# coding: utf-8
# The Hazard Library
# Copyright (C) 2014, GEM Foundation
#
# This program 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.
#
# This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports :class:`CauzziEtAl2014`,
:class:`CauzziEtAl2014NoSOF`,
:class:`CauzziEtAl2014FixedVs30`,
:class:`CauzziEtAl2014FixedVs30NoSOF`,
:class:`CauzziEtAl2014Eurocode8`,
:class:`CauzziEtAl2014Eurocode8NoSOF`,
"""
from __future__ import division
import numpy as np
# standard acceleration of gravity in m/s**2
from scipy.constants import g
from openquake.hazardlib.gsim.base import CoeffsTable, GMPE
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, PGV, SA
[docs]class CauzziEtAl2014(GMPE):
"""
Implements GMPE developed by Carlo Cauzzi et al (2014) and published
as C.Cauzzi, E. Faccioli, M. Vanini and A. Bianchini (2014) "Updated
predictive equations for broadband (0.0 - 10.0 s) horizontal response
spectra and peak ground motions, based on a global dataset of digital
acceleration records", Bulletin of Earthquake Engineering, In Press
Spectral acceleration (SA) values are obtained from displacement response
spectrum (DSR) values (as provided by the original equations) using the
following formula ::
SA = DSR * (2 * π / T) ** 2
"""
#: 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, peak
#: ground acceleration and peak ground velocity.
#: The original paper provides coefficients for PGA and PGV, while SA
#: is obtained from displacement response spectrum values.
#: Coefficients for PGA are taken from the SA (0.01 s) spectral
#: acceleration, as indicated in Page 11 (at the time of writing)
#: of Cauzzi et al. (2014)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
PGV,
SA
])
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
#: :attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types are inter-event, intra-event and
#: total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT,
const.StdDev.TOTAL
])
#: Required site parameter is only Vs30
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude and rake
REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag'))
#: Required distance measure is Rrup,
REQUIRES_DISTANCES = set(('rrup', ))
[docs] def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
# extract dictionaries of coefficients specific to required
# intensity measure type
C = self.COEFFS[imt]
mean = self._compute_mean(C, rup, dists, sites, imt)
stddevs = self._get_stddevs(C, stddev_types, sites.vs30.shape[0])
return mean, stddevs
def _compute_mean(self, C, rup, dists, sites, imt):
"""
Returns the mean ground motion acceleration and velocity
"""
mean = (self._get_magnitude_scaling_term(C, rup.mag) +
self._get_distance_scaling_term(C, rup.mag, dists.rrup) +
self._get_style_of_faulting_term(C, rup.rake) +
self._get_site_amplification_term(C, sites.vs30))
# convert from cm/s**2 to g for SA and from cm/s**2 to g for PGA (PGV
# is already in cm/s) and also convert from base 10 to base e.
if isinstance(imt, PGA):
mean = np.log((10 ** mean) * ((2 * np.pi / 0.01) ** 2) *
1e-2 / g)
elif isinstance(imt, SA):
mean = np.log((10 ** mean) * ((2 * np.pi / imt.period) ** 2) *
1e-2 / g)
else:
mean = np.log(10 ** mean)
return mean
def _get_magnitude_scaling_term(self, C, mag):
"""
Returns the magnitude term
"""
return C["c1"] + (C["m1"] * mag) + (C["m2"] * (mag ** 2.))
def _get_distance_scaling_term(self, C, mag, rrup):
"""
Returns the distance scaling parameter
"""
return (C["r1"] + C["r2"] * mag) * np.log10(rrup + C["r3"])
def _get_style_of_faulting_term(self, C, rake):
"""
Returns the style of faulting term. Cauzzi et al. determind SOF from
the plunge of the B-, T- and P-axes. For consistency with existing
GMPEs the Wells & Coppersmith model is preferred
"""
if rake > -150.0 and rake <= -30.0:
return C['fN']
elif rake > 30.0 and rake <= 150.0:
return C['fR']
else:
return C['fSS']
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification scaling term assuming
period dependent reference vs30
"""
return C["bV"] * np.log10(vs30 / C["VA"])
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return total standard deviation.
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(np.log(10.0 ** C['sM']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0 ** C['f']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0 ** C["tM"]) + np.zeros(num_sites))
return stddevs
#: Coefficient table constructed from the electronic suplements of the
#: original paper.
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt c1 m1 m2 r1 r2 r3 sB sC sD bV bV800 VA fN fR fSS f t s tM sM
pgv 0.44222 0.54822 -0.03195 -2.84578 0.24067 6.51697 0.19193 0.37062 0.49780 -0.69096 -0.75968 883.95654 -0.14333 0.01846 0.00499 0.23989 0.22130 0.32638 0.21494 0.32210
pga -2.19617 0.52375 -0.06094 -3.80190 0.35508 11.64156 0.21070 0.28251 0.28288 -0.31007 -0.70244 2319.18598 -0.02411 0.07246 -0.05632 0.25892 0.22145 0.34071 0.21622 0.33733
0.01000 -2.19617 0.52375 -0.06094 -3.80190 0.35508 11.64156 0.21070 0.28251 0.28288 -0.31007 -0.70244 2319.18598 -0.02411 0.07246 -0.05632 0.25892 0.22145 0.34071 0.21622 0.33733
0.02000 -1.81957 0.64537 -0.07188 -3.86449 0.35932 12.13501 0.19924 0.26576 0.25978 -0.28384 -0.66974 2528.80503 -0.02723 0.07709 -0.05900 0.25927 0.22664 0.34436 0.22083 0.34057
0.03000 -1.29436 0.69827 -0.07956 -4.04435 0.37652 13.31546 0.17812 0.23160 0.21528 -0.22882 -0.61914 3228.41863 -0.03333 0.08359 -0.06205 0.26104 0.23294 0.34986 0.22622 0.34542
0.04000 -0.69311 0.70887 -0.08461 -4.25696 0.39739 14.97013 0.18128 0.21829 0.18311 -0.15732 -0.60762 8228.73111 -0.03838 0.08985 -0.06550 0.26552 0.23708 0.35596 0.22936 0.35087
0.05000 -0.17390 0.70383 -0.08755 -4.41553 0.41403 15.96341 0.16785 0.18633 0.13929 -0.10000 -0.56395 30552.32717 -0.03900 0.09603 -0.07068 0.27026 0.24236 0.36301 0.23377 0.35734
0.06000 0.20698 0.69063 -0.08884 -4.49212 0.42330 16.19950 0.16276 0.16769 0.10260 -0.10000 -0.53674 23999.06953 -0.04909 0.10148 -0.07143 0.27506 0.24524 0.36851 0.23550 0.36210
0.07000 0.56089 0.67561 -0.08886 -4.54403 0.42592 17.37899 0.16545 0.15958 0.08629 -0.10000 -0.52661 20327.55501 -0.05142 0.10470 -0.07344 0.27995 0.24899 0.37466 0.23881 0.36797
0.08000 0.75873 0.66549 -0.08794 -4.53166 0.42019 18.14491 0.20829 0.19638 0.11730 -0.10000 -0.60087 37180.07136 -0.04357 0.10251 -0.07527 0.28597 0.24634 0.37744 0.23673 0.37124
0.09000 0.78466 0.66467 -0.08633 -4.44311 0.40965 17.79406 0.20581 0.20055 0.12392 -0.10000 -0.59993 36947.87877 -0.03861 0.10027 -0.07546 0.28797 0.24551 0.37842 0.23639 0.37256
0.10000 0.67594 0.67016 -0.08425 -4.29897 0.39502 16.94994 0.19823 0.20041 0.13130 -0.10000 -0.59237 36597.56005 -0.02830 0.10057 -0.07995 0.28649 0.24334 0.37588 0.23433 0.37011
0.15000 0.40604 0.63311 -0.07191 -3.86971 0.35272 13.75538 0.24891 0.30188 0.25319 -0.22732 -0.75495 5440.35206 -0.03000 0.09629 -0.07626 0.28885 0.23693 0.37359 0.22827 0.36816
0.20000 -0.09647 0.63942 -0.06256 -3.41543 0.30101 11.45346 0.28214 0.40589 0.36909 -0.43845 -0.89444 1898.28570 -0.00367 0.06934 -0.06339 0.29325 0.21597 0.36420 0.21125 0.36142
0.25000 -0.36474 0.64647 -0.05782 -3.19641 0.28216 9.36228 0.24732 0.40871 0.40913 -0.56473 -0.88696 1202.64389 -0.02305 0.06360 -0.05179 0.29578 0.20057 0.35738 0.19608 0.35487
0.30000 -0.50661 0.66511 -0.05609 -3.09389 0.27352 8.29352 0.20965 0.40013 0.43355 -0.65541 -0.85457 967.92555 -0.01800 0.05087 -0.04177 0.29559 0.19908 0.35638 0.19615 0.35475
0.35000 -0.66498 0.69532 -0.05579 -3.03494 0.26717 7.69133 0.20232 0.42138 0.48080 -0.74283 -0.87627 873.38167 -0.00557 0.04666 -0.04221 0.29822 0.20501 0.36189 0.20272 0.36060
0.40000 -1.02453 0.74771 -0.05627 -2.88529 0.25368 6.21199 0.18582 0.41073 0.52099 -0.81009 -0.85303 794.55322 0.00041 0.04039 -0.03849 0.29878 0.20686 0.36340 0.20517 0.36244
0.45000 -1.17672 0.78079 -0.05763 -2.84275 0.25137 5.64841 0.18870 0.41645 0.58079 -0.87518 -0.86429 759.83994 0.01422 0.03079 -0.03454 0.29805 0.20771 0.36328 0.20666 0.36269
0.50000 -1.36997 0.82603 -0.06010 -2.79376 0.24835 5.20211 0.19121 0.41638 0.61638 -0.91661 -0.87612 747.10634 0.00868 0.02813 -0.02979 0.29883 0.21714 0.36939 0.21634 0.36892
0.55000 -1.55323 0.88412 -0.06361 -2.77747 0.24613 5.27489 0.19226 0.42080 0.64732 -0.94899 -0.88733 734.26112 0.00799 0.02626 -0.02762 0.29885 0.22622 0.37481 0.22554 0.37440
0.60000 -1.75107 0.94565 -0.06767 -2.76600 0.24598 5.23265 0.18566 0.41514 0.66854 -0.98493 -0.88180 707.08862 0.00742 0.02143 -0.02280 0.29697 0.23121 0.37636 0.23076 0.37609
0.65000 -1.88122 0.99892 -0.07148 -2.78221 0.24813 5.15303 0.16946 0.40499 0.68145 -1.01531 -0.85948 681.46140 0.01964 0.01505 -0.02157 0.29546 0.23520 0.37764 0.23484 0.37743
0.70000 -2.00114 1.04148 -0.07438 -2.80158 0.25152 5.12145 0.16758 0.40847 0.69706 -1.03828 -0.86282 673.96919 0.02598 0.00784 -0.01734 0.29606 0.23154 0.37585 0.23123 0.37565
0.75000 -2.03150 1.06127 -0.07614 -2.84119 0.25837 5.05140 0.16810 0.40321 0.70806 -1.03136 -0.85797 675.69794 0.02393 0.00744 -0.01617 0.29516 0.22970 0.37401 0.22943 0.37384
0.80000 -2.07133 1.08084 -0.07718 -2.84934 0.25950 5.09282 0.15442 0.38450 0.70078 -1.02313 -0.82637 657.20618 0.02140 0.00595 -0.01382 0.29244 0.23006 0.37208 0.22985 0.37195
0.85000 -2.12629 1.10186 -0.07833 -2.85890 0.26066 5.09360 0.15046 0.37925 0.69694 -1.01448 -0.81378 653.81253 0.02111 0.00190 -0.00995 0.29283 0.23096 0.37295 0.23078 0.37284
0.90000 -2.20739 1.13188 -0.08033 -2.87081 0.26166 5.12333 0.15446 0.38373 0.70122 -1.00936 -0.82102 662.24399 0.02890 -0.00198 -0.00939 0.29463 0.23263 0.37539 0.23230 0.37519
0.95000 -2.36188 1.17734 -0.08311 -2.85892 0.25917 5.12452 0.16066 0.39195 0.70319 -1.00299 -0.83564 676.66342 0.03229 -0.00430 -0.00851 0.29599 0.23104 0.37549 0.23062 0.37523
1.00000 -2.48787 1.21348 -0.08543 -2.85438 0.25937 4.97808 0.15767 0.39033 0.69326 -0.98919 -0.82480 678.61227 0.03447 -0.00544 -0.00830 0.29632 0.23075 0.37557 0.23026 0.37527
1.05000 -2.60777 1.25860 -0.08916 -2.86981 0.26203 5.01070 0.15688 0.39261 0.68598 -0.97872 -0.81829 683.90149 0.03429 -0.00842 -0.00547 0.29568 0.23098 0.37520 0.23046 0.37488
1.10000 -2.62838 1.27243 -0.09030 -2.89573 0.26581 5.06805 0.15520 0.39118 0.67923 -0.96566 -0.80785 685.93100 0.03437 -0.01108 -0.00315 0.29497 0.23506 0.37717 0.23449 0.37682
1.15000 -2.59132 1.26481 -0.08941 -2.92124 0.26950 5.13234 0.14998 0.38534 0.66793 -0.95082 -0.79032 687.38032 0.03425 -0.01239 -0.00195 0.29347 0.23631 0.37679 0.23572 0.37642
1.20000 -2.54603 1.25372 -0.08811 -2.93364 0.27069 5.26212 0.14670 0.38201 0.65489 -0.93291 -0.77276 688.27701 0.03949 -0.01407 -0.00252 0.29204 0.23733 0.37631 0.23654 0.37582
1.25000 -2.55580 1.25980 -0.08840 -2.94364 0.27213 5.33342 0.14501 0.37993 0.64498 -0.92051 -0.76076 685.76052 0.04208 -0.01487 -0.00282 0.29203 0.23752 0.37643 0.23663 0.37587
1.30000 -2.58213 1.27342 -0.08931 -2.95778 0.27350 5.43995 0.14301 0.37814 0.63681 -0.90996 -0.75371 685.35201 0.04261 -0.01581 -0.00215 0.29238 0.23747 0.37666 0.23653 0.37607
1.35000 -2.62387 1.28932 -0.09025 -2.96503 0.27364 5.54729 0.14402 0.38307 0.63345 -0.90505 -0.75720 691.12873 0.04396 -0.01736 -0.00124 0.29288 0.23705 0.37679 0.23602 0.37615
1.40000 -2.68975 1.31897 -0.09247 -2.98400 0.27531 5.70097 0.14004 0.38039 0.62377 -0.89742 -0.74699 689.84833 0.04271 -0.01772 -0.00039 0.29308 0.23660 0.37667 0.23559 0.37603
1.45000 -2.77638 1.35624 -0.09515 -2.99792 0.27550 5.94070 0.13484 0.37520 0.61543 -0.89171 -0.73465 684.49344 0.03887 -0.01696 0.00046 0.29335 0.23552 0.37619 0.23466 0.37565
1.50000 -2.82394 1.37033 -0.09534 -2.98721 0.27234 6.09930 0.12798 0.36959 0.60455 -0.88586 -0.72026 676.46480 0.03223 -0.01537 0.00165 0.29396 0.23370 0.37554 0.23307 0.37514
1.55000 -2.90588 1.39722 -0.09655 -2.97899 0.26905 6.28192 0.12287 0.36364 0.59550 -0.87583 -0.70856 670.97370 0.02409 -0.01278 0.00245 0.29380 0.23272 0.37481 0.23234 0.37457
1.60000 -2.96975 1.42425 -0.09851 -2.99346 0.27022 6.45109 0.12067 0.35808 0.58753 -0.86203 -0.69746 669.33148 0.01925 -0.01059 0.00234 0.29367 0.23146 0.37392 0.23120 0.37376
1.65000 -3.02859 1.45304 -0.10087 -3.01323 0.27237 6.65655 0.11620 0.35115 0.57502 -0.84623 -0.68163 663.63941 0.01439 -0.00910 0.00286 0.29292 0.22990 0.37236 0.22973 0.37226
1.70000 -3.12245 1.48971 -0.10363 -3.02207 0.27256 6.86500 0.11428 0.34846 0.56561 -0.83510 -0.67387 660.37690 0.00678 -0.00737 0.00420 0.29190 0.22936 0.37123 0.22929 0.37119
1.75000 -3.19987 1.52368 -0.10624 -3.03232 0.27227 7.14934 0.11416 0.34785 0.56082 -0.82889 -0.67347 659.89859 -0.00070 -0.00529 0.00518 0.29151 0.22786 0.36999 0.22783 0.36998
1.80000 -3.26077 1.55130 -0.10817 -3.03437 0.27051 7.47770 0.11337 0.34476 0.55495 -0.82082 -0.66892 657.31268 -0.00618 -0.00387 0.00597 0.29135 0.22687 0.36926 0.22684 0.36924
1.85000 -3.29098 1.56827 -0.10919 -3.03635 0.26880 7.83299 0.11312 0.34130 0.55106 -0.81358 -0.66353 654.01003 -0.00837 -0.00380 0.00676 0.29147 0.22549 0.36851 0.22544 0.36849
1.90000 -3.33434 1.59160 -0.11069 -3.03755 0.26668 8.25080 0.10984 0.33541 0.54492 -0.80595 -0.65210 647.42662 -0.01042 -0.00346 0.00722 0.29117 0.22481 0.36786 0.22475 0.36782
1.95000 -3.41085 1.62526 -0.11311 -3.03978 0.26499 8.64936 0.10739 0.32993 0.54050 -0.79836 -0.64265 643.84469 -0.01343 -0.00272 0.00768 0.29106 0.22420 0.36740 0.22412 0.36735
2.00000 -3.48355 1.65630 -0.11541 -3.04422 0.26418 8.97465 0.10587 0.32567 0.53512 -0.79096 -0.63423 641.12234 -0.01624 -0.00200 0.00810 0.29064 0.22570 0.36799 0.22559 0.36792
2.05000 -3.52030 1.67315 -0.11650 -3.04776 0.26348 9.24329 0.10417 0.32327 0.53066 -0.78687 -0.62748 637.71419 -0.01916 -0.00125 0.00852 0.29077 0.22641 0.36852 0.22626 0.36843
2.10000 -3.54589 1.68458 -0.11712 -3.05154 0.26324 9.46251 0.10129 0.32091 0.52530 -0.78411 -0.61993 633.76275 -0.02232 -0.00011 0.00868 0.29078 0.22652 0.36859 0.22631 0.36847
2.15000 -3.51998 1.67924 -0.11654 -3.05979 0.26396 9.67757 0.10208 0.32128 0.52271 -0.77900 -0.61785 636.04837 -0.02311 0.00005 0.00883 0.29082 0.22669 0.36873 0.22647 0.36860
2.20000 -3.50314 1.67643 -0.11606 -3.06231 0.26355 9.93040 0.10278 0.32096 0.52074 -0.77392 -0.61601 638.09986 -0.02410 0.00055 0.00876 0.29051 0.22707 0.36872 0.22683 0.36857
2.25000 -3.53275 1.68544 -0.11635 -3.05247 0.26141 10.16094 0.10240 0.31955 0.51785 -0.76888 -0.61212 638.15989 -0.02558 0.00136 0.00858 0.28984 0.22745 0.36843 0.22718 0.36826
2.30000 -3.60342 1.70540 -0.11740 -3.03338 0.25815 10.31418 0.09956 0.31579 0.51215 -0.76471 -0.60390 633.54394 -0.02798 0.00311 0.00789 0.28910 0.22753 0.36789 0.22719 0.36769
2.35000 -3.68619 1.72887 -0.11879 -3.01436 0.25517 10.42855 0.09789 0.31213 0.50854 -0.76071 -0.59607 629.76830 -0.02955 0.00436 0.00733 0.28863 0.22782 0.36770 0.22743 0.36747
2.40000 -3.76890 1.75295 -0.12011 -2.99470 0.25151 10.60507 0.09740 0.30835 0.50697 -0.75593 -0.59006 627.24284 -0.03233 0.00608 0.00682 0.28778 0.22821 0.36729 0.22774 0.36699
2.45000 -3.84949 1.77916 -0.12167 -2.97976 0.24834 10.80435 0.09453 0.30209 0.50135 -0.74817 -0.57898 622.77023 -0.03674 0.00847 0.00631 0.28699 0.22864 0.36693 0.22801 0.36654
2.50000 -3.90026 1.79463 -0.12241 -2.96777 0.24585 10.97167 0.09307 0.29824 0.49625 -0.74155 -0.57157 621.65073 -0.04051 0.01000 0.00636 0.28603 0.22857 0.36614 0.22779 0.36566
2.55000 -3.89945 1.79362 -0.12188 -2.96242 0.24440 11.18663 0.09484 0.29818 0.49537 -0.73713 -0.57019 625.78648 -0.04262 0.01031 0.00689 0.28481 0.22845 0.36511 0.22758 0.36457
2.60000 -3.86982 1.78402 -0.12084 -2.96470 0.24441 11.35173 0.09761 0.29858 0.49647 -0.73326 -0.56987 630.55876 -0.04434 0.01057 0.00733 0.28379 0.22854 0.36437 0.22761 0.36379
2.65000 -3.82495 1.76847 -0.11938 -2.97056 0.24532 11.45210 0.10113 0.30108 0.49912 -0.73242 -0.57346 635.96331 -0.04539 0.01090 0.00745 0.28292 0.22860 0.36374 0.22763 0.36312
2.70000 -3.80109 1.75950 -0.11850 -2.97420 0.24620 11.52196 0.10288 0.30146 0.50077 -0.73182 -0.57310 637.51526 -0.04462 0.01112 0.00698 0.28211 0.22892 0.36330 0.22797 0.36270
2.75000 -3.77755 1.75143 -0.11780 -2.98021 0.24751 11.58461 0.10550 0.30223 0.50387 -0.73120 -0.57404 640.52762 -0.04389 0.01137 0.00650 0.28148 0.22969 0.36331 0.22877 0.36272
2.80000 -3.76752 1.74658 -0.11727 -2.98150 0.24810 11.64934 0.10739 0.30226 0.50559 -0.72925 -0.57380 643.06843 -0.04315 0.01156 0.00605 0.28134 0.23046 0.36369 0.22956 0.36312
2.85000 -3.73742 1.73659 -0.11647 -2.98759 0.24954 11.71770 0.10985 0.30317 0.50700 -0.72663 -0.57423 646.55736 -0.04207 0.01146 0.00574 0.28124 0.23093 0.36390 0.23007 0.36336
2.90000 -3.72850 1.73121 -0.11589 -2.98518 0.24993 11.74177 0.10928 0.30131 0.50503 -0.72336 -0.56831 644.99327 -0.04197 0.01152 0.00566 0.28121 0.23143 0.36420 0.23057 0.36365
2.95000 -3.72935 1.73050 -0.11578 -2.98645 0.25087 11.77062 0.10877 0.29929 0.50233 -0.71909 -0.56191 643.84307 -0.04184 0.01144 0.00570 0.28119 0.23209 0.36460 0.23125 0.36407
3.00000 -3.71812 1.72769 -0.11558 -2.99231 0.25238 11.83860 0.10820 0.29685 0.49837 -0.71271 -0.55475 643.30046 -0.04347 0.01153 0.00625 0.28126 0.23245 0.36488 0.23155 0.36431
3.05000 -3.69563 1.72062 -0.11502 -2.99884 0.25394 11.91947 0.10867 0.29591 0.49485 -0.70685 -0.55050 645.21356 -0.04527 0.01151 0.00697 0.28147 0.23245 0.36504 0.23149 0.36443
3.10000 -3.68132 1.71553 -0.11455 -3.00388 0.25519 12.00394 0.10901 0.29495 0.49264 -0.70262 -0.54692 645.89353 -0.04681 0.01157 0.00749 0.28183 0.23255 0.36539 0.23154 0.36475
3.15000 -3.67758 1.71551 -0.11464 -3.01184 0.25694 12.07426 0.10914 0.29381 0.49002 -0.69805 -0.54289 645.78046 -0.04796 0.01184 0.00771 0.28188 0.23322 0.36585 0.23216 0.36517
3.20000 -3.66593 1.71366 -0.11474 -3.02525 0.25985 12.10481 0.11009 0.29318 0.48849 -0.69400 -0.53969 646.19195 -0.04833 0.01181 0.00790 0.28159 0.23386 0.36604 0.23279 0.36535
3.25000 -3.66842 1.71635 -0.11515 -3.03629 0.26227 12.15194 0.11040 0.29166 0.48671 -0.69001 -0.53554 645.49501 -0.04900 0.01166 0.00832 0.28113 0.23431 0.36597 0.23322 0.36527
3.30000 -3.65687 1.71497 -0.11526 -3.04976 0.26504 12.18956 0.11103 0.28998 0.48496 -0.68509 -0.53134 645.71662 -0.04992 0.01153 0.00882 0.28036 0.23482 0.36571 0.23370 0.36499
3.35000 -3.64062 1.71287 -0.11532 -3.06390 0.26772 12.25324 0.11183 0.28856 0.48378 -0.68087 -0.52743 646.17985 -0.05006 0.01120 0.00924 0.27928 0.23574 0.36547 0.23462 0.36475
3.40000 -3.63206 1.71144 -0.11539 -3.07488 0.27018 12.27876 0.11288 0.28775 0.48310 -0.67774 -0.52491 647.36875 -0.04996 0.01058 0.00981 0.27831 0.23637 0.36514 0.23527 0.36443
3.45000 -3.62771 1.70915 -0.11531 -3.08127 0.27215 12.26229 0.11381 0.28728 0.48181 -0.67448 -0.52218 649.24296 -0.05044 0.00995 0.01060 0.27744 0.23661 0.36463 0.23550 0.36391
3.50000 -3.62410 1.70689 -0.11507 -3.08374 0.27302 12.28693 0.11421 0.28662 0.47950 -0.67061 -0.51896 650.57891 -0.05113 0.00950 0.01130 0.27665 0.23681 0.36416 0.23568 0.36343
3.55000 -3.61631 1.70252 -0.11463 -3.08602 0.27391 12.31137 0.11530 0.28701 0.47793 -0.66784 -0.51779 652.89978 -0.05214 0.00905 0.01213 0.27593 0.23712 0.36381 0.23596 0.36306
3.60000 -3.62944 1.70397 -0.11455 -3.08486 0.27417 12.32915 0.11619 0.28719 0.47545 -0.66385 -0.51570 655.62572 -0.05309 0.00855 0.01298 0.27545 0.23761 0.36377 0.23642 0.36300
3.65000 -3.63981 1.70469 -0.11438 -3.08283 0.27417 12.35133 0.11633 0.28693 0.47283 -0.66047 -0.51331 657.08250 -0.05417 0.00834 0.01362 0.27508 0.23802 0.36376 0.23679 0.36296
3.70000 -3.63959 1.70303 -0.11407 -3.08366 0.27452 12.39206 0.11607 0.28686 0.47000 -0.65741 -0.51079 658.04968 -0.05467 0.00822 0.01394 0.27465 0.23851 0.36376 0.23726 0.36294
3.75000 -3.63098 1.70020 -0.11378 -3.08944 0.27560 12.45756 0.11670 0.28808 0.46838 -0.65545 -0.51052 660.23090 -0.05540 0.00823 0.01424 0.27413 0.23895 0.36366 0.23767 0.36281
3.80000 -3.61948 1.69754 -0.11356 -3.09723 0.27689 12.54492 0.11705 0.28879 0.46630 -0.65366 -0.50974 661.36616 -0.05647 0.00842 0.01451 0.27355 0.23943 0.36353 0.23810 0.36265
3.85000 -3.61310 1.69563 -0.11338 -3.10319 0.27811 12.60729 0.11694 0.28836 0.46361 -0.65096 -0.50750 661.27330 -0.05730 0.00857 0.01473 0.27285 0.23980 0.36325 0.23843 0.36235
3.90000 -3.60313 1.69261 -0.11312 -3.10913 0.27943 12.66354 0.11575 0.28678 0.46035 -0.64829 -0.50365 659.01910 -0.05766 0.00871 0.01476 0.27228 0.24013 0.36305 0.23874 0.36213
3.95000 -3.59498 1.69040 -0.11297 -3.11561 0.28092 12.70325 0.11397 0.28446 0.45713 -0.64594 -0.49916 655.26563 -0.05792 0.00898 0.01464 0.27183 0.24044 0.36290 0.23903 0.36197
4.00000 -3.58792 1.68909 -0.11288 -3.12247 0.28228 12.75432 0.11199 0.28174 0.45344 -0.64282 -0.49398 651.48506 -0.05830 0.00927 0.01454 0.27131 0.24073 0.36271 0.23930 0.36176
4.05000 -3.57639 1.68687 -0.11271 -3.12842 0.28337 12.83276 0.10938 0.27822 0.44875 -0.63876 -0.48687 646.55144 -0.05897 0.00954 0.01459 0.27080 0.24102 0.36253 0.23955 0.36155
4.10000 -3.55612 1.68126 -0.11220 -3.13309 0.28421 12.90768 0.10684 0.27446 0.44431 -0.63412 -0.47920 641.77419 -0.05973 0.00936 0.01507 0.27015 0.24120 0.36216 0.23970 0.36116
4.15000 -3.52734 1.67174 -0.11128 -3.13478 0.28453 12.98967 0.10474 0.27085 0.44063 -0.62937 -0.47159 637.47538 -0.06001 0.00879 0.01573 0.26941 0.24151 0.36181 0.24000 0.36081
4.20000 -3.49975 1.66129 -0.11022 -3.13306 0.28445 13.04693 0.10219 0.26704 0.43640 -0.62478 -0.46322 632.18054 -0.06030 0.00825 0.01635 0.26875 0.24186 0.36156 0.24035 0.36055
4.25000 -3.47625 1.65178 -0.10920 -3.12958 0.28411 13.09465 0.09869 0.26243 0.43105 -0.61979 -0.45329 625.49569 -0.06104 0.00800 0.01689 0.26820 0.24201 0.36125 0.24047 0.36022
4.30000 -3.45023 1.64172 -0.10814 -3.12659 0.28371 13.17742 0.09633 0.25927 0.42668 -0.61549 -0.44614 621.12064 -0.06156 0.00765 0.01742 0.26774 0.24200 0.36091 0.24044 0.35986
4.35000 -3.42876 1.63314 -0.10724 -3.12457 0.28352 13.25349 0.09526 0.25737 0.42366 -0.61168 -0.44165 619.19388 -0.06201 0.00718 0.01803 0.26749 0.24180 0.36058 0.24022 0.35952
4.40000 -3.40994 1.62543 -0.10645 -3.12298 0.28350 13.32518 0.09468 0.25627 0.42110 -0.60856 -0.43837 618.56422 -0.06227 0.00667 0.01859 0.26733 0.24162 0.36034 0.24003 0.35928
4.45000 -3.40251 1.62151 -0.10599 -3.12171 0.28360 13.39387 0.09419 0.25529 0.41902 -0.60601 -0.43545 617.91658 -0.06276 0.00643 0.01901 0.26715 0.24176 0.36030 0.24016 0.35923
4.50000 -3.38958 1.61689 -0.10553 -3.12265 0.28397 13.48038 0.09335 0.25390 0.41692 -0.60397 -0.43234 616.41549 -0.06345 0.00629 0.01942 0.26693 0.24170 0.36010 0.24006 0.35900
4.55000 -3.37764 1.61338 -0.10521 -3.12559 0.28458 13.56710 0.09314 0.25291 0.41488 -0.60105 -0.42994 616.35231 -0.06356 0.00603 0.01970 0.26676 0.24178 0.36003 0.24014 0.35893
4.60000 -3.35837 1.60831 -0.10480 -3.13006 0.28531 13.67368 0.09337 0.25211 0.41312 -0.59780 -0.42841 617.34143 -0.06369 0.00583 0.01994 0.26671 0.24182 0.36002 0.24017 0.35891
4.65000 -3.33537 1.60205 -0.10426 -3.13400 0.28585 13.79023 0.09334 0.25090 0.41144 -0.59465 -0.42666 617.87888 -0.06418 0.00564 0.02030 0.26668 0.24168 0.35990 0.24001 0.35878
4.70000 -3.31365 1.59499 -0.10361 -3.13584 0.28622 13.89582 0.09352 0.24995 0.40986 -0.59126 -0.42482 618.96355 -0.06455 0.00520 0.02084 0.26660 0.24160 0.35979 0.23991 0.35866
4.75000 -3.30404 1.59030 -0.10309 -3.13427 0.28621 13.96089 0.09406 0.24927 0.40858 -0.58771 -0.42351 620.79136 -0.06471 0.00468 0.02138 0.26649 0.24160 0.35970 0.23991 0.35857
4.80000 -3.29858 1.58617 -0.10261 -3.13091 0.28606 14.00011 0.09466 0.24884 0.40746 -0.58437 -0.42265 622.86053 -0.06453 0.00409 0.02185 0.26629 0.24166 0.35959 0.23998 0.35847
4.85000 -3.29125 1.58239 -0.10220 -3.12908 0.28608 14.05150 0.09427 0.24761 0.40520 -0.58119 -0.42036 623.13747 -0.06490 0.00377 0.02230 0.26605 0.24170 0.35944 0.24000 0.35831
4.90000 -3.27782 1.57682 -0.10170 -3.12959 0.28663 14.09145 0.09402 0.24672 0.40323 -0.57816 -0.41829 623.63760 -0.06500 0.00331 0.02277 0.26576 0.24178 0.35928 0.24009 0.35815
4.95000 -3.26233 1.57143 -0.10127 -3.13211 0.28742 14.14737 0.09413 0.24636 0.40181 -0.57545 -0.41723 625.21144 -0.06506 0.00282 0.02324 0.26552 0.24173 0.35907 0.24003 0.35794
5.00000 -3.24400 1.56533 -0.10079 -3.13552 0.28824 14.20965 0.09482 0.24643 0.40111 -0.57286 -0.41746 628.30418 -0.06512 0.00232 0.02373 0.26529 0.24160 0.35882 0.23991 0.35768
5.05000 -3.22827 1.55960 -0.10030 -3.13785 0.28887 14.26194 0.09566 0.24676 0.40085 -0.57095 -0.41844 631.51724 -0.06553 0.00180 0.02435 0.26508 0.24137 0.35851 0.23966 0.35735
5.10000 -3.22439 1.55649 -0.10000 -3.13738 0.28930 14.28287 0.09600 0.24662 0.39985 -0.56892 -0.41839 633.72473 -0.06624 0.00150 0.02491 0.26485 0.24116 0.35820 0.23941 0.35702
5.15000 -3.21975 1.55387 -0.09980 -3.13940 0.29022 14.29155 0.09582 0.24580 0.39857 -0.56714 -0.41728 634.62404 -0.06710 0.00126 0.02546 0.26465 0.24099 0.35793 0.23919 0.35672
5.20000 -3.21329 1.55163 -0.09966 -3.14270 0.29120 14.32880 0.09500 0.24442 0.39691 -0.56594 -0.41517 633.56057 -0.06796 0.00106 0.02598 0.26449 0.24076 0.35766 0.23892 0.35642
5.25000 -3.21060 1.54936 -0.09941 -3.14217 0.29155 14.35743 0.09429 0.24328 0.39548 -0.56489 -0.41321 632.58995 -0.06850 0.00078 0.02645 0.26425 0.24053 0.35733 0.23865 0.35607
5.30000 -3.21169 1.54826 -0.09923 -3.14054 0.29161 14.39293 0.09337 0.24199 0.39368 -0.56353 -0.41101 631.51361 -0.06897 0.00058 0.02681 0.26405 0.24026 0.35700 0.23836 0.35572
5.35000 -3.20797 1.54483 -0.09880 -3.13778 0.29154 14.41551 0.09227 0.24034 0.39150 -0.56191 -0.40842 630.09308 -0.06945 0.00039 0.02718 0.26382 0.24002 0.35667 0.23809 0.35537
5.40000 -3.20537 1.54153 -0.09838 -3.13459 0.29141 14.43390 0.09114 0.23898 0.38910 -0.56068 -0.40609 629.00140 -0.06962 0.00012 0.02748 0.26358 0.23966 0.35624 0.23772 0.35494
5.45000 -3.20295 1.53878 -0.09802 -3.13229 0.29133 14.45675 0.09028 0.23779 0.38697 -0.55936 -0.40429 628.33068 -0.06949 -0.00015 0.02768 0.26322 0.23924 0.35570 0.23731 0.35440
5.50000 -3.19896 1.53475 -0.09754 -3.12834 0.29109 14.45681 0.08936 0.23646 0.38517 -0.55839 -0.40235 627.07836 -0.06912 -0.00048 0.02783 0.26281 0.23893 0.35518 0.23701 0.35389
5.55000 -3.19501 1.53082 -0.09706 -3.12423 0.29077 14.46352 0.08868 0.23555 0.38399 -0.55782 -0.40090 626.04641 -0.06815 -0.00096 0.02790 0.26247 0.23874 0.35481 0.23687 0.35355
5.60000 -3.19009 1.52727 -0.09663 -3.12210 0.29064 14.48643 0.08842 0.23516 0.38313 -0.55736 -0.40024 625.87900 -0.06718 -0.00147 0.02798 0.26215 0.23853 0.35443 0.23671 0.35321
5.65000 -3.18569 1.52367 -0.09615 -3.11904 0.29030 14.52126 0.08819 0.23451 0.38225 -0.55653 -0.39892 625.72287 -0.06634 -0.00215 0.02827 0.26178 0.23839 0.35406 0.23661 0.35286
5.70000 -3.18588 1.52052 -0.09565 -3.11304 0.28958 14.54133 0.08748 0.23358 0.38103 -0.55607 -0.39651 624.17968 -0.06540 -0.00301 0.02868 0.26150 0.23832 0.35380 0.23659 0.35264
5.75000 -3.18941 1.51809 -0.09516 -3.10499 0.28852 14.55922 0.08644 0.23243 0.37941 -0.55565 -0.39335 621.86286 -0.06441 -0.00376 0.02898 0.26124 0.23826 0.35358 0.23658 0.35245
5.80000 -3.18906 1.51435 -0.09461 -3.09747 0.28768 14.56508 0.08565 0.23134 0.37773 -0.55469 -0.39035 620.31159 -0.06312 -0.00450 0.02915 0.26093 0.23826 0.35335 0.23664 0.35225
5.85000 -3.19425 1.51214 -0.09417 -3.08848 0.28661 14.56773 0.08490 0.23007 0.37614 -0.55345 -0.38714 618.83601 -0.06202 -0.00513 0.02929 0.26057 0.23832 0.35312 0.23675 0.35206
5.90000 -3.20374 1.51111 -0.09381 -3.07883 0.28546 14.55397 0.08391 0.22841 0.37465 -0.55218 -0.38356 616.98071 -0.06103 -0.00570 0.02942 0.26019 0.23836 0.35287 0.23683 0.35184
5.95000 -3.21744 1.51116 -0.09351 -3.06789 0.28409 14.55107 0.08321 0.22712 0.37347 -0.55091 -0.38066 615.85224 -0.05980 -0.00629 0.02947 0.25985 0.23847 0.35269 0.23699 0.35169
6.00000 -3.24192 1.51451 -0.09349 -3.05603 0.28263 14.54023 0.08224 0.22569 0.37213 -0.54985 -0.37726 614.01945 -0.05880 -0.00695 0.02968 0.25952 0.23859 0.35253 0.23716 0.35156
6.05000 -3.26560 1.51749 -0.09346 -3.04447 0.28135 14.50699 0.08113 0.22402 0.37052 -0.54829 -0.37332 612.02342 -0.05756 -0.00773 0.02991 0.25919 0.23872 0.35237 0.23733 0.35144
6.10000 -3.28857 1.52000 -0.09340 -3.03280 0.28012 14.46278 0.08049 0.22286 0.36934 -0.54684 -0.37039 611.17171 -0.05622 -0.00855 0.03013 0.25876 0.23895 0.35221 0.23761 0.35131
6.15000 -3.30973 1.52264 -0.09340 -3.02282 0.27908 14.42994 0.08005 0.22189 0.36830 -0.54510 -0.36792 610.98538 -0.05497 -0.00931 0.03034 0.25831 0.23919 0.35205 0.23790 0.35117
6.20000 -3.32993 1.52506 -0.09341 -3.01359 0.27820 14.38798 0.07965 0.22095 0.36707 -0.54321 -0.36564 610.81209 -0.05392 -0.01002 0.03057 0.25789 0.23947 0.35193 0.23821 0.35107
6.25000 -3.34676 1.52702 -0.09341 -3.00610 0.27753 14.35898 0.07929 0.22007 0.36582 -0.54133 -0.36352 610.82703 -0.05301 -0.01074 0.03086 0.25749 0.23975 0.35182 0.23851 0.35099
6.30000 -3.36329 1.52902 -0.09345 -2.99973 0.27709 14.32124 0.07920 0.21951 0.36464 -0.53928 -0.36184 611.78360 -0.05223 -0.01153 0.03127 0.25712 0.24001 0.35173 0.23879 0.35090
6.35000 -3.38079 1.53168 -0.09353 -2.99422 0.27671 14.29255 0.07911 0.21898 0.36331 -0.53725 -0.36006 612.64429 -0.05159 -0.01231 0.03173 0.25678 0.24029 0.35168 0.23909 0.35086
6.40000 -3.39983 1.53521 -0.09370 -2.98898 0.27629 14.27435 0.07899 0.21825 0.36158 -0.53452 -0.35786 613.55575 -0.05111 -0.01305 0.03220 0.25649 0.24057 0.35165 0.23937 0.35083
6.45000 -3.41858 1.53795 -0.09378 -2.98231 0.27575 14.24012 0.07895 0.21757 0.36007 -0.53183 -0.35571 614.85439 -0.05055 -0.01377 0.03264 0.25626 0.24083 0.35167 0.23964 0.35085
6.50000 -3.43860 1.54042 -0.09381 -2.97478 0.27517 14.17735 0.07896 0.21686 0.35892 -0.52924 -0.35374 616.36384 -0.05013 -0.01447 0.03310 0.25601 0.24116 0.35171 0.23997 0.35090
6.55000 -3.45574 1.54230 -0.09385 -2.96916 0.27491 14.10650 0.07950 0.21654 0.35837 -0.52672 -0.35265 618.89548 -0.04960 -0.01523 0.03358 0.25575 0.24149 0.35175 0.24029 0.35093
6.60000 -3.46943 1.54365 -0.09391 -2.96570 0.27503 14.03234 0.08012 0.21628 0.35801 -0.52439 -0.35158 621.27509 -0.04886 -0.01604 0.03402 0.25546 0.24190 0.35182 0.24072 0.35100
6.65000 -3.48243 1.54461 -0.09393 -2.96167 0.27510 13.95189 0.08061 0.21610 0.35736 -0.52235 -0.35050 623.32922 -0.04793 -0.01689 0.03442 0.25517 0.24231 0.35189 0.24114 0.35108
6.70000 -3.49595 1.54598 -0.09400 -2.95782 0.27519 13.87486 0.08050 0.21545 0.35627 -0.52078 -0.34871 623.73353 -0.04731 -0.01762 0.03483 0.25487 0.24271 0.35195 0.24155 0.35115
6.75000 -3.51018 1.54771 -0.09408 -2.95361 0.27517 13.80520 0.08007 0.21465 0.35509 -0.51946 -0.34666 623.49453 -0.04679 -0.01827 0.03521 0.25460 0.24310 0.35202 0.24193 0.35122
6.80000 -3.52575 1.54997 -0.09421 -2.94928 0.27512 13.73739 0.07946 0.21369 0.35380 -0.51817 -0.34444 623.02510 -0.04648 -0.01883 0.03559 0.25432 0.24341 0.35204 0.24224 0.35123
6.85000 -3.53897 1.55162 -0.09430 -2.94583 0.27519 13.67606 0.07901 0.21290 0.35281 -0.51672 -0.34261 623.08139 -0.04634 -0.01937 0.03602 0.25402 0.24370 0.35201 0.24251 0.35120
6.90000 -3.55069 1.55266 -0.09433 -2.94212 0.27522 13.60932 0.07866 0.21218 0.35189 -0.51532 -0.34096 623.26769 -0.04600 -0.01998 0.03643 0.25379 0.24396 0.35203 0.24277 0.35120
6.95000 -3.55831 1.55260 -0.09429 -2.93899 0.27535 13.54281 0.07794 0.21109 0.35068 -0.51392 -0.33876 622.56098 -0.04574 -0.02052 0.03682 0.25362 0.24417 0.35206 0.24298 0.35123
7.00000 -3.56809 1.55301 -0.09430 -2.93598 0.27558 13.45438 0.07719 0.21004 0.34956 -0.51271 -0.33670 621.80126 -0.04549 -0.02101 0.03715 0.25347 0.24433 0.35206 0.24313 0.35122
7.05000 -3.57766 1.55338 -0.09431 -2.93294 0.27577 13.37088 0.07667 0.20926 0.34879 -0.51181 -0.33528 621.40619 -0.04528 -0.02145 0.03747 0.25333 0.24443 0.35203 0.24321 0.35118
7.10000 -3.58708 1.55349 -0.09429 -2.92957 0.27592 13.28415 0.07629 0.20878 0.34820 -0.51112 -0.33424 621.37176 -0.04492 -0.02195 0.03777 0.25313 0.24450 0.35193 0.24328 0.35108
7.15000 -3.59667 1.55373 -0.09428 -2.92607 0.27604 13.20200 0.07589 0.20843 0.34750 -0.51054 -0.33332 621.37831 -0.04428 -0.02252 0.03803 0.25288 0.24460 0.35182 0.24338 0.35097
7.20000 -3.60615 1.55373 -0.09426 -2.92216 0.27613 13.11767 0.07580 0.20844 0.34686 -0.50984 -0.33288 622.16965 -0.04338 -0.02315 0.03823 0.25258 0.24474 0.35170 0.24353 0.35086
7.25000 -3.61723 1.55394 -0.09424 -2.91732 0.27609 13.02800 0.07594 0.20872 0.34641 -0.50914 -0.33279 623.35415 -0.04259 -0.02383 0.03853 0.25226 0.24481 0.35152 0.24360 0.35068
7.30000 -3.62487 1.55359 -0.09418 -2.91318 0.27604 12.95324 0.07590 0.20884 0.34572 -0.50825 -0.33238 624.32210 -0.04205 -0.02449 0.03889 0.25197 0.24481 0.35132 0.24359 0.35047
7.35000 -3.62817 1.55233 -0.09406 -2.91027 0.27611 12.88774 0.07584 0.20896 0.34510 -0.50744 -0.33205 625.18334 -0.04161 -0.02508 0.03925 0.25171 0.24475 0.35109 0.24352 0.35023
7.40000 -3.63197 1.55119 -0.09396 -2.90734 0.27618 12.81727 0.07601 0.20924 0.34482 -0.50674 -0.33212 626.37969 -0.04122 -0.02572 0.03966 0.25140 0.24469 0.35082 0.24344 0.34995
7.45000 -3.63613 1.54988 -0.09384 -2.90420 0.27626 12.74165 0.07645 0.20970 0.34489 -0.50626 -0.33270 627.90131 -0.04074 -0.02637 0.04005 0.25102 0.24463 0.35051 0.24337 0.34963
7.50000 -3.64131 1.54912 -0.09376 -2.90122 0.27631 12.67079 0.07679 0.21008 0.34476 -0.50571 -0.33308 629.53021 -0.04038 -0.02698 0.04045 0.25063 0.24464 0.35024 0.24336 0.34934
7.55000 -3.64293 1.54723 -0.09360 -2.89904 0.27651 12.59374 0.07723 0.21055 0.34469 -0.50500 -0.33359 631.58148 -0.04009 -0.02758 0.04086 0.25024 0.24464 0.34996 0.24334 0.34905
7.60000 -3.64158 1.54447 -0.09340 -2.89763 0.27688 12.51041 0.07768 0.21109 0.34478 -0.50465 -0.33426 633.33745 -0.03970 -0.02818 0.04125 0.24986 0.24465 0.34969 0.24334 0.34877
7.65000 -3.64199 1.54204 -0.09320 -2.89544 0.27711 12.42342 0.07805 0.21153 0.34501 -0.50463 -0.33498 634.62256 -0.03936 -0.02874 0.04161 0.24949 0.24465 0.34942 0.24332 0.34849
7.70000 -3.64223 1.53959 -0.09299 -2.89299 0.27726 12.33712 0.07819 0.21173 0.34499 -0.50456 -0.33534 635.33264 -0.03904 -0.02925 0.04193 0.24908 0.24462 0.34912 0.24328 0.34818
7.75000 -3.64390 1.53761 -0.09281 -2.89039 0.27737 12.25380 0.07803 0.21171 0.34495 -0.50475 -0.33529 635.24475 -0.03879 -0.02968 0.04222 0.24865 0.24463 0.34882 0.24327 0.34786
7.80000 -3.64818 1.53609 -0.09265 -2.88687 0.27741 12.15977 0.07772 0.21150 0.34467 -0.50470 -0.33490 634.98650 -0.03860 -0.03004 0.04246 0.24822 0.24464 0.34851 0.24326 0.34754
7.85000 -3.65578 1.53539 -0.09254 -2.88214 0.27725 12.06494 0.07751 0.21139 0.34453 -0.50475 -0.33468 634.91282 -0.03857 -0.03042 0.04278 0.24779 0.24463 0.34820 0.24323 0.34722
7.90000 -3.66320 1.53473 -0.09244 -2.87764 0.27714 11.97055 0.07741 0.21138 0.34436 -0.50455 -0.33457 635.21525 -0.03847 -0.03081 0.04309 0.24737 0.24464 0.34791 0.24323 0.34692
7.95000 -3.66987 1.53350 -0.09228 -2.87251 0.27693 11.87446 0.07754 0.21148 0.34447 -0.50428 -0.33471 635.87781 -0.03822 -0.03125 0.04338 0.24698 0.24466 0.34765 0.24323 0.34665
8.00000 -3.67741 1.53248 -0.09214 -2.86723 0.27672 11.77290 0.07758 0.21140 0.34451 -0.50382 -0.33465 636.38112 -0.03798 -0.03165 0.04364 0.24660 0.24466 0.34738 0.24322 0.34636
8.05000 -3.68556 1.53196 -0.09205 -2.86265 0.27659 11.67567 0.07770 0.21125 0.34467 -0.50334 -0.33459 636.88334 -0.03770 -0.03200 0.04383 0.24623 0.24471 0.34715 0.24326 0.34613
8.10000 -3.69273 1.53131 -0.09196 -2.85842 0.27648 11.58296 0.07780 0.21107 0.34483 -0.50287 -0.33446 637.52578 -0.03727 -0.03239 0.04400 0.24587 0.24478 0.34695 0.24332 0.34592
8.15000 -3.70027 1.53113 -0.09191 -2.85483 0.27643 11.50093 0.07796 0.21110 0.34493 -0.50255 -0.33458 638.24185 -0.03678 -0.03283 0.04419 0.24549 0.24488 0.34674 0.24341 0.34570
8.20000 -3.70910 1.53127 -0.09189 -2.85085 0.27632 11.41484 0.07798 0.21094 0.34482 -0.50215 -0.33437 638.56300 -0.03637 -0.03326 0.04441 0.24515 0.24497 0.34657 0.24349 0.34552
8.25000 -3.71405 1.53053 -0.09182 -2.84807 0.27640 11.33431 0.07801 0.21074 0.34457 -0.50150 -0.33408 638.90350 -0.03609 -0.03365 0.04465 0.24482 0.24500 0.34636 0.24351 0.34530
8.30000 -3.71401 1.52859 -0.09168 -2.84678 0.27669 11.25740 0.07820 0.21073 0.34446 -0.50087 -0.33416 639.62908 -0.03582 -0.03403 0.04487 0.24452 0.24499 0.34613 0.24348 0.34506
8.35000 -3.71147 1.52564 -0.09145 -2.84506 0.27692 11.17477 0.07836 0.21069 0.34446 -0.50042 -0.33420 640.08567 -0.03561 -0.03439 0.04511 0.24421 0.24493 0.34588 0.24341 0.34480
8.40000 -3.70828 1.52251 -0.09120 -2.84327 0.27711 11.09458 0.07843 0.21048 0.34428 -0.49973 -0.33403 640.43031 -0.03557 -0.03470 0.04536 0.24390 0.24486 0.34561 0.24331 0.34451
8.45000 -3.70492 1.51949 -0.09095 -2.84177 0.27730 11.01618 0.07848 0.21020 0.34408 -0.49888 -0.33389 640.77957 -0.03566 -0.03493 0.04560 0.24360 0.24476 0.34532 0.24320 0.34422
8.50000 -3.70101 1.51653 -0.09073 -2.84084 0.27756 10.94108 0.07865 0.20995 0.34404 -0.49807 -0.33388 641.23273 -0.03587 -0.03516 0.04589 0.24329 0.24469 0.34506 0.24311 0.34394
8.55000 -3.69655 1.51361 -0.09051 -2.84020 0.27780 10.87704 0.07886 0.20977 0.34414 -0.49738 -0.33404 641.76200 -0.03614 -0.03536 0.04618 0.24299 0.24462 0.34480 0.24302 0.34366
8.60000 -3.69331 1.51124 -0.09033 -2.83955 0.27801 10.81736 0.07897 0.20960 0.34437 -0.49702 -0.33421 641.99995 -0.03642 -0.03556 0.04646 0.24273 0.24454 0.34456 0.24292 0.34341
8.65000 -3.68964 1.50873 -0.09014 -2.83855 0.27814 10.76133 0.07907 0.20941 0.34454 -0.49655 -0.33433 642.24736 -0.03673 -0.03574 0.04675 0.24248 0.24445 0.34431 0.24281 0.34315
8.70000 -3.68494 1.50615 -0.08995 -2.83809 0.27834 10.70580 0.07892 0.20902 0.34451 -0.49603 -0.33411 641.93651 -0.03702 -0.03590 0.04702 0.24222 0.24438 0.34408 0.24272 0.34291
8.75000 -3.67902 1.50331 -0.08975 -2.83792 0.27857 10.65300 0.07885 0.20869 0.34442 -0.49539 -0.33402 641.82451 -0.03730 -0.03607 0.04727 0.24196 0.24432 0.34385 0.24264 0.34266
8.80000 -3.67386 1.50058 -0.08954 -2.83708 0.27867 10.60343 0.07875 0.20846 0.34432 -0.49491 -0.33401 641.59434 -0.03765 -0.03618 0.04751 0.24164 0.24424 0.34357 0.24254 0.34237
8.85000 -3.67023 1.49842 -0.08938 -2.83633 0.27880 10.55335 0.07854 0.20813 0.34412 -0.49449 -0.33375 641.11623 -0.03794 -0.03626 0.04770 0.24130 0.24416 0.34328 0.24246 0.34207
8.90000 -3.66639 1.49625 -0.08922 -2.83540 0.27888 10.50440 0.07824 0.20767 0.34379 -0.49402 -0.33324 640.31599 -0.03816 -0.03637 0.04788 0.24100 0.24411 0.34303 0.24239 0.34181
8.95000 -3.66133 1.49363 -0.08903 -2.83464 0.27903 10.44595 0.07786 0.20706 0.34338 -0.49344 -0.33253 639.20049 -0.03832 -0.03648 0.04805 0.24070 0.24406 0.34279 0.24232 0.34155
9.00000 -3.65766 1.49139 -0.08887 -2.83353 0.27910 10.39062 0.07765 0.20655 0.34298 -0.49260 -0.33204 638.62628 -0.03838 -0.03659 0.04817 0.24039 0.24402 0.34254 0.24228 0.34130
9.05000 -3.65239 1.48867 -0.08867 -2.83290 0.27926 10.33533 0.07756 0.20615 0.34258 -0.49170 -0.33165 638.33321 -0.03836 -0.03671 0.04827 0.24006 0.24396 0.34227 0.24222 0.34102
9.10000 -3.64690 1.48576 -0.08845 -2.83195 0.27939 10.27836 0.07752 0.20579 0.34214 -0.49072 -0.33125 638.20891 -0.03833 -0.03686 0.04839 0.23970 0.24391 0.34198 0.24216 0.34073
9.15000 -3.64157 1.48325 -0.08828 -2.83170 0.27957 10.22930 0.07741 0.20543 0.34149 -0.48955 -0.33074 638.13166 -0.03833 -0.03694 0.04845 0.23939 0.24388 0.34174 0.24212 0.34049
9.20000 -3.63586 1.48065 -0.08810 -2.83136 0.27971 10.18312 0.07743 0.20518 0.34093 -0.48833 -0.33038 638.30542 -0.03828 -0.03706 0.04855 0.23912 0.24385 0.34153 0.24208 0.34027
9.25000 -3.63066 1.47830 -0.08793 -2.83108 0.27983 10.13866 0.07756 0.20500 0.34052 -0.48721 -0.33025 638.63157 -0.03811 -0.03720 0.04860 0.23887 0.24381 0.34133 0.24204 0.34007
9.30000 -3.62851 1.47677 -0.08782 -2.83022 0.27987 10.08957 0.07764 0.20483 0.34007 -0.48621 -0.33014 638.74158 -0.03787 -0.03733 0.04861 0.23864 0.24377 0.34113 0.24200 0.33987
9.35000 -3.62562 1.47518 -0.08772 -2.82982 0.27997 10.04380 0.07782 0.20473 0.33973 -0.48524 -0.33024 639.15016 -0.03747 -0.03745 0.04856 0.23841 0.24372 0.34093 0.24195 0.33967
9.40000 -3.62436 1.47400 -0.08764 -2.82879 0.27996 9.99974 0.07797 0.20466 0.33943 -0.48455 -0.33038 639.36804 -0.03696 -0.03759 0.04847 0.23819 0.24367 0.34074 0.24190 0.33949
9.45000 -3.62523 1.47346 -0.08760 -2.82729 0.27987 9.95685 0.07797 0.20450 0.33896 -0.48393 -0.33030 639.26908 -0.03646 -0.03770 0.04837 0.23798 0.24363 0.34058 0.24188 0.33932
9.50000 -3.62919 1.47408 -0.08765 -2.82573 0.27972 9.91763 0.07786 0.20425 0.33836 -0.48331 -0.32993 638.93940 -0.03601 -0.03783 0.04829 0.23779 0.24364 0.34045 0.24188 0.33920
9.55000 -3.63372 1.47473 -0.08770 -2.82383 0.27952 9.87629 0.07789 0.20402 0.33789 -0.48264 -0.32973 638.83798 -0.03559 -0.03794 0.04822 0.23758 0.24366 0.34032 0.24192 0.33907
9.60000 -3.63729 1.47500 -0.08772 -2.82203 0.27935 9.83293 0.07803 0.20384 0.33754 -0.48202 -0.32968 638.98631 -0.03515 -0.03806 0.04814 0.23739 0.24366 0.34018 0.24191 0.33894
9.65000 -3.63679 1.47426 -0.08767 -2.82143 0.27937 9.79248 0.07821 0.20378 0.33724 -0.48149 -0.32979 639.36121 -0.03464 -0.03819 0.04805 0.23718 0.24362 0.34001 0.24188 0.33876
9.70000 -3.63345 1.47266 -0.08757 -2.82157 0.27952 9.75051 0.07849 0.20378 0.33700 -0.48088 -0.33007 640.04153 -0.03415 -0.03830 0.04795 0.23696 0.24350 0.33977 0.24177 0.33853
9.75000 -3.62789 1.47059 -0.08746 -2.82268 0.27984 9.70906 0.07876 0.20376 0.33670 -0.48023 -0.33036 640.73373 -0.03376 -0.03838 0.04786 0.23673 0.24339 0.33953 0.24166 0.33829
9.80000 -3.62191 1.46839 -0.08733 -2.82392 0.28019 9.66572 0.07905 0.20371 0.33648 -0.47960 -0.33062 641.29444 -0.03324 -0.03848 0.04774 0.23650 0.24333 0.33933 0.24161 0.33809
9.85000 -3.61411 1.46573 -0.08718 -2.82568 0.28061 9.62628 0.07941 0.20373 0.33625 -0.47891 -0.33088 641.97901 -0.03269 -0.03864 0.04765 0.23631 0.24329 0.33916 0.24157 0.33793
9.90000 -3.60461 1.46255 -0.08699 -2.82759 0.28106 9.58888 0.07984 0.20387 0.33617 -0.47839 -0.33134 642.78018 -0.03200 -0.03883 0.04754 0.23614 0.24324 0.33901 0.24153 0.33779
9.95000 -3.59478 1.45928 -0.08680 -2.82954 0.28152 9.55086 0.08024 0.20396 0.33610 -0.47787 -0.33174 643.69598 -0.03124 -0.03901 0.04739 0.23600 0.24319 0.33888 0.24148 0.33765
10.0000 -3.58474 1.45589 -0.08659 -2.83142 0.28196 9.51260 0.08065 0.20402 0.33612 -0.47735 -0.33219 644.70999 -0.03045 -0.03919 0.04722 0.23589 0.24313 0.33876 0.24142 0.33754
""")
[docs]class CauzziEtAl2014NoSOF(CauzziEtAl2014):
"""
Returns the Cauzzi et al (GMPE) for the case when no style-of-faulting is
input. This modifies both the expected ground motion as well as the
inter-event (and thus total) standard deviations.
"""
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag',))
def _compute_mean(self, C, rup, dists, sites, imt):
"""
Returns the mean ground motion acceleration and velocity
"""
mean = (self._get_magnitude_scaling_term(C, rup.mag) +
self._get_distance_scaling_term(C, rup.mag, dists.rrup) +
self._get_site_amplification_term(C, sites.vs30))
# convert from cm/s**2 to g for SA and from m/s**2 to g for PGA (PGV
# is already in cm/s) and also convert from base 10 to base e.
if isinstance(imt, PGA):
mean = np.log((10 ** mean) * ((2 * np.pi / 0.01) ** 2) *
1e-2 / g)
elif isinstance(imt, SA):
mean = np.log((10 ** mean) * ((2 * np.pi / imt.period) ** 2) *
1e-2 / g)
else:
mean = np.log(10 ** mean)
return mean
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Returns the standard deviation terms assuming no style-of-faulting
is known
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(np.log(10.0 ** C['s']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0 ** C['f']) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0 ** C["t"]) + np.zeros(num_sites))
return stddevs
[docs]class CauzziEtAl2014FixedVs30(CauzziEtAl2014):
"""
Implements the Cauzzi et al (2014) model for the case in which
the reference Vs30 in the site amplification term is fixed at 800 m/s
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification scaling term assuming
period dependent reference vs30
"""
return C["bV800"] * np.log10(vs30 / 800.)
[docs]class CauzziEtAl2014FixedVs30NoSOF(CauzziEtAl2014NoSOF):
"""
Implements the Cauzzi et al (2014) model for the case in which
the reference Vs30 in the site amplification term is fixed at 800 m/s
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification scaling term assuming the reference
Vs30 is fixed at 800 m/s
"""
return C["bV800"] * np.log10(vs30 / 800.)
[docs]class CauzziEtAl2014Eurocode8(CauzziEtAl2014):
"""
Implmements the Cauzzi et al. (2014) GMPE for the case in which
the Eurocode 8 site classification is preferred
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification term on the basis of Eurocode 8
site class
"""
s_b, s_c, s_d = self._get_site_dummy_variables(vs30)
return (C["sB"] * s_b) + (C["sC"] * s_c) + (C["sD"] * s_d)
def _get_site_dummy_variables(self, vs30):
"""
Returns the Eurocode 8 site class dummy variable
"""
s_b = np.zeros_like(vs30)
s_c = np.zeros_like(vs30)
s_d = np.zeros_like(vs30)
s_b[np.logical_and(vs30 >= 360., vs30 < 800.)] = 1.0
s_c[np.logical_and(vs30 >= 180., vs30 < 360.)] = 1.0
s_d[vs30 < 180] = 1.0
return s_b, s_c, s_d
[docs]class CauzziEtAl2014Eurocode8NoSOF(CauzziEtAl2014NoSOF):
"""
Implmements the Cauzzi et al. (2014) GMPE for the case in which
the Eurocode 8 site classification is preferred and style of faulting
is not specified.
"""
def _get_site_amplification_term(self, C, vs30):
"""
Returns the site amplification term on the basis of Eurocode 8
site class
"""
s_b, s_c, s_d = self._get_site_dummy_variables(vs30)
return (C["sB"] * s_b) + (C["sC"] * s_c) + (C["sD"] * s_d)
def _get_site_dummy_variables(self, vs30):
"""
Returns the Eurocode 8 site class dummy variable
"""
s_b = np.zeros_like(vs30)
s_c = np.zeros_like(vs30)
s_d = np.zeros_like(vs30)
s_b[np.logical_and(vs30 >= 360., vs30 < 800.)] = 1.0
s_c[np.logical_and(vs30 >= 180., vs30 < 360.)] = 1.0
s_d[vs30 < 180.] = 1.0
return s_b, s_c, s_d