# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2015-2019 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 Mon August 24, 2021
Authors: elena.manea@infp.ro, laurentiu.danciu@sed.ethz.ch
Module exports: `ManeaEtAl2021`
"""
import numpy as np
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA
from scipy.constants import g
def _compute_magnitude_term(C, mag):
"""
Compute magnitude term
"""
term01 = mag - 5.7
mag_term = C['phi0'] + C['phi1'] * term01 + C['phi2'] * term01**2
return mag_term
def _compute_distance_term(C, rhypo, backarc):
"""
Compute distance term and regional term
"""
term = C['phi3'] * np.log(rhypo) + _compute_arc_regional_term(
C, backarc) * rhypo
return term
def _compute_arc_regional_term(C, backarc):
"""
Compute regional term - location with respect to the arc:
fore-arc sites (2 used in the paper / 0 in OQ),
back-arc sites (0 used in the paper/ 1 in OQ),
along-arc sites (1 used in the paper / 2 in OQ)
"""
term = np.zeros(len(backarc))
# fore-arc sites
term[backarc == 0] = C['phi7']
# back-arc sites
term[backarc == 1] = C['phi6']
# along-arc sites
term[backarc == 2] = C['phi5']
return term
def _compute_depth_term(C, hypo_depth):
return C['phi4']*hypo_depth
def _get_site_amplification(C, sites):
"""
Compute site terms - dummy terms + amplif
"""
ssa, ssb, ssc = _get_site_type_dummy_variables(sites)
return ((ssc*C['phi11'] + ssb*C['phi10'] +
+ ssa*C['phi9']) * np.ones(len(sites.vs30)) +
+ _compute_site_amplif(C, sites))
def _get_site_type_dummy_variables(sites):
"""
Get site type dummy variables, three different EC8 site classes
The recording sites are classified into 3 classes,
based on the shear wave velocity intervals in the uppermost 30 m, Vs30,
according to the EC8 (CEN 2003):
class A: Vs30 > 800 m/s
class B: Vs30 = 360 − 800 m/s
class C: Vs30 = 180 - 360 m/s
"""
ssa = np.zeros(len(sites.vs30))
ssb = np.zeros(len(sites.vs30))
ssc = np.zeros(len(sites.vs30))
# SClass C; 180 m/s <= Vs30 <= 360 m/s.
idx = (sites.vs30 >= 180.0) & (sites.vs30 < 360.0)
ssc[idx] = 1.0
# Class B; 360 m/s <= Vs30 <= 800 m/s.
idx = (sites.vs30 >= 360.0) & (sites.vs30 < 800)
ssb[idx] = 1.0
# Class A; Vs30 > 800 m/s.
idx = (sites.vs30 >= 800.0)
ssa[idx] = 1.0
return ssa, ssb, ssc
def _compute_site_amplif(C, sites):
"""
Compute site amplification using fundamental frequency of resonance(f0)
If f0 is not defined, please set it equal with the reference frequency
(fref=15, attributed to the reference site condition-rock sites)
"""
return C['phi8'] * np.log(sites.f0/15)
[docs]def get_mean_values(C, ctx):
"""
Returns the mean values for a specific IMT
"""
mean = (_compute_magnitude_term(C, ctx.mag) +
_compute_distance_term(C, ctx.rhypo, ctx.backarc) +
_compute_depth_term(C, ctx.hypo_depth) +
_get_site_amplification(C, ctx))
return mean
[docs]class ManeaEtAl2021(GMPE):
"""
Implements the Subduction GMPE developed by Elena Florinela Manea,
Carmen Ortanza Cioflan and Laurentiu Danciu, otherwise known as the
"Ground-motion models for Vrancea intermediate-depth earthquakes
(Earthquake Spectra,2021,87552930211032985), for subduction inslab events.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is the geometric mean component
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GEOMETRIC_MEAN
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT}
#: Required site measure as Vs30, fundamental frequency of resonance
#: (if unknown set it as 15 - rock sites),
REQUIRES_SITES_PARAMETERS = {'vs30', 'f0', 'backarc'}
#: Required rupture parameters are magnitude and depth for the inslab model
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'hypo_depth'}
#: Required distance measure is hypocentral distance
REQUIRES_DISTANCES = {'rhypo'}
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi):
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
# compute mean and convert from cm/s**2 to g
mean[m] = np.log(np.exp(get_mean_values(C, ctx)) * 1e-2 / g)
# Get standard deviations
tau[m] = C["tau"]
phi[m] = C["phi"]
sig[m] = C['sigma']
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt phi0 phi1 phi2 phi3 phi4 phi5 phi6 phi7 phi8 phi9 phi10 phi11 phi tau sigma
pga 4.025595 1.621585 -0.292480 0.214168 -0.007613 -0.012832 -0.016391 -0.007789 -0.079350 -0.312903 -0.220612 -0.216223 0.692827 0.241538 0.733723
0.0500 3.952591 1.504418 -0.313232 0.333729 -0.007394 -0.013859 -0.017524 -0.008054 -0.057029 -0.598011 -0.444958 -0.428217 0.719027 0.218638 0.751533
0.1000 2.614581 1.406083 -0.345507 0.702137 -0.007345 -0.015811 -0.020344 -0.009906 -0.078821 -0.519976 -0.238897 -0.258565 0.749747 0.186531 0.772603
0.1500 5.432465 1.466375 -0.374716 0.075349 -0.007155 -0.012035 -0.017251 -0.007230 -0.103554 -0.453729 -0.226770 -0.261769 0.743654 0.248487 0.784071
0.2000 5.595978 1.543539 -0.396745 -0.035388 -0.006680 -0.011705 -0.016533 -0.007998 -0.086191 -0.054641 0.236662 0.354709 0.721183 0.259187 0.766344
0.2500 7.200716 1.654710 -0.392268 -0.401341 -0.006585 -0.009857 -0.014155 -0.006217 -0.091235 0.048698 0.131088 0.240840 0.745346 0.305120 0.805382
0.3000 7.961656 1.763811 -0.383947 -0.597177 -0.006754 -0.008640 -0.012733 -0.005281 -0.099966 0.053849 0.117093 0.200180 0.745312 0.344535 0.821094
0.3500 7.302146 1.825933 -0.400855 -0.489150 -0.006894 -0.009029 -0.012891 -0.005852 -0.100287 0.166838 0.252812 0.295754 0.746893 0.335421 0.818753
0.4000 7.496009 1.912918 -0.390131 -0.542885 -0.006664 -0.009455 -0.012652 -0.005911 -0.094347 0.192523 0.231624 0.257723 0.764606 0.327001 0.831596
0.4500 7.250573 1.991307 -0.385370 -0.453492 -0.007012 -0.010327 -0.013020 -0.006531 -0.083213 0.118375 0.111060 0.121214 0.776354 0.326521 0.842224
0.5000 7.052669 2.037875 -0.387456 -0.405306 -0.007599 -0.010856 -0.013115 -0.006926 -0.077841 0.166895 0.106499 0.094953 0.772706 0.336974 0.842987
0.5500 6.967267 2.077844 -0.411739 -0.382824 -0.007991 -0.010992 -0.013050 -0.006983 -0.072419 0.145601 0.074511 0.053116 0.772536 0.329396 0.839830
0.6000 7.004557 2.108458 -0.416254 -0.412492 -0.008011 -0.010684 -0.012434 -0.006634 -0.071739 0.113151 0.010839 -0.020847 0.766393 0.335123 0.836460
0.6500 6.956747 2.149386 -0.418802 -0.407586 -0.008154 -0.010426 -0.011887 -0.006405 -0.074530 0.013880 -0.102924 -0.152134 0.757849 0.329303 0.826303
0.7000 6.732008 2.181437 -0.398318 -0.375138 -0.008368 -0.010341 -0.011572 -0.006401 -0.075376 -0.069936 -0.171714 -0.229259 0.753294 0.355305 0.832883
0.7500 6.585760 2.187655 -0.439662 -0.354944 -0.008359 -0.010191 -0.011258 -0.006328 -0.083573 -0.160015 -0.245907 -0.320181 0.754468 0.346585 0.830267
0.8000 6.093086 2.206244 -0.449031 -0.257233 -0.008489 -0.010544 -0.011435 -0.006749 -0.085265 -0.202901 -0.262145 -0.355927 0.740951 0.350736 0.819771
0.8500 5.948997 2.229070 -0.445908 -0.238133 -0.008727 -0.010581 -0.011197 -0.006770 -0.089310 -0.204653 -0.294351 -0.409076 0.735361 0.353616 0.815966
0.9000 5.337920 2.238156 -0.456065 -0.127986 -0.008709 -0.011154 -0.011390 -0.007350 -0.091805 -0.173925 -0.254632 -0.378706 0.726668 0.346358 0.804991
0.9500 4.998766 2.258973 -0.458789 -0.076782 -0.008583 -0.011468 -0.011461 -0.007643 -0.090701 -0.126019 -0.231895 -0.353432 0.716099 0.339620 0.792552
1.0000 4.897982 2.282278 -0.450046 -0.089679 -0.008454 -0.011468 -0.011081 -0.007639 -0.090177 -0.027730 -0.186378 -0.302624 0.705812 0.336331 0.781849
1.1000 4.615709 2.333505 -0.426365 -0.104075 -0.007995 -0.011435 -0.010927 -0.007699 -0.089359 0.127145 -0.071883 -0.166692 0.705873 0.329173 0.778853
1.2000 5.009129 2.383702 -0.408751 -0.249553 -0.007674 -0.010710 -0.009937 -0.007028 -0.088494 0.174421 -0.042242 -0.112955 0.691329 0.333641 0.767628
1.3000 4.839285 2.433264 -0.400524 -0.271119 -0.007346 -0.010318 -0.009494 -0.006859 -0.089278 0.245378 0.019830 -0.029044 0.680833 0.326774 0.755192
1.4000 4.434322 2.471533 -0.387664 -0.236810 -0.006950 -0.010354 -0.009473 -0.007066 -0.087648 0.293191 0.095394 0.055729 0.669157 0.317031 0.740459
1.5000 4.169711 2.496787 -0.378644 -0.215603 -0.006742 -0.010223 -0.009220 -0.007100 -0.087498 0.276668 0.093114 0.065743 0.656745 0.312779 0.727423
1.6000 4.211424 2.518935 -0.370811 -0.255826 -0.006395 -0.009916 -0.008852 -0.006838 -0.086538 0.225123 0.047277 0.026968 0.651815 0.305979 0.720060
1.7000 4.097084 2.541586 -0.355083 -0.278278 -0.006068 -0.009539 -0.008515 -0.006585 -0.087183 0.223726 0.060206 0.043074 0.652182 0.296756 0.716524
1.8000 4.307410 2.559459 -0.344041 -0.369365 -0.005661 -0.008915 -0.007809 -0.006008 -0.087453 0.191436 0.051648 0.033602 0.649543 0.285686 0.709593
1.9000 3.797734 2.571833 -0.332671 -0.292231 -0.005335 -0.009113 -0.007997 -0.006293 -0.087638 0.171411 0.051321 0.038333 0.639571 0.266418 0.692842
2.0000 3.370490 2.589052 -0.319873 -0.233897 -0.004889 -0.009358 -0.008212 -0.006594 -0.088846 0.170065 0.061527 0.055814 0.647108 0.254443 0.695334
2.1000 2.956452 2.607204 -0.302444 -0.175029 -0.004635 -0.009644 -0.008408 -0.006870 -0.085729 0.162500 0.091491 0.093258 0.656329 0.240549 0.699021
2.2000 2.901685 2.624680 -0.284117 -0.193166 -0.004464 -0.009569 -0.008262 -0.006733 -0.081777 0.151522 0.104528 0.110614 0.660777 0.230285 0.699755
2.3000 2.813618 2.627550 -0.268304 -0.204068 -0.004394 -0.009455 -0.008090 -0.006665 -0.081409 0.144908 0.109549 0.129229 0.661932 0.226109 0.699485
2.4000 3.074816 2.640652 -0.252432 -0.296135 -0.004003 -0.008974 -0.007624 -0.006186 -0.080854 0.119768 0.095382 0.117497 0.663796 0.214714 0.697658
2.5000 2.807016 2.640416 -0.238659 -0.267752 -0.003614 -0.009039 -0.007689 -0.006335 -0.079027 0.082256 0.093179 0.124254 0.668324 0.208346 0.700046
2.6000 2.904319 2.643930 -0.224966 -0.316500 -0.003303 -0.008770 -0.007338 -0.006019 -0.077719 0.047052 0.065673 0.096888 0.676112 0.201788 0.705581
2.7000 2.875456 2.645508 -0.214820 -0.332043 -0.002971 -0.008667 -0.007238 -0.005922 -0.075891 0.001728 0.038158 0.072240 0.682245 0.198367 0.710498
2.8000 2.794017 2.646570 -0.203554 -0.336384 -0.002743 -0.008603 -0.007175 -0.005889 -0.075500 -0.022875 0.025633 0.064037 0.689871 0.196452 0.717297
2.9000 2.522889 2.643149 -0.190522 -0.303117 -0.002634 -0.008660 -0.007322 -0.005997 -0.075814 -0.020022 0.040952 0.081952 0.695800 0.194110 0.722369
3.0000 2.312946 2.648337 -0.175360 -0.278351 -0.002380 -0.008692 -0.007397 -0.006100 -0.076898 -0.049648 0.024080 0.070438 0.701986 0.192013 0.727773
3.1000 2.151450 2.650207 -0.160228 -0.263009 -0.002268 -0.008633 -0.007413 -0.006112 -0.077856 -0.115408 0.008491 0.057257 0.704771 0.185422 0.728755
3.2000 2.056625 2.648915 -0.149747 -0.262495 -0.002000 -0.008587 -0.007414 -0.006122 -0.077166 -0.144040 -0.006955 0.047906 0.707167 0.183832 0.730670
3.3000 5.269873 2.650354 -0.135319 -1.031899 -0.001053 -0.004761 -0.004093 -0.002263 -0.076361 -0.301840 -0.138659 -0.072602 0.717227 0.184126 0.740484
3.4000 5.762147 2.645678 -0.124965 -1.167761 -0.000678 -0.004030 -0.003429 -0.001564 -0.078144 -0.362487 -0.180988 -0.112920 0.727447 0.184205 0.750407
3.5000 5.131832 2.638281 -0.116809 -1.040917 -0.000575 -0.004605 -0.004028 -0.002170 -0.077762 -0.369328 -0.177531 -0.107450 0.725887 0.181784 0.748302
3.6000 5.021665 2.636266 -0.103422 -1.035700 -0.000491 -0.004530 -0.004006 -0.002101 -0.076775 -0.396029 -0.182224 -0.109471 0.733950 0.179405 0.755558
3.7000 4.835488 2.636399 -0.089750 -1.018651 -0.000303 -0.004526 -0.004038 -0.002126 -0.077561 -0.392749 -0.172060 -0.095269 0.741616 0.177857 0.762645
3.8000 4.627948 2.636029 -0.076824 -0.994568 -0.000150 -0.004543 -0.004103 -0.002203 -0.078754 -0.399887 -0.161466 -0.082044 0.744687 0.177263 0.765494
3.9000 1.121060 2.633780 -0.066457 -0.196526 -0.000691 -0.008375 -0.007568 -0.006192 -0.079827 -0.269073 -0.050528 0.024293 0.765880 0.177242 0.786121
4.0000 0.952929 2.636896 -0.049726 -0.180697 -0.000491 -0.008384 -0.007596 -0.006219 -0.080341 -0.273917 -0.048731 0.029321 0.774264 0.177968 0.794454
4.1000 0.961349 2.648192 -0.023919 -0.203557 -0.000302 -0.008256 -0.007453 -0.006119 -0.080701 -0.293124 -0.047317 0.033262 0.778548 0.182263 0.799598
4.2000 0.828220 2.661316 0.000315 -0.191451 -0.000151 -0.008255 -0.007463 -0.006138 -0.080785 -0.302693 -0.051699 0.032576 0.786332 0.182392 0.807208
4.3000 0.839092 2.656932 0.009474 -0.214055 0.000061 -0.008125 -0.007333 -0.006007 -0.079667 -0.304442 -0.049018 0.041007 0.796289 0.179591 0.816289
4.4000 0.804939 2.651500 0.016900 -0.223459 0.000293 -0.008056 -0.007263 -0.005954 -0.079516 -0.328959 -0.056073 0.037063 0.797705 0.176905 0.817085
4.5000 0.600590 2.643826 0.023140 -0.191230 0.000471 -0.008172 -0.007384 -0.006121 -0.080837 -0.346529 -0.065766 0.030399 0.805124 0.174718 0.823863
4.6000 0.609642 2.634749 0.031878 -0.207898 0.000557 -0.008015 -0.007214 -0.005997 -0.081246 -0.378450 -0.082195 0.017602 0.807041 0.176093 0.826029
4.7000 0.555030 2.624061 0.036834 -0.208140 0.000644 -0.008006 -0.007193 -0.005984 -0.081187 -0.392058 -0.087627 0.012655 0.811518 0.176248 0.830437
4.8000 0.405500 2.614079 0.042089 -0.187945 0.000750 -0.008050 -0.007258 -0.006046 -0.081087 -0.404887 -0.092405 0.008914 0.816722 0.176637 0.835605
4.9000 0.242533 2.604766 0.048724 -0.165201 0.000853 -0.008104 -0.007351 -0.006131 -0.081669 -0.412782 -0.095936 0.006237 0.822804 0.176873 0.841600
5.0000 0.034662 2.595820 0.055424 -0.133164 0.000955 -0.008179 -0.007481 -0.006264 -0.082231 -0.415797 -0.092658 0.012042 0.827872 0.176553 0.846488
5.1000 -0.081979 2.587119 0.061763 -0.123442 0.001090 -0.008151 -0.007499 -0.006276 -0.082921 -0.429938 -0.089073 0.016195 0.834572 0.176364 0.853003
5.2000 -0.249066 2.577884 0.068770 -0.101407 0.001212 -0.008234 -0.007583 -0.006383 -0.082476 -0.424205 -0.079496 0.028762 0.841251 0.174192 0.859096
5.3000 -0.338950 2.568046 0.076142 -0.095754 0.001287 -0.008226 -0.007585 -0.006387 -0.082091 -0.423397 -0.075478 0.035186 0.847640 0.171850 0.864884
5.4000 -0.623212 2.560750 0.079686 -0.049798 0.001409 -0.008385 -0.007780 -0.006543 -0.081040 -0.388027 -0.052914 0.056856 0.853866 0.171347 0.870888
5.5000 -0.604771 2.550260 0.090096 -0.072397 0.001594 -0.008266 -0.007651 -0.006458 -0.080097 -0.402135 -0.043697 0.071949 0.859402 0.172879 0.876618
5.6000 -0.639384 2.538733 0.101040 -0.081970 0.001653 -0.008155 -0.007577 -0.006371 -0.080495 -0.418025 -0.037315 0.081465 0.865244 0.164453 0.880734
5.7000 -0.739179 2.530967 0.108785 -0.077048 0.001833 -0.008144 -0.007577 -0.006394 -0.080578 -0.411862 -0.024578 0.094688 0.866586 0.163912 0.881951
5.8000 -0.892723 2.523105 0.116266 -0.057205 0.001919 -0.008164 -0.007637 -0.006448 -0.080507 -0.431490 -0.015450 0.103633 0.869301 0.161580 0.884190
5.9000 -1.315659 2.513765 0.124501 0.023737 0.001937 -0.008465 -0.007971 -0.006799 -0.080693 -0.415834 0.004600 0.125270 0.870787 0.155898 0.884633
6.0000 -1.410412 2.506959 0.131751 0.029681 0.002057 -0.008441 -0.007970 -0.006791 -0.080021 -0.411275 0.014911 0.137719 0.872233 0.153245 0.885593
6.1000 -1.779048 2.499572 0.137823 0.114078 0.002217 -0.008957 -0.008405 -0.007260 -0.079338 -0.417246 -0.018151 0.101433 0.865988 0.149447 0.878789
6.2000 -1.949350 2.492869 0.144747 0.135361 0.002337 -0.008991 -0.008466 -0.007318 -0.079277 -0.418337 0.001653 0.119978 0.868436 0.147816 0.880926
6.3000 -2.040512 2.485843 0.151142 0.139510 0.002439 -0.008988 -0.008468 -0.007316 -0.079847 -0.417087 0.021930 0.138143 0.871654 0.145691 0.883745
6.4000 -2.061646 2.478410 0.158019 0.131269 0.002506 -0.008911 -0.008406 -0.007245 -0.079136 -0.417063 0.030345 0.146480 0.875096 0.143556 0.886792
6.5000 -2.146219 2.470837 0.165034 0.139223 0.002571 -0.008901 -0.008427 -0.007265 -0.078674 -0.423313 0.034515 0.148782 0.874003 0.142450 0.885536
6.6000 -2.152551 2.463297 0.171719 0.128148 0.002679 -0.008801 -0.008348 -0.007163 -0.077909 -0.446100 0.032629 0.148052 0.876552 0.140831 0.887793
6.7000 -2.138325 2.456315 0.177916 0.112966 0.002837 -0.008744 -0.008285 -0.007098 -0.076566 -0.438987 0.035094 0.152092 0.877505 0.140113 0.888621
6.8000 -2.160192 2.448234 0.184721 0.105756 0.002990 -0.008751 -0.008276 -0.007083 -0.074384 -0.423937 0.044650 0.164666 0.881340 0.140697 0.892500
6.9000 -2.290402 2.441229 0.190884 0.124898 0.003075 -0.008846 -0.008364 -0.007175 -0.072423 -0.418936 0.054664 0.174472 0.883473 0.139439 0.894409
7.0000 -2.397502 2.434074 0.196971 0.135832 0.003188 -0.008829 -0.008378 -0.007214 -0.072835 -0.419921 0.061951 0.182703 0.885949 0.139733 0.896901
7.1000 -2.436700 2.427000 0.203163 0.134903 0.003279 -0.008789 -0.008356 -0.007189 -0.071864 -0.430437 0.060083 0.180965 0.886775 0.139301 0.897650
7.2000 -2.549058 2.419390 0.208920 0.149705 0.003352 -0.008836 -0.008392 -0.007226 -0.072061 -0.434239 0.062306 0.181259 0.890337 0.139268 0.901163
7.3000 -2.357014 2.413523 0.215577 0.093224 0.003566 -0.008613 -0.008130 -0.006958 -0.070514 -0.436228 0.058741 0.181447 0.891032 0.138999 0.901809
7.4000 -2.423501 2.405897 0.220664 0.100303 0.003603 -0.008628 -0.008152 -0.006979 -0.069940 -0.441199 0.060592 0.181813 0.894874 0.139167 0.905630
7.5000 -2.453612 2.398102 0.226071 0.099083 0.003640 -0.008601 -0.008122 -0.006968 -0.069555 -0.446268 0.060839 0.183217 0.896089 0.139740 0.906920
7.6000 -2.603462 2.391606 0.230925 0.120985 0.003740 -0.008659 -0.008191 -0.007049 -0.070554 -0.456967 0.066954 0.189882 0.890583 0.140775 0.901641
7.7000 -2.679675 2.386746 0.234973 0.123845 0.003833 -0.008630 -0.008183 -0.007040 -0.070766 -0.472204 0.086189 0.209543 0.892594 0.146015 0.904458
7.8000 -2.691767 2.379787 0.240702 0.117456 0.003919 -0.008607 -0.008172 -0.007031 -0.069837 -0.458075 0.092924 0.217087 0.894976 0.146680 0.906917
7.9000 -2.781496 2.371842 0.246096 0.131388 0.003890 -0.008613 -0.008213 -0.007030 -0.069085 -0.479308 0.089821 0.211131 0.896757 0.147023 0.908729
8.0000 -2.901346 2.365853 0.250960 0.149531 0.004011 -0.008698 -0.008305 -0.007111 -0.068199 -0.467973 0.091263 0.213052 0.901146 0.146867 0.913035
8.1000 -3.045008 2.359509 0.256370 0.172975 0.004162 -0.008885 -0.008466 -0.007291 -0.066343 -0.456402 0.106187 0.230562 0.895943 0.147787 0.908050
8.2000 -3.092243 2.352116 0.260626 0.179196 0.004140 -0.008868 -0.008461 -0.007274 -0.065301 -0.469387 0.098897 0.221791 0.896335 0.147584 0.908404
8.3000 -3.097478 2.344849 0.264811 0.174304 0.004165 -0.008817 -0.008424 -0.007231 -0.064763 -0.469697 0.093763 0.218110 0.896688 0.147747 0.908778
8.4000 -3.185070 2.338723 0.269213 0.186137 0.004242 -0.008827 -0.008464 -0.007267 -0.064400 -0.478334 0.093348 0.216641 0.897821 0.148492 0.910018
8.5000 -3.350357 2.331819 0.273119 0.218186 0.004231 -0.008941 -0.008593 -0.007402 -0.063994 -0.483229 0.094545 0.217275 0.898920 0.149444 0.911258
8.6000 -3.330392 2.328035 0.280075 0.175555 0.004659 -0.008753 -0.008392 -0.007198 -0.064588 -0.420103 0.178036 0.302854 0.889291 0.152424 0.902259
8.7000 -3.392340 2.321025 0.284445 0.180877 0.004717 -0.008749 -0.008407 -0.007202 -0.063835 -0.421852 0.183748 0.309511 0.888169 0.153201 0.901285
8.8000 -3.456748 2.313342 0.288613 0.189188 0.004737 -0.008763 -0.008437 -0.007206 -0.061785 -0.428406 0.189497 0.312399 0.889024 0.151440 0.901830
8.9000 -3.434744 2.306339 0.292976 0.174187 0.004809 -0.008661 -0.008357 -0.007127 -0.062125 -0.438823 0.195710 0.319989 0.887006 0.152840 0.900078
9.0000 -3.433326 2.299317 0.297524 0.165413 0.004876 -0.008620 -0.008324 -0.007081 -0.061014 -0.439115 0.204649 0.327306 0.884734 0.152638 0.897804
9.1000 -3.491904 2.291504 0.302632 0.168939 0.004913 -0.008595 -0.008323 -0.007077 -0.060686 -0.435906 0.216078 0.338931 0.878472 0.151907 0.891510
9.2000 -3.511270 2.284402 0.307237 0.165634 0.004941 -0.008562 -0.008291 -0.007048 -0.060177 -0.429080 0.220544 0.343661 0.878234 0.152354 0.891352
9.3000 -3.453968 2.277751 0.311614 0.143382 0.005018 -0.008466 -0.008162 -0.006922 -0.060223 -0.427530 0.222052 0.345689 0.877773 0.153055 0.891017
9.4000 -3.540874 2.270059 0.315538 0.157709 0.004975 -0.008506 -0.008205 -0.006987 -0.059648 -0.419388 0.230555 0.352981 0.874911 0.153508 0.888276
9.5000 -3.566015 2.262472 0.319397 0.157093 0.004961 -0.008492 -0.008186 -0.006992 -0.059754 -0.403957 0.237209 0.360211 0.874452 0.153758 0.887867
9.6000 -3.703056 2.253803 0.322444 0.186570 0.004812 -0.008614 -0.008316 -0.007140 -0.058755 -0.403818 0.250112 0.369341 0.877059 0.154630 0.890586
9.7000 -3.702683 2.247372 0.326258 0.179027 0.004860 -0.008600 -0.008268 -0.007091 -0.057804 -0.402150 0.257712 0.374427 0.879543 0.155256 0.893141
9.8000 -3.670173 2.240554 0.329974 0.164013 0.004901 -0.008512 -0.008185 -0.007010 -0.057201 -0.394873 0.263624 0.380283 0.881711 0.156561 0.895503
9.9000 -3.665753 2.233205 0.334535 0.154174 0.004926 -0.008418 -0.008095 -0.006933 -0.058529 -0.412660 0.265804 0.382110 0.881617 0.157471 0.895570
10.000 -3.589180 2.227312 0.337769 0.127973 0.005004 -0.008280 -0.007953 -0.006790 -0.057341 -0.404070 0.270101 0.390929 0.884076 0.157986 0.898081
""")
