# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2013-2021 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:`KaleEtAl2015Turkey`
:class:`KaleEtAl2015Iran`.
"""
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 _compute_anelestic_attenuation_term(C, ctx):
"""
Compute and return anelastic attenuation term in equation 5,
page 970.
"""
f_aat = np.zeros_like(ctx.rjb)
idx = ctx.rjb > 80.0
f_aat[idx] = C["b10"] * (ctx.rjb[idx] - 80.0)
return f_aat
def _compute_faulting_style_term(C, rake):
"""
Compute and return style-of-faulting term in equation 4,
page 970.
"""
Fn = float(rake > -135.0 and rake < -45.0)
Fr = float(rake > 45.0 and rake < 135.0)
return C['b8'] * Fn + C['b9'] * Fr
def _compute_geometric_decay_term(c1, C, mag, ctx):
"""
Compute and return geometric decay term in equation 3,
page 970.
"""
return (
(C['b4'] + C['b5'] * (mag - c1)) *
np.log(np.sqrt(ctx.rjb ** 2.0 + C['b6'] ** 2.0)))
def _compute_magnitude_scaling_term(c1, C, mag):
"""
Compute and return magnitude scaling term in equation 2,
page 970.
"""
if mag <= c1:
return C['b1'] + C['b2'] * (mag - c1) + C['b3'] * (8.5 - mag) ** 2
else:
return C['b1'] + C['b7'] * (mag - c1) + C['b3'] * (8.5 - mag) ** 2
def _compute_mean(CONSTS, C, mag, ctx, rake):
"""
Compute and return mean value without site conditions,
that is equations 2-5, page 970.
"""
c1 = CONSTS['c1']
mean = (
_compute_magnitude_scaling_term(c1, C, mag) +
_compute_geometric_decay_term(c1, C, mag, ctx) +
_compute_faulting_style_term(C, rake) +
_compute_anelestic_attenuation_term(C, ctx))
return mean
def _compute_non_linear_term(CONSTS, C, pga_only, ctx):
"""
Compute non-linear term, equation 6, page 970.
"""
Vref = CONSTS['Vref']
Vcon = CONSTS['Vcon']
c = CONSTS['c']
n = CONSTS['n']
lnS = np.zeros_like(ctx.vs30)
# equation (6a)
idx = ctx.vs30 < Vref
lnS[idx] = (
C['sb1'] * np.log(ctx.vs30[idx] / Vref) +
C['sb2'] * np.log(
(pga_only[idx] + c * (ctx.vs30[idx] / Vref) ** n) /
((pga_only[idx] + c) * (ctx.vs30[idx] / Vref) ** n)))
# equation (6b)
idx = ctx.vs30 >= Vref
new_sites = ctx.vs30[idx]
new_sites[new_sites > Vcon] = Vcon
lnS[idx] = C['sb1'] * np.log(new_sites / Vref)
return lnS
def _compute_weight_std(C, mag):
"""
Common part of equations 8 and 9, page 971.
"""
if mag < 6.0:
return C['a1']
elif mag >= 6.0 and mag < 6.5:
return C['a1'] + (C['a2'] - C['a1']) * ((mag - 6.0) / 0.5)
else:
return C['a2']
[docs]class KaleEtAl2015Turkey(GMPE):
"""
Implements GMPE developed by O. Kale, S. Akkar, A. Ansari and H. Hamzehloo
as published in "A ground-motion predictive model for Iran and Turkey for
horizontal PGA, PGV and 5%-damped response spectrum: Investigation of
possible regional effects", Bulletin of the Seismological Society of
America (2015), 105(2A): 963 - 980. The class implements the equations for
Joyner-Boore distance and based on manuscript provided by the original
authors.
Version calibrated for the Turkey case
"""
#: The supported tectonic region type is active shallow crust.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: The supported intensity measure types are PGA, PGV, and SA, see table
#: 5, page 973
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: The supported intensity measure component is 'geometric mean', see
#: section 'Functional Form of the GMPEs and Regression Analyses', page 970
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: The supported standard deviations are total, inter and intra event, see
#: table 3 and equations 8 & 9, pages 972 and 971
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: The required site parameter is vs30, see equation 6, page 970.
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: The required rupture parameters are rake and magnitude, see equations
#: 2 and 4, page 970.
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: The required distance parameter is 'Joyner-Boore' distance, see
#: equation 3, page 970.
REQUIRES_DISTANCES = {'rjb'}
[docs] def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
Implement equation 1, page 970.
"""
# compute median PGA on rock, needed to compute non-linear site
# amplification
C_pga = self.COEFFS[PGA()]
median_pga = np.exp(
_compute_mean(self.CONSTS, C_pga, ctx.mag, ctx, ctx.rake))
for m, imt in enumerate(imts):
# compute mean value by adding nonlinear site amplification terms
C = self.COEFFS[imt]
mean[m] = (
_compute_mean(self.CONSTS, C, ctx.mag, ctx, ctx.rake) +
_compute_non_linear_term(self.CONSTS, C, median_pga, ctx))
# Return standard deviations as defined in p. 971.
weight = _compute_weight_std(C, ctx.mag)
std_intra = weight * C["sd1"]
std_inter = weight * C["sd2"]
sig[m] = np.sqrt(std_intra ** 2. + std_inter ** 2.)
tau[m] = std_inter
phi[m] = std_intra
#: Coefficient tables obtained by joining tables 2, 3, 4, 5
#: and electronic supplementary
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 a1 a2 sd1 sd2 sb1 sb2
pga 1.74221 0.193 -0.07049 -1.18164 0.170 8.0 -0.354 -0.01329 -0.09158 -0.00156 0.570 0.450 1.0521 0.7203 -0.41997 -0.28846
pgv 5.58266 0.193 -0.13822 -0.94043 0.170 8.0 -0.354 -0.17037 -0.08609 -0.00052 0.560 0.460 1.0449 0.6452 -0.72057 -0.19688
0.010 1.75746 0.193 -0.06981 -1.18362 0.170 8.0 -0.354 -0.01349 -0.09158 -0.00156 0.574 0.453 1.0444 0.7150 -0.41729 -0.28685
0.020 1.78825 0.193 -0.07058 -1.18653 0.170 8.0 -0.354 -0.01189 -0.09158 -0.00160 0.577 0.455 1.0424 0.7137 -0.39998 -0.28241
0.030 1.87916 0.193 -0.06976 -1.19699 0.170 8.0 -0.354 -0.00748 -0.09158 -0.00170 0.581 0.458 1.0459 0.7113 -0.34799 -0.26842
0.040 2.00393 0.193 -0.06732 -1.21315 0.170 8.0 -0.354 0.00788 -0.09158 -0.00182 0.584 0.460 1.0557 0.7155 -0.27572 -0.24759
0.050 2.16076 0.193 -0.06226 -1.24101 0.170 8.0 -0.354 0.03907 -0.09158 -0.00197 0.588 0.463 1.0609 0.7166 -0.21231 -0.22385
0.075 2.52625 0.193 -0.05082 -1.30390 0.170 8.0 -0.354 0.08131 -0.09158 -0.00235 0.597 0.469 1.0692 0.7677 -0.13909 -0.17798
0.100 2.72364 0.193 -0.05217 -1.32996 0.170 8.0 -0.354 0.10000 -0.09158 -0.00267 0.606 0.475 1.0429 0.7735 -0.26492 -0.28832
0.110 2.79879 0.193 -0.05423 -1.33631 0.170 8.0 -0.354 0.10000 -0.09158 -0.00277 0.610 0.478 1.0324 0.7871 -0.31346 -0.31798
0.120 2.87745 0.193 -0.05676 -1.34267 0.170 8.0 -0.354 0.10000 -0.09158 -0.00285 0.613 0.480 1.0208 0.7783 -0.36002 -0.34246
0.130 2.89671 0.193 -0.05922 -1.33525 0.170 8.0 -0.354 0.09500 -0.09158 -0.00291 0.617 0.483 1.0216 0.7598 -0.40424 -0.36297
0.140 2.91231 0.193 -0.06162 -1.32731 0.170 8.0 -0.354 0.08169 -0.09158 -0.00295 0.621 0.485 1.0194 0.7517 -0.44592 -0.38036
0.150 2.91835 0.193 -0.06397 -1.31888 0.170 8.0 -0.354 0.06727 -0.09158 -0.00296 0.624 0.488 1.0063 0.7442 -0.48496 -0.39525
0.160 2.92057 0.193 -0.06626 -1.30999 0.170 8.0 -0.354 0.05460 -0.09158 -0.00295 0.628 0.490 0.9980 0.7380 -0.52137 -0.40811
0.170 2.91550 0.193 -0.06850 -1.30069 0.170 8.0 -0.354 0.04338 -0.09158 -0.00292 0.631 0.493 0.9896 0.7484 -0.55520 -0.41930
0.180 2.90336 0.193 -0.07069 -1.29102 0.170 8.0 -0.354 0.03335 -0.09158 -0.00288 0.635 0.495 0.9854 0.7472 -0.58656 -0.42911
0.190 2.88447 0.193 -0.07284 -1.28102 0.170 8.0 -0.354 0.02435 -0.09158 -0.00282 0.639 0.498 0.9801 0.7310 -0.61558 -0.43774
0.200 2.85623 0.193 -0.07494 -1.27072 0.170 8.0 -0.354 0.01620 -0.09158 -0.00275 0.642 0.500 0.9781 0.7213 -0.64239 -0.44574
0.220 2.78548 0.193 -0.07902 -1.24942 0.170 8.0 -0.354 0.00201 -0.09158 -0.00258 0.649 0.505 0.9712 0.7120 -0.69002 -0.45499
0.240 2.70779 0.193 -0.08294 -1.22742 0.170 8.0 -0.354 -0.00996 -0.09158 -0.00240 0.657 0.510 0.9699 0.6901 -0.73062 -0.45939
0.260 2.62349 0.193 -0.08672 -1.20502 0.170 8.0 -0.354 -0.02021 -0.09158 -0.00226 0.664 0.515 0.9611 0.6732 -0.76530 -0.45988
0.280 2.53452 0.193 -0.09036 -1.18250 0.170 8.0 -0.354 -0.02913 -0.09158 -0.00215 0.671 0.520 0.9466 0.6714 -0.79499 -0.45739
0.300 2.44252 0.193 -0.09387 -1.16008 0.170 8.0 -0.354 -0.03697 -0.09158 -0.00204 0.678 0.525 0.9407 0.6547 -0.82052 -0.45287
0.320 2.34886 0.193 -0.09726 -1.13796 0.170 8.0 -0.354 -0.04395 -0.09158 -0.00194 0.686 0.530 0.9515 0.6515 -0.84256 -0.44255
0.340 2.25469 0.193 -0.10054 -1.11632 0.170 8.0 -0.354 -0.05021 -0.09158 -0.00185 0.693 0.535 0.9448 0.6490 -0.86167 -0.43399
0.360 2.16096 0.193 -0.10372 -1.09527 0.170 8.0 -0.354 -0.05588 -0.09158 -0.00177 0.700 0.540 0.9344 0.6545 -0.87832 -0.42592
0.380 2.06843 0.193 -0.10679 -1.07492 0.170 8.0 -0.354 -0.06106 -0.09158 -0.00168 0.700 0.545 0.9406 0.6504 -0.89288 -0.41829
0.400 1.97772 0.193 -0.10977 -1.05535 0.170 8.0 -0.354 -0.06582 -0.09158 -0.00161 0.700 0.550 0.9430 0.6413 -0.90568 -0.41105
0.420 1.88929 0.193 -0.11266 -1.03659 0.170 8.0 -0.354 -0.07021 -0.09158 -0.00153 0.695 0.550 0.9449 0.6316 -0.91697 -0.40417
0.440 1.80350 0.193 -0.11547 -1.01869 0.170 8.0 -0.354 -0.07430 -0.08070 -0.00146 0.689 0.550 0.9444 0.6357 -0.92698 -0.39760
0.460 1.72061 0.193 -0.11819 -1.00165 0.170 8.0 -0.354 -0.07813 -0.05565 -0.00140 0.684 0.550 0.9438 0.6483 -0.93589 -0.39133
0.480 1.64078 0.193 -0.12084 -0.98547 0.170 8.0 -0.354 -0.08172 -0.03289 -0.00133 0.679 0.550 0.9441 0.6528 -0.94384 -0.38532
0.500 1.56410 0.193 -0.12342 -0.97014 0.170 8.0 -0.354 -0.08511 -0.01297 -0.00127 0.673 0.550 0.9519 0.6496 -0.95097 -0.37956
0.550 1.38635 0.193 -0.12955 -0.93538 0.170 8.0 -0.354 -0.09286 0.00000 -0.00113 0.660 0.550 0.9950 0.6487 -0.96584 -0.36610
0.600 1.22784 0.193 -0.13530 -0.90533 0.170 8.0 -0.354 -0.09980 0.00000 -0.00099 0.647 0.550 1.0137 0.6535 -0.97746 -0.35382
0.650 1.08684 0.193 -0.14070 -0.87944 0.170 8.0 -0.354 -0.10613 0.00000 -0.00087 0.633 0.550 1.0208 0.6655 -0.98670 -0.34252
0.700 0.96118 0.193 -0.14577 -0.85717 0.170 8.0 -0.354 -0.11201 0.00000 -0.00076 0.620 0.550 1.0406 0.6683 -0.99416 -0.33206
0.750 0.84856 0.193 -0.15056 -0.83799 0.170 8.0 -0.354 -0.11756 0.00000 -0.00066 0.620 0.550 1.0489 0.6582 -1.00027 -0.32233
0.800 0.74687 0.193 -0.15509 -0.82143 0.170 8.0 -0.354 -0.12285 0.00000 -0.00056 0.620 0.550 1.0375 0.6562 -1.00532 -0.31322
0.850 0.65430 0.193 -0.15938 -0.80711 0.170 8.0 -0.354 -0.12796 0.00000 -0.00047 0.620 0.550 1.0394 0.6470 -1.00956 -0.30466
0.900 0.56939 0.193 -0.16345 -0.79468 0.170 8.0 -0.354 -0.13293 0.00000 -0.00038 0.620 0.550 1.0423 0.6488 -1.01314 -0.29659
0.950 0.49101 0.193 -0.16731 -0.78385 0.170 8.0 -0.354 -0.13782 0.00000 -0.00030 0.620 0.550 1.0512 0.6383 -1.01619 -0.28896
1.000 0.41833 0.193 -0.17099 -0.77438 0.170 8.0 -0.354 -0.14267 0.00000 -0.00022 0.620 0.550 1.0534 0.6342 -1.01881 -0.28172
1.100 0.28765 0.193 -0.17784 -0.75874 0.170 8.0 -0.354 -0.14621 0.00000 -0.00008 0.620 0.550 1.0679 0.6204 -1.01720 -0.26827
1.200 0.17365 0.193 -0.18409 -0.74652 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.0859 0.6250 -1.00204 -0.25599
1.300 0.07306 0.193 -0.18983 -0.73683 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.0731 0.6291 -0.98810 -0.24469
1.400 -0.01759 0.193 -0.19511 -0.72905 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.0873 0.6199 -0.97519 -0.23423
1.500 -0.10161 0.193 -0.19999 -0.72272 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.0988 0.6173 -0.96317 -0.22449
1.600 -0.18105 0.193 -0.20452 -0.71752 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1058 0.6120 -0.95193 -0.21538
1.700 -0.25586 0.193 -0.20873 -0.71319 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1108 0.5923 -0.94136 -0.20682
1.800 -0.32454 0.193 -0.21266 -0.70957 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1301 0.5859 -0.93141 -0.19876
1.900 -0.38743 0.193 -0.21633 -0.70650 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1503 0.5787 -0.92199 -0.19112
2.000 -0.45413 0.193 -0.21978 -0.70389 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1594 0.5724 -0.91305 -0.18388
2.200 -0.58191 0.193 -0.22606 -0.69970 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1600 0.5943 -0.89645 -0.17043
2.400 -0.68595 0.193 -0.23166 -0.69654 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1567 0.6100 -0.88129 -0.15815
2.600 -0.78166 0.193 -0.23667 -0.69410 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1543 0.6053 -0.86735 -0.14685
2.800 -0.87027 0.193 -0.24119 -0.69218 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1563 0.6098 -0.85444 -0.13639
3.000 -0.95276 0.193 -0.24530 -0.69065 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1596 0.6251 -0.84242 -0.12665
3.200 -1.02993 0.193 -0.24903 -0.68940 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1615 0.6362 -0.83118 -0.11754
3.400 -1.10242 0.193 -0.25246 -0.68837 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.1266 0.6360 -0.82062 -0.10899
3.600 -1.17077 0.193 -0.25560 -0.68752 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.0930 0.6231 -0.81066 -0.10092
3.800 -1.23542 0.193 -0.25850 -0.68681 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.0749 0.6244 -0.80124 -0.09329
4.000 -1.29675 0.193 -0.26119 -0.68620 0.170 8.0 -0.354 -0.14621 0.00000 0.00000 0.620 0.550 1.0373 0.5409 -0.79231 -0.08605
""")
#: equation constants (that are IMT independent)
CONSTS = {
# coefficients in page 970 and table 4, page 973
'c1': 6.75,
'Vref': 750.0,
'Vcon': 1000.0,
'c': 2.5,
'n': 3.2
}
[docs]class KaleEtAl2015Iran(KaleEtAl2015Turkey):
"""
Implements GMPE developed by O. Kale, S. Akkar, A. Ansari and H. Hamzehloo
as published in "A ground-motion predictive model for Iran and Turkey for
horizontal PGA, PGV and 5%-damped response spectrum: Investigation of
possible regional effects", Bulletin of the Seismological Society of
America (2015), 105(2A): 963 - 980. The class implements the equations for
Joyner-Boore distance and based on manuscript provided by the original
authors.
Version calibrated for the Iran case
"""
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 a1 a2 sd1 sd2 sb1 sb2
pgv 5.791000 0.047 -0.19327 -0.89157 0.050 8.0 0.042 0.000000 -0.08609 0.0 0.700 0.440 0.9852 0.3439 -0.72057 -0.19688
pga 1.529870 0.047 -0.10875 -1.00954 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.690 0.500 0.9713 0.3953 -0.41997 -0.28846
0.010 1.530080 0.047 -0.10858 -1.00954 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.690 0.500 0.9721 0.3919 -0.41729 -0.28685
0.020 1.547250 0.047 -0.10732 -1.01066 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.690 0.500 0.9723 0.3957 -0.39998 -0.28241
0.030 1.622140 0.047 -0.10346 -1.02788 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.690 0.500 0.9754 0.3970 -0.34799 -0.26842
0.040 1.751330 0.047 -0.09582 -1.05283 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.690 0.500 0.9960 0.4091 -0.27572 -0.24759
0.050 1.920470 0.047 -0.09060 -1.07963 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.710 0.500 0.9909 0.4396 -0.21231 -0.22385
0.075 2.395390 0.047 -0.09060 -1.13842 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.740 0.500 0.9698 0.4632 -0.13909 -0.17798
0.100 2.700430 0.047 -0.09060 -1.17035 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.500 0.9943 0.4377 -0.26492 -0.28832
0.110 2.740200 0.047 -0.09076 -1.16529 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.500 1.0025 0.4518 -0.31346 -0.31798
0.120 2.743950 0.047 -0.09127 -1.15646 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.500 1.0074 0.4644 -0.36002 -0.34246
0.130 2.727860 0.047 -0.09378 -1.14151 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.490 1.0286 0.4636 -0.40424 -0.36297
0.140 2.706020 0.047 -0.09640 -1.12693 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.480 1.0320 0.4757 -0.44592 -0.38036
0.150 2.684530 0.047 -0.09872 -1.11281 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.470 1.0457 0.4603 -0.48496 -0.39525
0.160 2.659010 0.047 -0.10150 -1.09920 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.460 1.0681 0.4508 -0.52137 -0.40811
0.170 2.625670 0.047 -0.10401 -1.08611 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.450 1.0723 0.4486 -0.55520 -0.41930
0.180 2.591290 0.047 -0.10647 -1.07358 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.450 1.0806 0.4398 -0.58656 -0.42911
0.190 2.555960 0.047 -0.10889 -1.06160 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.450 1.0799 0.4353 -0.61558 -0.43774
0.200 2.519780 0.047 -0.11128 -1.05018 0.050 8.0 0.042 -0.130260 -0.09158 0.0 0.760 0.450 1.0862 0.4163 -0.64239 -0.44574
0.220 2.445350 0.047 -0.11594 -1.02896 0.050 8.0 0.042 -0.083930 -0.09158 0.0 0.760 0.450 1.0809 0.4186 -0.69002 -0.45499
0.240 2.369090 0.047 -0.12046 -1.00982 0.050 8.0 0.042 -0.038850 -0.09158 0.0 0.760 0.450 1.0631 0.4074 -0.73062 -0.45939
0.260 2.292110 0.047 -0.12485 -0.99260 0.050 8.0 0.042 0.000000 -0.09158 0.0 0.760 0.450 1.0491 0.4021 -0.76530 -0.45988
0.280 2.215510 0.047 -0.12911 -0.97712 0.050 8.0 0.042 0.000000 -0.09158 0.0 0.760 0.450 1.0422 0.3908 -0.79499 -0.45739
0.300 2.140300 0.047 -0.13326 -0.96321 0.050 8.0 0.042 0.000000 -0.08973 0.0 0.760 0.450 1.0166 0.3896 -0.82052 -0.45287
0.320 2.067340 0.047 -0.13729 -0.95071 0.050 8.0 0.042 0.000000 -0.08183 0.0 0.760 0.450 1.0083 0.3781 -0.84256 -0.44255
0.340 1.997350 0.047 -0.14122 -0.93945 0.050 8.0 0.042 0.000000 -0.07010 0.0 0.760 0.450 1.0026 0.3923 -0.86167 -0.43399
0.360 1.930870 0.047 -0.14504 -0.92931 0.050 8.0 0.042 0.000000 -0.04750 0.0 0.760 0.450 0.9987 0.3908 -0.87832 -0.42592
0.380 1.868300 0.047 -0.14877 -0.92014 0.050 8.0 0.042 0.000000 -0.02277 0.0 0.760 0.450 0.9966 0.4017 -0.89288 -0.41829
0.400 1.809870 0.047 -0.15240 -0.91185 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 0.9993 0.4105 -0.90568 -0.41105
0.420 1.755660 0.047 -0.15594 -0.90433 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 0.9990 0.4179 -0.91697 -0.40417
0.440 1.705630 0.047 -0.15940 -0.89750 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 0.9950 0.4236 -0.92698 -0.39760
0.460 1.659630 0.047 -0.16277 -0.89128 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 0.9873 0.4346 -0.93589 -0.39133
0.480 1.617450 0.047 -0.16606 -0.88560 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 0.9757 0.4596 -0.94384 -0.38532
0.500 1.578790 0.047 -0.16928 -0.88040 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 0.9728 0.4772 -0.95097 -0.37956
0.550 1.495230 0.047 -0.17700 -0.86922 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 0.9936 0.4778 -0.96584 -0.36610
0.600 1.425760 0.047 -0.18430 -0.86011 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 1.0137 0.4353 -0.97746 -0.35382
0.650 1.365020 0.047 -0.19121 -0.85261 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 1.0170 0.4330 -0.98670 -0.34252
0.700 1.308850 0.047 -0.19777 -0.84636 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.450 1.0321 0.4161 -0.99416 -0.33206
0.750 1.254680 0.047 -0.20401 -0.84111 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.463 1.0328 0.4203 -1.00027 -0.32233
0.800 1.201420 0.047 -0.20994 -0.83664 0.050 8.0 0.042 0.000000 0.00000 0.0 0.760 0.475 1.0256 0.4290 -1.00532 -0.31322
0.850 1.149110 0.047 -0.21559 -0.83282 0.050 8.0 0.042 0.000000 0.00000 0.0 0.770 0.488 1.0124 0.4120 -1.00956 -0.30466
0.900 1.098490 0.047 -0.22099 -0.82953 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.500 1.0020 0.3758 -1.01314 -0.29659
0.950 1.050420 0.047 -0.22614 -0.82667 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.513 0.9917 0.3677 -1.01619 -0.28896
1.000 1.005570 0.047 -0.23107 -0.82417 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.525 0.9741 0.3773 -1.01881 -0.28172
1.100 0.925840 0.047 -0.24031 -0.82003 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.550 0.9656 0.3540 -1.01720 -0.26827
1.200 0.855520 0.047 -0.24882 -0.81676 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.575 0.9671 0.3627 -1.00204 -0.25599
1.300 0.787690 0.047 -0.25667 -0.81414 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9561 0.3779 -0.98810 -0.24469
1.400 0.718900 0.047 -0.26395 -0.81200 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9560 0.3703 -0.97519 -0.23423
1.500 0.651500 0.047 -0.27072 -0.81023 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9651 0.3815 -0.96317 -0.22449
1.600 0.589490 0.047 -0.27703 -0.80876 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9741 0.3927 -0.95193 -0.21538
1.700 0.532580 0.047 -0.28293 -0.80751 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9700 0.3873 -0.94136 -0.20682
1.800 0.477180 0.047 -0.28845 -0.80644 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9537 0.4025 -0.93141 -0.19876
1.900 0.426200 0.047 -0.29363 -0.80552 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9452 0.4161 -0.92199 -0.19112
2.000 0.379480 0.047 -0.29851 -0.80472 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9411 0.4242 -0.91305 -0.18388
2.200 0.294500 0.047 -0.30745 -0.80342 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9419 0.4278 -0.89645 -0.17043
2.400 0.209520 0.047 -0.31544 -0.80240 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9381 0.4450 -0.88129 -0.15815
2.600 0.124530 0.047 -0.32264 -0.80159 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9270 0.4518 -0.86735 -0.14685
2.800 0.039550 0.047 -0.32915 -0.80093 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9335 0.4726 -0.85444 -0.13639
3.000 -0.045430 0.047 -0.33507 -0.80039 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9334 0.4895 -0.84242 -0.12665
3.200 -0.130410 0.047 -0.34048 -0.79994 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.9354 0.5096 -0.83118 -0.11754
3.400 -0.215390 0.047 -0.34545 -0.79956 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.8628 0.4473 -0.82062 -0.10899
3.600 -0.300380 0.047 -0.35002 -0.79924 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.8392 0.4401 -0.81066 -0.10092
3.800 -0.385360 0.047 -0.35424 -0.79896 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.8146 0.4577 -0.80124 -0.09329
4.000 -0.470340 0.047 -0.35815 -0.79872 0.050 8.0 0.042 0.000000 0.00000 0.0 0.780 0.600 0.8094 0.4547 -0.79231 -0.08605
""")
#: equation constants (that are IMT independent)
CONSTS = {
# coefficients in page 970 and table 4, page 973
'c1': 7.0,
'Vref': 750.0,
'Vcon': 1000.0,
'c': 2.5,
'n': 3.2
}