Source code for openquake.hazardlib.gsim.cauzzi_faccioli_2008

# coding: utf-8
# The Hazard Library
# Copyright (C) 2012-2014, 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:`CauzziFaccioli2008`.
"""
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 CauzziFaccioli2008(GMPE): """ Implements GMPE developed by Carlo Cauzzi and Ezio Faccioli and published as "Broadband (0.05 to 20s) prediction of displacement response spectra based on worldwide digital records" (Journal of Seismology, 2008, volume 12, pages 453-475). This class implements the prediction equations for horizontal peak ground acceleration, peak ground velocity and 5%-damped spectral acceleration (equation 2, page 462, plus faulting style term as given in equation 5, page 465). Coefficients for PGV are not present in the original paper but were developed for the SHARE (http://www.share-eu.org/) project. Hypocentral distances are clipped at 15 km (as for Faccioli's personal communication). 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, #: see end of 'Introduction', page 454. 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. 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`, #: see paragraph 'On functional forms', page 462. DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation type is only total, see paragraph 'On #: functional forms', page 462. DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([ const.StdDev.TOTAL ]) #: Required site parameter is only Vs30 (used to distinguish rock #: and deep soils), see paragraph 'On functional forms', page 463. REQUIRES_SITES_PARAMETERS = set(('vs30', )) #: Required rupture parameters are magnitude and rake, see paragraph 'On #: functional forms', page 463 REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag')) #: Required distance measure is Rhypo, see paragraph 'Distance', page 456. REQUIRES_DISTANCES = set(('rhypo', ))
[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.mag, dists, sites.vs30, rup.rake, imt) stddevs = self._get_stddevs(C, stddev_types, sites.vs30.shape[0]) return mean, stddevs
def _compute_term_1_2(self, C, mag): """ Compute terms 1 and 2 in equation 2 page 462. """ return C['a1'] + C['a2'] * mag def _compute_term_3(self, C, rhypo): """ Compute term 3 in equation 2 page 462. Distances are clipped at 15 km (as per Ezio Faccioli's personal communication.) """ d = rhypo d[d <= 15.0] = 15.0 return C['a3'] * np.log10(d) def _compute_site_term(self, C, vs30): """ Compute site term as a function of vs30: 4th, 5th and 6th terms in equation 2 page 462. """ # for rock values the site term is zero site_term = np.zeros_like(vs30) # hard soil site_term[(vs30 >= 360) & (vs30 < 800)] = C['aB'] # medium soil site_term[(vs30 >= 180) & (vs30 < 360)] = C['aC'] # soft soil site_term[vs30 < 180] = C['aD'] return site_term def _compute_faulting_style_term(self, C, rake): """ Compute faulting style term as a function of rake angle value as given in equation 5 page 465. """ if rake > -120.0 and rake <= -60.0: return C['aN'] elif rake > 30.0 and rake <= 150.0: return C['aR'] else: return C['aS'] def _compute_mean(self, C, mag, dists, vs30, rake, imt): """ Compute mean value for PGV, PGA and Displacement responce spectrum, as given in equation 2, page 462 with the addition of the faulting style term as given in equation 5, page 465. Converts also displacement responce spectrum values to SA. """ mean = (self._compute_term_1_2(C, mag) + self._compute_term_3(C, dists.rhypo) + self._compute_site_term(C, vs30) + self._compute_faulting_style_term(C, rake)) # 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) / 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): """ Return total standard deviation. """ stddevs = [] for stddev_type in stddev_types: assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES stddevs.append(np.log(10 ** C['sigma']) + np.zeros(num_sites)) return stddevs #: Coefficient table constructed from the electronic suplements of the #: original paper. COEFFS = CoeffsTable(sa_damping=5, table="""\ IMT a1 a2 aN aR aS a3 aB aC aD sigma pgv -2.0500000 0.7710000 -0.0300000 0.0100000 0.0100000 -1.4190000 0.1600000 0.3600000 0.4800000 0.3090000 pga -1.2960000 0.5560000 -0.0600000 0.0940000 -0.0130000 -1.5820000 0.2200000 0.3040000 0.3320000 0.3410000 0.05 -2.8853436 0.5241770 -0.1002050 0.1323607 -0.0104223 -1.7131617 0.1590351 0.1913741 0.1662669 0.3569631 0.10 -1.9083649 0.4879421 -0.0893446 0.1273364 -0.0141940 -1.7141846 0.2191124 0.2180647 0.1599583 0.3698820 0.15 -1.9913830 0.5218353 -0.0733947 0.1189461 -0.0178601 -1.6011819 0.2516196 0.3149463 0.2929666 0.3701501 0.20 -2.1855097 0.5575823 -0.0410869 0.1014822 -0.0242622 -1.5157781 0.2795653 0.4209394 0.3950845 0.3735782 0.25 -2.2986747 0.5918757 -0.0505207 0.0853928 -0.0144371 -1.4772492 0.2468365 0.4352964 0.4414190 0.3658115 0.30 -2.3197219 0.6141047 -0.0423759 0.0653264 -0.0096095 -1.4608963 0.2027381 0.4325227 0.4545156 0.3574604 0.35 -2.3532043 0.6301540 -0.0290204 0.0569969 -0.0117476 -1.4526222 0.1948161 0.4572770 0.5023281 0.3576558 0.40 -2.4625603 0.6520124 -0.0248118 0.0514677 -0.0113052 -1.4182980 0.1736606 0.4457811 0.5335752 0.3571774 0.45 -2.4967480 0.6641638 -0.0098857 0.0366742 -0.0112005 -1.4072543 0.1769518 0.4470774 0.5839604 0.3542876 0.50 -2.5409604 0.6736385 -0.0050996 0.0283795 -0.0095620 -1.3894703 0.1855959 0.4482634 0.6360733 0.3585923 0.55 -2.5528057 0.6813095 -0.0013096 0.0256173 -0.0098734 -1.3833845 0.1834712 0.4509198 0.6792498 0.3587491 0.60 -2.6105531 0.6942826 -0.0009457 0.0166886 -0.0062698 -1.3683149 0.1785156 0.4451175 0.6919865 0.3566331 0.65 -2.5991259 0.7000182 0.0057530 0.0075781 -0.0050956 -1.3658287 0.1614781 0.4327439 0.6945308 0.3550096 0.70 -2.6256918 0.7102002 0.0021694 0.0050372 -0.0026038 -1.3609069 0.1479847 0.4247098 0.6955686 0.3550060 0.75 -2.6965075 0.7273575 0.0028068 0.0020510 -0.0016181 -1.3612589 0.1450193 0.4164749 0.7043074 0.3526839 0.80 -2.7389002 0.7403566 0.0036660 -0.0040497 0.0005981 -1.3610415 0.1380784 0.4042236 0.7036039 0.3496514 0.85 -2.7914083 0.7553379 0.0032023 -0.0059857 0.0016152 -1.3691674 0.1406749 0.4031042 0.7086573 0.3504153 0.90 -2.7973391 0.7611568 0.0107582 -0.0055180 -0.0015391 -1.3755505 0.1451434 0.4082058 0.7090638 0.3545320 0.95 -2.8305291 0.7686452 0.0163434 -0.0048616 -0.0039647 -1.3722514 0.1501412 0.4134206 0.7030495 0.3545101 1.00 -2.8634011 0.7772102 0.0201847 -0.0026251 -0.0063816 -1.3692034 0.1464775 0.4066130 0.6863604 0.3558715 1.05 -2.8680321 0.7801400 0.0181339 -0.0022563 -0.0057100 -1.3655567 0.1448087 0.4020379 0.6707605 0.3557457 1.10 -2.8936464 0.7879813 0.0170920 -0.0027664 -0.0050829 -1.3658939 0.1389319 0.3901474 0.6569073 0.3558140 1.15 -2.9355453 0.7992595 0.0171742 -0.0037400 -0.0046909 -1.3693257 0.1331251 0.3811657 0.6394404 0.3543397 1.20 -2.9532117 0.8044803 0.0219944 -0.0055788 -0.0058288 -1.3657305 0.1279489 0.3723968 0.6233881 0.3533761 1.25 -2.9782632 0.8090258 0.0250012 -0.0077949 -0.0061059 -1.3591759 0.1263850 0.3690539 0.6091518 0.3537186 1.30 -3.0054272 0.8146208 0.0275714 -0.0091296 -0.0065852 -1.3550484 0.1235212 0.3666377 0.5942269 0.3533137 1.35 -3.0314767 0.8208146 0.0284279 -0.0104723 -0.0063730 -1.3565895 0.1254993 0.3712946 0.5845589 0.3528877 1.40 -3.0466187 0.8270614 0.0267230 -0.0095818 -0.0060518 -1.3607541 0.1224343 0.3655060 0.5695337 0.3525659 1.45 -3.0654260 0.8330859 0.0250260 -0.0091609 -0.0055125 -1.3639165 0.1208328 0.3614019 0.5593142 0.3517607 1.50 -3.0896821 0.8399120 0.0221389 -0.0092808 -0.0042695 -1.3666268 0.1165296 0.3568769 0.5511064 0.3496758 1.55 -3.1171695 0.8476929 0.0174047 -0.0069108 -0.0033789 -1.3700564 0.1122110 0.3507933 0.5427573 0.3472015 1.60 -3.1370747 0.8536100 0.0140424 -0.0050005 -0.0028569 -1.3707941 0.1080054 0.3419899 0.5315377 0.3449319 1.65 -3.1433377 0.8570622 0.0092720 -0.0042635 -0.0013202 -1.3699352 0.1006163 0.3323793 0.5154721 0.3425114 1.70 -3.1579402 0.8610034 0.0013194 -0.0032280 0.0012934 -1.3689420 0.0985499 0.3287989 0.5044447 0.3398077 1.75 -3.1654876 0.8635322 -0.0079932 -0.0012780 0.0039846 -1.3692309 0.0977796 0.3266681 0.4968893 0.3376558 1.80 -3.1627827 0.8650292 -0.0143883 0.0012671 0.0052926 -1.3701685 0.0950735 0.3202899 0.4885798 0.3359642 1.85 -3.1615383 0.8667376 -0.0192120 0.0026373 0.0064626 -1.3707310 0.0931597 0.3135946 0.4817112 0.3342168 1.90 -3.1522848 0.8676873 -0.0239616 0.0049096 0.0071912 -1.3712825 0.0870145 0.3043254 0.4719422 0.3329950 1.95 -3.1431538 0.8680758 -0.0296569 0.0076970 0.0079890 -1.3715113 0.0829618 0.2976415 0.4651566 0.3310917 2.00 -3.1421699 0.8685196 -0.0344938 0.0095700 0.0088897 -1.3693361 0.0834894 0.2950648 0.4603763 0.3298747 2.05 -3.1474772 0.8700464 -0.0393413 0.0120142 0.0095059 -1.3678657 0.0844281 0.2941582 0.4593924 0.3293833 2.10 -3.1614270 0.8732865 -0.0447820 0.0151246 0.0100114 -1.3671317 0.0841764 0.2931830 0.4587144 0.3285693 2.15 -3.1760473 0.8759402 -0.0493498 0.0172018 0.0106142 -1.3650601 0.0852595 0.2939214 0.4593409 0.3278627 2.20 -3.1872939 0.8778648 -0.0545726 0.0196852 0.0112416 -1.3620672 0.0857041 0.2932367 0.4571966 0.3263398 2.25 -3.1929032 0.8782645 -0.0599400 0.0229501 0.0115343 -1.3562898 0.0843744 0.2908264 0.4528229 0.3244696 2.30 -3.1964880 0.8785770 -0.0639389 0.0266334 0.0111443 -1.3495460 0.0795512 0.2845144 0.4457230 0.3223445 2.35 -3.2061680 0.8796669 -0.0656158 0.0294290 0.0103948 -1.3421863 0.0763004 0.2788990 0.4404207 0.3206195 2.40 -3.2124688 0.8800817 -0.0683920 0.0323025 0.0100710 -1.3351181 0.0754372 0.2733777 0.4367805 0.3189619 2.45 -3.2173552 0.8802805 -0.0721574 0.0364129 0.0095688 -1.3273998 0.0721815 0.2667552 0.4308779 0.3177777 2.50 -3.2208583 0.8799805 -0.0756910 0.0404754 0.0089382 -1.3195408 0.0695631 0.2620014 0.4254937 0.3163032 2.55 -3.2244744 0.8798919 -0.0783250 0.0432722 0.0084324 -1.3134787 0.0692867 0.2610122 0.4237224 0.3143530 2.60 -3.2355390 0.8810115 -0.0801680 0.0454326 0.0078271 -1.3074378 0.0701497 0.2596374 0.4210976 0.3123591 2.65 -3.2599554 0.8841480 -0.0813756 0.0477987 0.0069265 -1.3014910 0.0719688 0.2594378 0.4205230 0.3105163 2.70 -3.2834526 0.8875307 -0.0809548 0.0505024 0.0054163 -1.2962006 0.0727993 0.2577696 0.4195371 0.3091150 2.75 -3.3028676 0.8902376 -0.0802845 0.0533437 0.0037658 -1.2914620 0.0739445 0.2565391 0.4206958 0.3081833 2.80 -3.3164602 0.8923488 -0.0802537 0.0557539 0.0024698 -1.2879074 0.0743410 0.2546159 0.4215031 0.3071375 2.85 -3.3328281 0.8947180 -0.0796644 0.0580173 0.0010041 -1.2839725 0.0757831 0.2532998 0.4205388 0.3058747 2.90 -3.3508249 0.8973864 -0.0791587 0.0602144 -0.0003880 -1.2784672 0.0744210 0.2492444 0.4155354 0.3047832 2.95 -3.3692426 0.8999885 -0.0781803 0.0620852 -0.0017386 -1.2727125 0.0735201 0.2458899 0.4118983 0.3039768 3.00 -3.3883104 0.9025955 -0.0780050 0.0639634 -0.0027770 -1.2667687 0.0731364 0.2427131 0.4066463 0.3032581 3.05 -3.4089144 0.9050712 -0.0777145 0.0652581 -0.0035732 -1.2604383 0.0736191 0.2410029 0.4021932 0.3026315 3.10 -3.4302607 0.9080662 -0.0769700 0.0655633 -0.0040268 -1.2557977 0.0742839 0.2393353 0.3988910 0.3020134 3.15 -3.4449030 0.9101579 -0.0762476 0.0656209 -0.0042581 -1.2520585 0.0755457 0.2377807 0.3968486 0.3013446 3.20 -3.4566489 0.9116875 -0.0754699 0.0652424 -0.0043002 -1.2482556 0.0774894 0.2365001 0.3945458 0.3004223 3.25 -3.4709224 0.9137012 -0.0750555 0.0646868 -0.0041063 -1.2445079 0.0789917 0.2354185 0.3926102 0.2991849 3.30 -3.4861508 0.9163004 -0.0747234 0.0645185 -0.0040099 -1.2419588 0.0798637 0.2339357 0.3916166 0.2978846 3.35 -3.5022077 0.9190528 -0.0728415 0.0636728 -0.0040702 -1.2394832 0.0810714 0.2330698 0.3913265 0.2964171 3.40 -3.5203978 0.9217943 -0.0713307 0.0624610 -0.0038150 -1.2364777 0.0832514 0.2332679 0.3918926 0.2952740 3.45 -3.5408118 0.9246496 -0.0705947 0.0611375 -0.0032988 -1.2327771 0.0853155 0.2337748 0.3915468 0.2941983 3.50 -3.5601771 0.9273972 -0.0702652 0.0597769 -0.0026400 -1.2292914 0.0870118 0.2338685 0.3903120 0.2931537 3.55 -3.5854744 0.9307797 -0.0701598 0.0587242 -0.0020068 -1.2249578 0.0889839 0.2347028 0.3893576 0.2924559 3.60 -3.6138749 0.9347379 -0.0696739 0.0574896 -0.0013891 -1.2206922 0.0907968 0.2354381 0.3877713 0.2923746 3.65 -3.6416871 0.9388613 -0.0692068 0.0565333 -0.0009180 -1.2172276 0.0919148 0.2355807 0.3855391 0.2924609 3.70 -3.6667806 0.9426348 -0.0691106 0.0560806 -0.0005845 -1.2141418 0.0924525 0.2361611 0.3830481 0.2925229 3.75 -3.6928280 0.9462948 -0.0696536 0.0557950 -0.0001683 -1.2107893 0.0938360 0.2378644 0.3816221 0.2925011 3.80 -3.7192534 0.9500416 -0.0701051 0.0554917 0.0002090 -1.2073914 0.0949498 0.2392272 0.3789399 0.2923401 3.85 -3.7461033 0.9539773 -0.0700016 0.0545840 0.0006554 -1.2041114 0.0956039 0.2397455 0.3759065 0.2919152 3.90 -3.7715185 0.9577344 -0.0694757 0.0537659 0.0009270 -1.2004853 0.0951864 0.2388567 0.3723133 0.2916133 3.95 -3.7952464 0.9613004 -0.0691349 0.0532504 0.0011510 -1.1969673 0.0942025 0.2372400 0.3688114 0.2914914 4.00 -3.8152625 0.9646448 -0.0689546 0.0527977 0.0013845 -1.1946064 0.0928633 0.2348112 0.3656192 0.2911708 4.05 -3.8340273 0.9678713 -0.0685971 0.0522826 0.0015856 -1.1923050 0.0911828 0.2316196 0.3621850 0.2908003 4.10 -3.8534471 0.9710945 -0.0682666 0.0512167 0.0020157 -1.1895800 0.0897472 0.2282775 0.3595744 0.2902313 4.15 -3.8717479 0.9740822 -0.0672992 0.0497144 0.0024451 -1.1867849 0.0882628 0.2250725 0.3574817 0.2897667 4.20 -3.8885736 0.9768598 -0.0662365 0.0482856 0.0028051 -1.1838169 0.0862260 0.2215819 0.3542480 0.2894828 4.25 -3.9059444 0.9798431 -0.0649702 0.0467729 0.0030837 -1.1807954 0.0830785 0.2173570 0.3501377 0.2890718 4.30 -3.9254943 0.9828558 -0.0633793 0.0449200 0.0033809 -1.1773877 0.0811116 0.2146505 0.3474807 0.2884671 4.35 -3.9449954 0.9856556 -0.0619490 0.0428895 0.0037976 -1.1740278 0.0803051 0.2133299 0.3459795 0.2880207 4.40 -3.9627506 0.9879447 -0.0605603 0.0408345 0.0042235 -1.1700078 0.0796258 0.2124220 0.3448773 0.2876482 4.45 -3.9817401 0.9904571 -0.0593444 0.0391547 0.0045623 -1.1659322 0.0789487 0.2114441 0.3438778 0.2874406 4.50 -4.0002776 0.9929580 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