1315 1.06 2.2574 -2.1 -0.5 50 7.5416 3.5746 0.4971 0.0352 0.009 0. 0.2695 3.8787 0.9196 0.1208 7.3691 0. -0.3539 -0.008918 -0.002128 5.2164 -0.7766 -0.2662 -0.006439 0.231541 0. 300 1.315 0.6579 -0.8469 0.393 800. 0.4341 0.3087 0.5377 0.4299 0.7999 0.5309
0.3 -1.0514 0.165 -0.2313 -0.165 0.2313 9.1908 5.167 1.06 2.344 -2.1 -0.5 50 7.56 3.6232 0.4919 0.0352 -0.0004 0. 0.2695 4.0711 0.8829 0.1175 6.8789 0. -0.2688 -0.008251 -0.001812 5.1954 -0.8501 -0.2405 -0.006704 0.207277 0.001 300 1.3514 0.6362 -0.8999 0.408 800. 0.4363 0.3119 0.5395 0.4338 0.7997 0.5307
0.4 -1.3794 0.165 -0.2146 -0.165 0.2146 6.5459 5.2317 1.06 2.4709 -2.1 -0.5 50 7.5735 3.6945 0.4807 0.0352 -0.0155 0. 0.2695 4.3745 0.8302 0.106 6.5334 0. -0.1793 -0.007267 -0.001274 5.0899 -0.9431 -0.1975 -0.007125 0.165464 0.004 300 1.4051 0.6049 -0.9618 0.462 800. 0.4396 0.3165 0.5422 0.4399 0.7988 0.531
0.5 -1.6508 0.165 -0.1972 -0.165 0.1972 5.2305 5.2893 1.06 2.5567 -2.1 -0.5 50 7.5778 3.7401 0.4707 0.0352 -0.0278 0.0991 0.2695 4.6099 0.7884 0.1061 6.526 0. -0.1428 -0.006492 -0.001074 4.7854 -1.0044 -0.1633 -0.007435 0.133828 0.01 300 1.4402 0.5507 -0.9945 0.524 800. 0.4419 0.3199 0.5433 0.4446 0.7966 0.5313
0.75 -2.1511 0.165 -0.162 -0.165 0.162 3.7896 5.4109 1.06 2.6812 -2.1 -0.5 50 7.5808 3.7941 0.4575 0.0352 -0.0477 0.1982 0.2695 5.0376 0.6754 0.1 6.5 0. -0.1138 -0.005147 -0.001115 4.3304 -1.0602 -0.1028 -0.00812 0.085153 0.034 300 1.528 0.3582 -1.0225 0.658 800. 0.4459 0.3255 0.5294 0.4533 0.7792 0.5309
1 -2.5365 0.165 -0.14 -0.165 0.14 3.3024 5.5106 1.06 2.7474 -2.1 -0.5 50 7.5814 3.8144 0.4522 0.0352 -0.0559 0.2154 0.2695 5.3411 0.6196 0.1 6.5 0. -0.1062 -0.004277 -0.001197 4.1667 -1.0941 -0.0699 -0.008444 0.058595 0.067 300 1.6523 0.2003 -1.0002 0.78 800. 0.4484 0.3291 0.5105 0.4594 0.7504 0.5302
1.5 -3.0686 0.165 -0.1184 -0.165 0.1184 2.8498 5.6705 1.06 2.8161 -2.1 -0.5 50 7.5817 3.8284 0.4501 0.0352 -0.063 0.2154 0.2695 5.7688 0.5101 0.1 6.5 0. -0.102 -0.002979 -0.001675 4.0029 -1.1142 -0.0425 -0.007707 0.031787 0.143 300 1.8872 0.0356 -0.9245 0.96 800. 0.4515 0.3335 0.4783 0.468 0.7136 0.5276
2 -3.4148 0.1645 -0.11 -0.1645 0.11 2.5417 5.7981 1.06 2.8514 -2.1 -0.5 50 7.5818 3.833 0.45 0.0352 -0.0665 0.2154 0.2695 6.0723 0.3917 0.1 6.5 0. -0.1009 -0.002301 -0.002349 3.8949 -1.1154 -0.0302 -0.004792 0.019716 0.203 300 2.1348 0. -0.8626 1.11 800. 0.4534 0.3363 0.4681 0.4681 0.7035 0.5167
3 -3.9013 0.1168 -0.104 -0.1168 0.104 2.1488 5.9983 1.06 2.8875 -2.1 -0.5 50 7.5818 3.8361 0.45 0.016 -0.0516 0.2154 0.2695 6.5 0.1244 0.1 6.5 0. -0.1003 -0.001344 -0.003306 3.7928 -1.1081 -0.0129 -0.001828 0.009643 0.277 300 3.5752 0. -0.7882 1.291 800. 0.4558 0.3398 0.4617 0.4617 0.7006 0.4917
4 -4.2466 0.0732 -0.102 -0.0732 0.102 1.8957 6.1552 1.06 2.9058 -2.1 -0.5 50 7.5818 3.8369 0.45 0.0062 -0.0448 0.2154 0.2695 6.8035 0.0086 0.1 6.5 0. -0.1001 -0.001084 -0.003566 3.7443 -1.0603 -0.0016 -0.001523 0.005379 0.309 300 3.8646 0. -0.7195 1.387 800. 0.4574 0.3419 0.4571 0.4571 0.7001 0.4682
5 -4.5143 0.0484 -0.101 -0.0484 0.101 1.7228 6.2856 1.06 2.9169 -2.1 -0.5 50 7.5818 3.8376 0.45 0.0029 -0.0424 0.2154 0.2695 7.0389 0. 0.1 6.5 0. -0.1001 -0.00101 -0.00364 3.709 -0.9872 0. -0.00144 0.003223 0.321 300 3.7292 0. -0.656 1.433 800. 0.4584 0.3435 0.4535 0.4535 0.7 0.4517
7.5 -5.0009 0.022 -0.101 -0.022 0.101 1.5737 6.5428 1.06 2.932 -2.1 -0.5 50 7.5818 3.838 0.45 0.0007 -0.0348 0.2154 0.2695 7.4666 0. 0.1 6.5 0. -0.1 -0.000964 -0.003686 3.6632 -0.8274 0. -0.001369 0.001134 0.329 300 2.3763 0. -0.5202 1.46 800. 0.4601 0.3459 0.4471 0.4471 0.7 0.4167
10 -5.3461 0.0124 -0.1 -0.0124 0.1 1.5265 6.7415 1.06 2.9396 -2.1 -0.5 50 7.5818 3.838 0.45 0.0003 -0.0253 0.2154 0.2695 7.77 0. 0.1 6.5 0. -0.1 -0.00095 -0.0037 3.623 -0.7053 0. -0.001361 0.000515 0.33 300 1.7679 0. -0.4068 1.464 800. 0.4612 0.3474 0.4426 0.4426 0.7 0.3755
""",
)
