class ChaoEtAl2020SInter(GMPE):
"""
Chao et al. (2020) for Subduction Interface.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGD, PGV, SA}
DEFINED_FOR_REFERENCE_VELOCITY = 1180
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
REQUIRES_DISTANCES = {'rrup'}
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'ztor'}
REQUIRES_SITES_PARAMETERS = {'vs30', 'vs30measured', 'z1pt0'}
REQUIRES_ATTRIBUTES = {'manila', 'aftershocks', 'geology'}
def __init__(self, manila=False, aftershocks=False, geology=True,
**kwargs):
"""
Aditional parameters.
"""
super().__init__(manila=manila, aftershocks=aftershocks,
geology=geology, **kwargs)
# Manila or Ryukyu subduction zone
self.manila = manila
# aftershocks or mainshocks
self.aftershocks = aftershocks
# geology True for KS17, False for seismic (receiver function)
# only used for inferred vs30, otherwise use vs30measured
self.geology = geology
def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
trt = self.DEFINED_FOR_TECTONIC_REGION_TYPE
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
s = CONSTANTS
med = mean[m]
med += _ftype(trt, self.SUFFIX, C, ctx)
med += (ctx.ztor - self.CONST_FAULT['href']) * C[
'c14' + self.SUFFIX]
med += (ctx.mag - s['mag_ref']) * C['c8' + self.SBCR]
med += (5 - ctx.mag) * np.heaviside(5 - ctx.mag, 0.5) \
* C['c11' + self.SBCR]
med += _fh(trt, self.SBCR, self.MC, self.CONST_FAULT['C4'],
C, ctx.mag, ctx.rrup)
med += (ctx.rrup - s['rrup_ref']) * C['c21' + self.SBCR]
med += _ffault(trt, self.MC, self.SUFFIX, C, ctx.mag)
med += C['c6'] * self.aftershocks + C['c7'] * self.manila
med += _fvs30(self.geology, C, ctx)
sa1180 = np.exp(med + math.log(1180/s['vs30_ref']) * C['c24'])
med += _fc(C, imt, ctx.vs30, sa1180)
med += np.log(ctx.vs30 / s['vs30_ref']) * C['c24']
med += _fz1pt0(C, ctx)
sig[m], tau[m], phi[m] = get_stddevs(self.SBCR, C, ctx.mag)
COEFFS = CoeffsTable(sa_damping=5, table="""\
imt c1 c2 c3 c4_if c4_is c6 c7 c8_cr c8_sb c10 c11_cr c11_sb c13 c14_cr c14_if c14_is c17_cr c17_sb c19_cr c19_sb c21_cr c21_sb c23 c24 c25 c26 c27 c28 c29_if c29_is tau1_cr tau2_cr tau1_sb tau2_sb phiss1_cr phiss2_cr phiss1_sb phiss2_sb phis2s
pga -0.5192892547128840 -0.6150055029113330 -0.6487900726643910 -0.5859618870941580 0.2995078226527580 -0.1252895878217900 0.1860213693406720 0.4128529204313240 0.6654099729223670 -0.1376176044286790 -0.0000003768045793 -0.0000002632651801 -0.0000003479033210 0.0325013808122898 0.0188003326071965 0.0066214814780273 -1.3033352051553600 -1.4222150700864700 0.3874353293578060 0.1816390684494260 -0.0034295741595448 -0.0034489780547407 -2.5525572055834000 -0.4820755783830470 0.0636111092153052 -0.5680621936097360 -0.6441908224323110 -0.6148407238174470 -0.4944663117848010 -0.4948250053327020 0.3674988948492440 0.3156766103555770 0.2747114934261350 0.5404436414423900 0.5284243730959070 0.4400249261948010 0.4358918335042310 0.4982604989025690 0.3435860891378130
0.01 -0.5185435292277630 -0.6139978370809050 -0.6485291075803880 -0.5838899830711630 0.3025167286045810 -0.1244749736423930 0.1818440946548220 0.4133627969553290 0.6662082185566420 -0.1377874122648280 -0.0000016455914614 -0.0000010168484829 -0.0000015396189431 0.0325478379384533 0.0187424764459864 0.0065978989650052 -1.3050707375477800 -1.4244518028964800 0.3865358127626830 0.1799727376957520 -0.0034138067537784 -0.0034249196892139 -2.5491215932210800 -0.4817847143782920 0.0637979244436324 -0.5671019863928200 -0.6430624549208040 -0.6134855454872920 -0.4962061562087430 -0.5019638690208290 0.3672959719907850 0.3154146574183840 0.2733100640145130 0.5413688232186000 0.5279530156395120 0.4402345932395540 0.4366852410606870 0.4979773327789170 0.3437466383316600
0.02 -0.4925935193382860 -0.5849494939894080 -0.6149768931486030 -0.5994558769715950 0.2896423927820520 -0.1255022048822760 0.1913815871815020 0.3989282252665750 0.6316076153041100 -0.1329759746961010 -0.0010277552092071 -0.0000007415198554 -0.0000009243529219 0.0330191056515263 0.0184348278192339 0.0069331416349393 -1.3381199569179700 -1.4144452691294700 0.3918303510961290 0.1909212976216070 -0.0031761225955272 -0.0036500842576487 -2.5020049297189400 -0.4722757215196650 0.0649888427251637 -0.5300330753401030 -0.6092543141804070 -0.5783932279622350 -0.4567832202723850 -0.4843335992997120 0.3672096025203770 0.3193604175283950 0.2727371846461310 0.5590662841638730 0.5212490565944880 0.4457229793375830 0.4284446929672800 0.4997055429236690 0.3492753254041860
0.03 -0.4773436137435830 -0.5646500549184690 -0.5823569579995780 -0.6229871080555090 0.2895352598530250 -0.1281741601414120 0.1959394907475940 0.3700049726661150 0.5722615232020440 -0.1233348788754380 -0.0013400986538279 -0.0000008780800013 -0.0000010741358947 0.0343101384872960 0.0183116904998815 0.0075119701817267 -1.3673880371344400 -1.4049670408467200 0.4087284138519370 0.2120199290459480 -0.0031597614295051 -0.0039690305196895 -2.3679999172581600 -0.4533571902303470 0.0688570330004100 -0.4674371210038970 -0.5547847971008720 -0.5162080030607480 -0.3909967282502120 -0.4568941706767360 0.3659401986651120 0.3269487169641220 0.2754713073378610 0.5782229669599770 0.5138814813317350 0.4562412368820710 0.4231963576524820 0.5062146219159800 0.3642070292163550
0.05 -0.4384226473479580 -0.5082028496350560 -0.4996495791530560 -0.5509927916841400 0.4201424505033270 -0.1278113776092280 0.2242032272922090 0.3277716179853340 0.5335838412677030 -0.1092566090939630 -0.0009524028343619 -0.0000009362783788 -0.0000012076824503 0.0374313441023976 0.0179647463512188 0.0086002417698971 -1.4043378692826500 -1.4529353769070100 0.4227955124257500 0.2059482358996180 -0.0037038172429266 -0.0042767503271602 -2.0984569938797400 -0.4174769587709540 0.0796477449779514 -0.3278239226800660 -0.4273786543769590 -0.3669057022159870 -0.3673342531461080 -0.4926026405594960 0.3613130559351250 0.3457148557860690 0.2827051741664680 0.6026422039770350 0.5030028370059200 0.4708951658491060 0.4104373460235670 0.5195083771826150 0.4080959377619060
0.075 -0.3477680472987080 -0.3945396148772630 -0.3644851574401720 -0.3788975825498850 0.6660790354369400 -0.1257199250776420 0.2590114609066670 0.3280509470422620 0.5915580071627310 -0.1093481802115360 -0.0010601014177568 -0.0000014458228879 -0.0000014938956048 0.0400261494009523 0.0180580974419972 0.0092132504242451 -1.4072088973593200 -1.5212012494801500 0.4079055422317920 0.1599483130475640 -0.0046735359569929 -0.0044253262161005 -1.8571475913759100 -0.4031497826702400 0.0849015681692710 -0.2257128580612920 -0.3307477951183650 -0.2557559184395190 -0.4531985082804610 -0.5341761350472270 0.3646238141279680 0.3603139641158800 0.2932224947572630 0.6001445469340250 0.5039997875438060 0.4668928640936500 0.4088583646551290 0.5248133353055360 0.4440557923094290
0.1 -0.2464419641482460 -0.2774153233972800 -0.2419849681859750 -0.2159572988522690 0.8837635057027910 -0.1221833768730910 0.2890209915658740 0.3609773912176570 0.6796403235589960 -0.1203234194869740 -0.0095781938365105 -0.0091311877263691 -0.0000017618182496 0.0406923890414978 0.0187576968592212 0.0091770608487944 -1.3775350561906300 -1.5588146355752500 0.3826772642202150 0.1180456788835990 -0.0054981782655166 -0.0044752635101850 -1.6933015535378400 -0.4106809740578840 0.0822852228887146 -0.1971657286502670 -0.3034342387568920 -0.2273780092606650 -0.5595380222575010 -0.5995654008335480 0.3773149612260230 0.3622412109534710 0.3058662966967730 0.5804476608541280 0.5174927775766600 0.4518314029734340 0.4208300424568200 0.5207449309209680 0.4560381766578650
0.15 -0.0771751272296130 -0.1082252757155910 -0.0939554515669245 -0.0188559515947778 1.1045574548438600 -0.1151312333331240 0.3489251001067520 0.4435666368994170 0.8206717947215570 -0.1478533042267330 -0.0797000195466235 -0.1061400711142910 -0.0116149978331732 0.0385365803750634 0.0208403778461626 0.0084255538167330 -1.3047454734934800 -1.5546509544985100 0.3387081858027680 0.0762391834452875 -0.0060699037646678 -0.0043559591434871 -1.4739793205860400 -0.4462238803701860 0.0708425313555023 -0.2504635484625670 -0.3579852182163120 -0.2973613635520170 -0.7066557777245760 -0.6646730464270010 0.4205159985547740 0.3393429192383280 0.3335166881059750 0.5289137551348660 0.5530955106299720 0.4276458197094800 0.4552933469697380 0.5112791219012840 0.4393051343517960
0.2 0.0405594808831559 -0.0077282823725784 -0.0329357162076816 0.0977204826995843 1.1425790790134700 -0.1057191168540270 0.3722539227241170 0.5259387014440060 0.8944652896530820 -0.1753118327644590 -0.1628405724059960 -0.1905540130924890 -0.0703516281536629 0.0344218267917848 0.0220145357833909 0.0074084568455730 -1.2525154396822100 -1.5299381829848600 0.2988014581902580 0.0598123873775724 -0.0057279870130134 -0.0038467366062087 -1.3537154633193600 -0.4806650787981650 0.0627269858251427 -0.3514329644238130 -0.4494836594136780 -0.4211846625506190 -0.7761270389945640 -0.6765718066660800 0.4710484094826400 0.3078985636442060 0.3678152527072530 0.4963277349205770 0.5816461579655670 0.4175140424711400 0.4781484644913840 0.5035988500569350 0.4117968194252760
0.25 0.1161360079386870 0.0455512686241350 -0.0218646332100325 0.1828656137015420 1.1166678356454500 -0.0959115648679502 0.3639273275607390 0.5926458211482060 0.9514471984717970 -0.1975481854813300 -0.2376907309394700 -0.2386263420394340 -0.1392336794544470 0.0301984485118963 0.0220498416898711 0.0063660608238311 -1.2210171934017700 -1.5075909330134600 0.2681747226996620 0.0472484189561765 -0.0050865192380324 -0.0032636166820230 -1.3112990269528600 -0.5135409274151990 0.0616544496255378 -0.4563389214185420 -0.5390065111345010 -0.5398009092490380 -0.8288006277909410 -0.6846682992304260 0.5148599316146770 0.2855216261744740 0.3995944962541640 0.4770587925609880 0.5994129051899660 0.4166683191773280 0.4900244567390270 0.4964417374025240 0.3893046381000030
0.3 0.1659191261450740 0.0725370613365805 -0.0359674153322261 0.2295701498524820 1.0576588366467200 -0.0882656506919790 0.3427750060884890 0.6483788027762600 0.9819984405493800 -0.2161260130183380 -0.2965674398979590 -0.2665884284153660 -0.2169703936280970 0.0263787728828427 0.0216264161548529 0.0053861646702039 -1.2047472906024600 -1.4854043484828200 0.2441324298126210 0.0419492390586564 -0.0043698926044844 -0.0027135380939124 -1.3252507728285300 -0.5429162086543740 0.0645387790445636 -0.5550263121051320 -0.6210404997811030 -0.6445535318562390 -0.8538221721074140 -0.6735161372595090 0.5463002600989580 0.2736557189233880 0.4272231091987260 0.4656311763164020 0.6091651025639550 0.4221564137529650 0.4957367311495720 0.4906316632512320 0.3720915588780540
0.4 0.2142056666127370 0.0871536549688902 -0.0785690467168578 0.2764151479005750 0.9207449431454760 -0.0817387187650157 0.2621885450896460 0.7417540614842620 1.0112737345534200 -0.2472511509254110 -0.3436334917221890 -0.2565078736132940 -0.3586252797911450 0.0205765954005230 0.0202875364431140 0.0038382219060837 -1.1921038099281000 -1.4558697162866900 0.2098186797110940 0.0408684583105697 -0.0031642937062858 -0.0017940043857435 -1.4077075423307700 -0.5972162270181300 0.0741639723226930 -0.7281908574894840 -0.7628684799249960 -0.8199077697170760 -0.8746936616440970 -0.6381631348609450 0.5808849727025450 0.2713662162845130 0.4653458134731120 0.4672831153779370 0.6113503193815050 0.4361192706099510 0.4955634501806600 0.4867080815561310 0.3527750902276900
0.5 0.2236254270212470 0.0737703256835049 -0.1248626176144320 0.2932144086137190 0.8027962857692040 -0.0840244330603874 0.1721136232246120 0.8151053466925040 1.0356710065186700 -0.2717014152455810 -0.3293921568751970 -0.1956967186201360 -0.4758435322483390 0.0165224891710283 0.0187963908607794 0.0026597132484042 -1.1860778618169400 -1.4381584618490300 0.1912179053378480 0.0410520296595116 -0.0023448358088493 -0.0011582034067666 -1.5070859378876100 -0.6493752154999540 0.0836822599658712 -0.8748820619897430 -0.8876408712201270 -0.9615402715827100 -0.8939061858589470 -0.6160880182479380 0.5949464334180670 0.2871764340948960 0.4832505926756100 0.4803914686955640 0.6007190809790290 0.4486042327739210 0.4926763166550150 0.4858212403211350 0.3446261711175850
0.75 0.1528039303532890 -0.0248167903571809 -0.2511392119124840 0.1388909993170780 0.4519964034477110 -0.1046230174209790 0.0270194376114289 0.9406307668392510 1.0243375273572300 -0.3135419875863270 -0.2250006281710770 -0.0911523105914097 -0.6780831702704660 0.0110013901513618 0.0160522319622777 0.0012402638358105 -1.1698623108011400 -1.3625787842858000 0.1791792655901220 0.0659622332730993 -0.0013043059118461 -0.0005882173264089 -1.5844202517297500 -0.7429284095282450 0.1035767308819100 -1.1534790724423800 -1.1395651591115200 -1.2323996821315000 -0.8389026019711570 -0.5147492098368240 0.5850050231740750 0.3462884754383560 0.4785627709562630 0.5185233324163180 0.5620391824549910 0.4718500465503010 0.4894503194326150 0.4871171137374260 0.3419011444574020
1.0 0.0183554539383078 -0.1591378376284470 -0.3854397008591480 -0.0815004332093187 0.1288852589717840 -0.1246837038142780 -0.0535877846749373 1.0248278846159400 0.9984729722811390 -0.3393133894939400 -0.1276588419069730 -0.0409136585181734 -0.7992367966752370 0.0086318100105947 0.0146222483242542 0.0009003395366128 -1.1508125147275900 -1.3000691876438900 0.1832396128840250 0.0943261823256111 -0.0008735093977044 -0.0003997330115688 -1.4244083078078700 -0.7989976385952170 0.1185000096002400 -1.3487217771603600 -1.3270174440744400 -1.4337289163009600 -0.7382346855789400 -0.4287560627663270 0.5652851427812200 0.3922029871907690 0.4481274157753080 0.5644306606646860 0.5259679896173710 0.4845488048918390 0.4855760478703810 0.4913162411271670 0.3475742684982780
1.5 -0.2926406493971360 -0.4394400484356270 -0.6634745672889770 -0.5698164868777540 -0.4777414376471740 -0.1367512471546550 -0.1185422683336340 1.1535846852560400 0.9228592531769220 -0.3551593410006160 -0.0316373719436222 -0.0058305420526171 -0.9286080973093520 0.0062127909966995 0.0114205875168941 0.0006726268670384 -1.1172685240682800 -1.1760450613418900 0.1958900128843000 0.1499938137415910 -0.0005279011472397 -0.0005031399510306 -0.8544827391292060 -0.8438703395779730 0.1413533804677000 -1.5948082564095300 -1.5616885373157400 -1.6940289391677400 -0.5338216528196720 -0.2734691164270120 0.5400623156625950 0.4389989898505710 0.3998380606154830 0.6147869472762440 0.4771405443244140 0.4911661512017220 0.4858319625974600 0.4862020347407820 0.3584781550167080
2.0 -0.6164896637512180 -0.7252715132235520 -0.9386642110776790 -1.0016397597173700 -0.9827809560644520 -0.1204851699381740 -0.1574596881853990 1.2561590239982100 0.9157149198331690 -0.3487315863272320 -0.0067392342056503 -0.0008274455605290 -0.8998831651883260 0.0045185743588915 0.0076239354167913 0.0004849758370595 -1.0938451612547300 -1.0683876519211600 0.2093417950110930 0.1991110124549130 -0.0003935827881709 -0.0008887392881376 -0.4424325390151640 -0.8536333300862120 0.1558153259573340 -1.7120254817165000 -1.6704563706071200 -1.8185653745450900 -0.4237829724483130 -0.2166062958480880 0.5306044642337280 0.4525458066815850 0.3651681953582200 0.6249992145898750 0.4491015982391830 0.4851846396569770 0.4819819680840680 0.4774435589161110 0.3657798632961100
3.0 -1.2120217913721900 -1.2593110926431200 -1.4636739356095600 -1.6980520879594500 -1.7669432223057700 -0.0595654650319802 -0.2204723665783100 1.3973296744797800 0.9588403924773120 -0.3233624830738870 -0.0000028831797237 -0.0000043740923315 -0.7774992929692280 0.0001846487026116 0.0015942173971129 -0.0000443776256955 -1.0585068691241300 -0.9286291899300890 0.2337544609389410 0.2596941009305470 -0.0003265684501350 -0.0016673660346856 -0.0238666422441761 -0.8486298188632920 0.1646442443399270 -1.7746560709922100 -1.7136221908604800 -1.8823684494043700 -0.3206735394784300 -0.2094181559654280 0.5341895930662030 0.4630363429223910 0.3632239046532420 0.5759362561116940 0.4215979819838170 0.4631745228225680 0.4732577539251810 0.4497578024830470 0.3748448621655020
4.0 -1.7187620785302500 -1.7255326287093000 -1.9157987949568300 -2.2378527680411400 -2.3717405638272600 0.0060780094038531 -0.2907358910284120 1.4863934712127500 1.0614239334825600 -0.3008016678137440 -0.0000002303764802 -0.0000003167873542 -0.5992793127354700 -0.0045086409598014 -0.0033339971710007 -0.0004426514054550 -1.0347965137315500 -0.8267625726198150 0.2561912331555940 0.2946206159118700 -0.0002970204994493 -0.0024918478847597 0.0000000000000000 -0.8369401809898650 0.1609560550301920 -1.7432239926968500 -1.6657097551617700 -1.8532526872794200 -0.3155245227823960 -0.2880704899694910 0.5512683175278550 0.4723731595661930 0.3842160013347000 0.5005221059354860 0.4088763842852300 0.4389155701811710 0.4595536649184570 0.4197110255834490 0.3802459556632600
5.0 -2.2524124481564500 -2.2233337887420500 -2.3988731729506100 -2.7681880158076700 -2.9912308138027000 0.1087794828940540 -0.2475264997327470 1.5711476167331400 1.0248966641608600 -0.2757023074987770 -0.0000002893187016 -0.0000007071111743 -0.6712278770777070 -0.0080289129978441 -0.0055089260712685 0.0002598589919845 -0.9844367319831440 -0.7634431186144020 0.2732908377032170 0.3203152022108220 -0.0006897102389096 -0.0030925027294924 0.0000000000000000 -0.8223177494406110 0.1455355246584370 -1.6392650516693500 -1.5448698990426400 -1.7280816734851900 -0.1970906573510090 -0.2362019597302050 0.5684528701196870 0.4816961813462040 0.4683567199764780 0.4119013474002300 0.4034142608449920 0.4200274542874700 0.4420885624015020 0.3737143966344340 0.3884066340183610
pgv 2.9029349822540100 2.7442184267612700 2.5956072627404700 2.7208097262709800 3.2025577336977900 -0.1446177480065630 -0.0413092466691142 0.8212932944431650 0.8048031763759270 -0.2099764391081720 -0.0000106980728248 -0.0000492798570503 -0.2820776116949390 0.0155391426948740 0.0171590486230531 0.0030037011458330 -1.2265529440479100 -1.3749132391246600 0.3076583015302820 0.2104730674561660 -0.0009692157684588 -0.0006985849374855 -6.1179459855387300 -0.6707577779339960 0.0957650492780946 0.3935242034563910 0.3928190325309850 0.3150238242701770 -0.3632617170998910 -0.2432876895838630 0.4386543757769160 0.3740824694470210 0.3305136472559800 0.5673397303206320 0.5590865385354610 0.4351807257924570 0.4801642015831750 0.4853170221825470 0.2740663767048480
pgd 2.4541041890538500 2.3782401415145500 2.2914153189502800 2.0838396593163400 1.9313699400126300 -0.2352916881091410 0.0713994939700537 1.5616444489691000 1.4936921369303000 -0.1676096441841540 -0.0000019923442846 -0.0000232740338163 -0.2069439338171460 -0.0032395363349413 0.0109930765184774 0.0052177204872172 -1.0191698911307200 -1.1559670502824900 0.2068132897445940 0.1789279177790470 -0.0018437138641425 -0.0013634189684089 0.0000000000000000 -0.7422544318623790 0.1490020084340320 -0.4228777481185350 -0.3833592619351370 -0.4612451842659720 -0.3050704862339770 -0.2043152093014790 0.6449844035380140 0.4977962177812710 0.5366022406101780 0.7130676587043830 0.7016130925807040 0.4750313723101500 0.5971604738380890 0.5707298418086840 0.3229783037503560
""")
CONST_FAULT = {'C4': 0.3, 'href': 0}
# subduction or crustal
SBCR = "_sb"
SUFFIX = "_if"
MC = 7.1
class BozorgniaCampbell2016VH(GMPE):
"""
Implements the GMPE by Bozorgnia & Campbell (2016) vertical-to-horizontal
ratio for ground motions from the PEER NGA-West2 Project
This V/H model is combined from VGMPE by Bozorgnia and Campbell (2016) as
the vertical model, and HGMPE by Campbell and Bozorgnia (2014) as the
horizontal model.
**Reference:**
Bozorgnia, Y. & Campbell, K. (2016). Ground Motion Model for the
Vertical-to-Horizontal (V/H) Ratios of PGA, PGV, and Response Spectra
*Earthquake Spectra*, 32(2), 951-978.
Implements the global model that uses datasets from California, Taiwan,
the Middle East, and other similar active tectonic regions to represent
a typical or average Q region.
Applies the average attenuation case (Dc20=0)
"""
VGMPE = bozorgnia_campbell_2016.BozorgniaCampbell2016()
HGMPE = campbell_bozorgnia_2014.CampbellBozorgnia2014()
#: 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 velocity and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is the
#: :attr:`~openquake.hazardlib.const.IMC.VERTICAL_TO_HORIZONTAL_RATIO`
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = (
const.IMC.VERTICAL_TO_HORIZONTAL_RATIO)
#: Supported standard deviation types are inter-event, intra-event
#: and total; see the section for "Aleatory Variability Model".
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
}
#: Required site parameters are taken from the V and H models
REQUIRES_SITES_PARAMETERS = (VGMPE.REQUIRES_SITES_PARAMETERS
| HGMPE.REQUIRES_SITES_PARAMETERS)
#: Required rupture parameters are taken from the V and H models
REQUIRES_RUPTURE_PARAMETERS = (VGMPE.REQUIRES_RUPTURE_PARAMETERS
| HGMPE.REQUIRES_RUPTURE_PARAMETERS)
#: Required distance measures are taken from the V and H models
REQUIRES_DISTANCES = (VGMPE.REQUIRES_DISTANCES | HGMPE.REQUIRES_DISTANCES)
def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
mean_, sig_, tau_, phi_ = contexts.get_mean_stds(
[self.VGMPE, self.HGMPE], ctx, imts)
for m, imt in enumerate(imts):
# V/H model, Equation 1 and 12 (in natural log units)
mean[m] = mean_[0, m] - mean_[1, m]
# Get standard deviations
C = self.COEFFS[imt]
t = _get_tau_vh(C, ctx.mag, tau_[0, m], tau_[1, m])
p = _get_phi_vh(C, ctx.mag, phi_[0, m], phi_[1, m])
sig[m] = np.sqrt(t**2 + p**2)
tau[m] = t
phi[m] = p
#: Table of regression coefficients obtained from supplementary material
#: published together with the EQS paper
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT rhow1 rhow2 rhob1 rhob2
0.010 0.783 0.718 0.916 0.893
0.020 0.785 0.718 0.917 0.891
0.030 0.784 0.703 0.919 0.884
0.050 0.782 0.678 0.931 0.877
0.075 0.781 0.681 0.933 0.909
0.100 0.778 0.657 0.944 0.900
0.150 0.775 0.653 0.946 0.875
0.200 0.774 0.630 0.946 0.826
0.250 0.770 0.642 0.945 0.784
0.300 0.757 0.658 0.949 0.819
0.400 0.750 0.661 0.953 0.719
0.500 0.742 0.666 0.955 0.716
0.750 0.730 0.688 0.965 0.718
1.000 0.721 0.684 0.967 0.765
1.500 0.707 0.663 0.967 0.796
2.000 0.691 0.664 0.966 0.799
3.000 0.652 0.629 0.956 0.822
4.000 0.669 0.613 0.945 0.839
5.000 0.665 0.586 0.921 0.860
7.500 0.586 0.573 0.898 0.685
10.00 0.639 0.547 0.854 0.720
PGA 0.782 0.720 0.915 0.893
PGV 0.754 0.680 0.882 0.699
""")
class NRCan15SiteTerm(GMPE):
"""
Implements a modified GMPE class that can be used to account for local
soil conditions in the estimation of ground motion.
:param gmpe_name:
The name of a GMPE class
"""
# Parameters
REQUIRES_SITES_PARAMETERS = set(('vs30'))
REQUIRES_DISTANCES = set()
REQUIRES_RUPTURE_PARAMETERS = set()
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = ''
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set()
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set()
DEFINED_FOR_TECTONIC_REGION_TYPE = ''
DEFINED_FOR_REFERENCE_VELOCITY = None
def __init__(self, gmpe_name):
super().__init__(gmpe_name=gmpe_name)
self.gmpe = registry[gmpe_name]()
self.set_parameters()
#
# Check if this GMPE has the necessary requirements
if not (hasattr(self.gmpe, 'DEFINED_FOR_REFERENCE_VELOCITY')
or 'vs30' in self.gmpe.REQUIRES_SITES_PARAMETERS):
tmps = '{:s} does not use vs30 nor a defined reference velocity'
msg = tmps.format(str(self.gmpe))
raise AttributeError(msg)
#
# Check compatibility of reference velocity
if hasattr(self.gmpe, 'DEFINED_FOR_REFERENCE_VELOCITY'):
assert (self.gmpe.DEFINED_FOR_REFERENCE_VELOCITY >= 760
and self.gmpe.DEFINED_FOR_REFERENCE_VELOCITY <= 800)
def get_mean_and_stddevs(self, sites, rup, dists, imt, stds_types):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for spec of input and result values.
"""
# Prepare sites
sites_rock = copy.deepcopy(sites)
sites_rock.vs30 = np.ones_like(sites_rock.vs30) * 760.
# compute mean and standard deviation
mean, stddvs = self.gmpe.get_mean_and_stddevs(sites_rock, rup, dists,
imt, stds_types)
if not str(imt) == 'PGA':
# compute mean and standard deviation on rock
mean_rock, stddvs_rock = self.gmpe.get_mean_and_stddevs(
sites_rock, rup, dists, imt, stds_types)
else:
mean_rock = mean
fa = self.BA08_AB06(sites.vs30, imt, np.exp(mean_rock))
mean = np.log(np.exp(mean) * fa)
return mean, stddvs
def BA08_AB06(self, vs30, imt, pgar):
"""
Computes amplification factor similarly to what is done in the 2015
version of the Canada building code. An initial version of this code
was kindly provided by Michal Kolaj - Geological Survey of Canada
:param vs30:
Can be either a scalar or a :class:`~numpy.ndarray` instance
:param imt:
The intensity measure type
:param pgar:
The value of hazard on rock (vs30=760). Can be either a scalar or
a :class:`~numpy.ndarray` instance. Unit of measure is fractions
of gravity acceleration.
:return:
A scalar or a :class:`~numpy.ndarray` instance with the
amplification factor.
"""
fa = np.ones_like(vs30)
if np.isscalar(vs30):
vs30 = np.array([vs30])
if np.isscalar(pgar):
pgar = np.array([pgar])
#
# Fixing vs30 for hard rock to 1999 m/s. Beyond this threshold the
# motion will not be deamplified further
vs = copy.copy(vs30)
vs[vs >= 2000] = 1999.
#
# Computing motion on rock
idx = np.where(vs30 > 760)
if np.size(idx) > 0:
"""
# This is the original implementation - Since this code is
# experimental we keep it for possible further developments
# For values of Vs30 greater than 760 a linear interpolation is
# used between the gm factor at 2000 m/s and 760 m/s
C2 = self.COEFFS_AB06r[imt]
fa[idx] = 10**(np.interp(np.log10(vs[idx]),
np.log10([760.0, 2000.0]),
np.log10([1.0, C2['c']])))
"""
C = self.COEFFS_BA08[imt]
nl = BooreAtkinson2008()._get_site_amplification_non_linear(
vs[idx], pgar[idx], C)
lin = BooreAtkinson2008()._get_site_amplification_linear(
vs[idx], C)
tmp = np.exp(nl + lin)
fa[idx] = tmp
#
# For values of Vs30 lower than 760 the amplification is computed
# using the site term of Boore and Atkinson (2008)
idx = np.where(vs < 760.)
if np.size(idx) > 0:
C = self.COEFFS_BA08[imt]
nl = BooreAtkinson2008()._get_site_amplification_non_linear(
vs[idx], pgar[idx], C)
lin = BooreAtkinson2008()._get_site_amplification_linear(
vs[idx], C)
fa[idx] = np.exp(nl + lin)
return fa
COEFFS_AB06r = CoeffsTable(sa_damping=5,
table="""\
IMT c
pgv 1.230
pga 0.891
0.05 0.891
0.10 1.072
0.20 1.318
0.30 1.380
0.50 1.380
1.00 1.288
2.00 1.230
5.00 1.148
10.0 1.072
""")
COEFFS_BA08 = CoeffsTable(sa_damping=5,
table="""\
IMT blin b1 b2
pgv -0.60 -0.50 -0.06
pga -0.36 -0.64 -0.14
0.010 -0.36 -0.64 -0.14
0.020 -0.34 -0.63 -0.12
0.030 -0.33 -0.62 -0.11
0.040 -0.31 -0.61 -0.11
0.050 -0.29 -0.64 -0.11
0.060 -0.25 -0.64 -0.11
0.075 -0.23 -0.64 -0.11
0.090 -0.23 -0.64 -0.12
0.100 -0.25 -0.60 -0.13
0.120 -0.26 -0.56 -0.14
0.150 -0.28 -0.53 -0.18
0.170 -0.29 -0.53 -0.19
0.200 -0.31 -0.52 -0.19
0.240 -0.38 -0.52 -0.16
0.250 -0.39 -0.52 -0.16
0.300 -0.44 -0.52 -0.14
0.360 -0.48 -0.51 -0.11
0.400 -0.50 -0.51 -0.10
0.460 -0.55 -0.50 -0.08
0.500 -0.60 -0.50 -0.06
0.600 -0.66 -0.49 -0.03
0.750 -0.69 -0.47 -0.00
0.850 -0.69 -0.46 -0.00
1.000 -0.70 -0.44 -0.00
1.500 -0.72 -0.40 -0.00
2.000 -0.73 -0.38 -0.00
3.000 -0.74 -0.34 -0.00
4.000 -0.75 -0.31 -0.00
5.000 -0.75 -0.291 -0.00
7.500 -0.692 -0.247 -0.00
10.00 -0.650 -0.215 -0.00
""")
class ChaoEtAl2020SInter(GMPE):
"""
Chao et al. (2020) for Subduction Interface.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGD, PGV, SA])
DEFINED_FOR_REFERENCE_VELOCITY = 1180
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
REQUIRES_DISTANCES = {'rrup'}
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'ztor'}
REQUIRES_SITES_PARAMETERS = {'vs30', 'vs30measured', 'z1pt0'}
def __init__(self,
manila=False,
aftershocks=False,
geology=True,
**kwargs):
"""
Aditional parameters.
"""
super().__init__(manila=manila,
aftershocks=aftershocks,
geology=geology,
**kwargs)
# Manila or Ryukyu subduction zone
self.manila = manila
# aftershocks or mainshocks
self.aftershocks = aftershocks
# geology True for KS17, False for seismic (receiver function)
# only used for inferred vs30, otherwise use vs30measured
self.geology = geology
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 dictionary of coefficients specific to required
# intensity measure type
C = self.COEFFS[imt]
s = self.CONSTANTS
med = np.zeros(len(sites.vs30))
med += self._ftype(C, rup)
med += (rup.ztor - self.CONST_FAULT['href']) * C['c14' + self.SUFFIX]
med += (rup.mag - s['mag_ref']) * C['c8' + self.SBCR]
med += (5 - rup.mag) * np.heaviside(5 - rup.mag, 0.5) \
* C['c11' + self.SBCR]
med += self._fh(C, rup.mag, dists.rrup)
med += (dists.rrup - s['rrup_ref']) * C['c21' + self.SBCR]
med += self._ffault(C, rup.mag)
med += C['c6'] * self.aftershocks + C['c7'] * self.manila
med += self._fvs30(C, sites)
sa1180 = np.exp(med + math.log(1180 / s['vs30_ref']) * C['c24'])
med += self._fc(C, imt, sites.vs30, sa1180)
med += np.log(sites.vs30 / s['vs30_ref']) * C['c24']
med += self._fz1pt0(C, sites)
stddevs = self.get_stddevs(C, rup.mag, stddev_types)
return med, stddevs
def get_stddevs(self, C, mag, stddev_types):
"""
Standard deviation.
tau: between event stddev ln(g)
phis2s: between site stddev in ln(g)
phiss: single station stddev in ln(g)
"""
stddevs = []
f = self.SBCR
f_mag = 0.5 * (min(6.5, max(4.5, mag)) - 4.5)
tau = C[f'tau1{f}'] + (C[f'tau2{f}'] - C[f'tau1{f}']) * f_mag
phiss = C[f'phiss1{f}'] + (C[f'phiss2{f}'] - C[f'phiss1{f}']) * f_mag
phis2s = C['phis2s']
phi = math.sqrt(phis2s**2 + phiss**2)
for stddev in stddev_types:
assert stddev in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev == const.StdDev.TOTAL:
stddevs.append(math.sqrt(tau**2 + phi**2))
elif stddev == const.StdDev.INTER_EVENT:
stddevs.append(tau)
elif stddev == const.StdDev.INTRA_EVENT:
stddevs.append(phi)
return stddevs
def _c19a(self, mag):
"""
First input into 19th/20th multiplier.
"""
return min(mag, self.MC)
def _fc(self, C, imt, vs30, sa1180):
"""
C value factor [23].
"""
s = self.CONSTANTS
if imt.name in ["PGD", "PGV"]:
c = 2400
else:
c = 2.4
return (-1.5 * np.log(vs30 / s['vs30_ref']) - np.log(sa1180 + c)
+ np.log(sa1180 + c * (vs30 / s['vs30_ref']) ** 1.5)) \
* np.heaviside(s['vs30_ref'] - vs30, 0.5) * C['c23']
def _ffault(self, C, mag):
"""
Other fault specific factors.
"""
return (6 - mag) * np.heaviside(6 - mag, 0.5) * C['c13'] \
+ (mag - self.MC) * np.heaviside(mag - self.MC, 0.5) \
* C['c29' + self.SUFFIX]
def _ftype(self, C, rup):
"""
Factor based on the type of fault.
"""
return C['c4' + self.SUFFIX]
def _fh(self, C, mag, rrup):
"""
Factors using `h` (coefficients 17-22).
"""
s = self.CONSTANTS
h = self._hm(mag)
hf = np.log((rrup**s['n'] + h**s['n'])**(1 / s['n']) /
(s['rrup_ref']**s['n'] + h**s['n'])**(1 / s['n']))
return hf * C['c17' + self.SBCR] \
+ hf * C['c19' + self.SBCR] * (self._c19a(mag) - s['mag_ref'])
def _fvs30(self, C, sites):
"""
Source of Vs30 factor.
vs30measured available for Kuo17 (measured)
self.geology True for KS17 (inferred)
self.geology False for Receiver Function (inferred)
"""
return np.where(sites.vs30measured, C['c26'],
C['c27'] if self.geology else C['c28'])
def _fz1pt0(self, C, sites):
"""
z1pt0 factor.
"""
result = np.zeros_like(sites.z1pt0)
idx = sites.z1pt0 >= 0
if sum(idx) == 0:
return result
z1pt0_ref = np.exp(-4.08 / 2 * np.log(
(sites.vs30**2 + 355.4**2) / (1750**2 + 355.4**2)))
result[idx] = np.log(sites.z1pt0[idx] / z1pt0_ref) * C['c25']
return result
def _hm(self, mag):
"""
H factor for coefficients 17-22.
"""
return 10 * np.exp(self.CONST_FAULT['C4'] *
(mag - self.MC) * np.heaviside(mag - self.MC, 0.5))
COEFFS = CoeffsTable(sa_damping=5,
table="""\
imt c1 c2 c3 c4_if c4_is c6 c7 c8_cr c8_sb c10 c11_cr c11_sb c13 c14_cr c14_if c14_is c17_cr c17_sb c19_cr c19_sb c21_cr c21_sb c23 c24 c25 c26 c27 c28 c29_if c29_is tau1_cr tau2_cr tau1_sb tau2_sb phiss1_cr phiss2_cr phiss1_sb phiss2_sb phis2s
pga -0.5192892547128840 -0.6150055029113330 -0.6487900726643910 -0.5859618870941580 0.2995078226527580 -0.1252895878217900 0.1860213693406720 0.4128529204313240 0.6654099729223670 -0.1376176044286790 -0.0000003768045793 -0.0000002632651801 -0.0000003479033210 0.0325013808122898 0.0188003326071965 0.0066214814780273 -1.3033352051553600 -1.4222150700864700 0.3874353293578060 0.1816390684494260 -0.0034295741595448 -0.0034489780547407 -2.5525572055834000 -0.4820755783830470 0.0636111092153052 -0.5680621936097360 -0.6441908224323110 -0.6148407238174470 -0.4944663117848010 -0.4948250053327020 0.3674988948492440 0.3156766103555770 0.2747114934261350 0.5404436414423900 0.5284243730959070 0.4400249261948010 0.4358918335042310 0.4982604989025690 0.3435860891378130
0.01 -0.5185435292277630 -0.6139978370809050 -0.6485291075803880 -0.5838899830711630 0.3025167286045810 -0.1244749736423930 0.1818440946548220 0.4133627969553290 0.6662082185566420 -0.1377874122648280 -0.0000016455914614 -0.0000010168484829 -0.0000015396189431 0.0325478379384533 0.0187424764459864 0.0065978989650052 -1.3050707375477800 -1.4244518028964800 0.3865358127626830 0.1799727376957520 -0.0034138067537784 -0.0034249196892139 -2.5491215932210800 -0.4817847143782920 0.0637979244436324 -0.5671019863928200 -0.6430624549208040 -0.6134855454872920 -0.4962061562087430 -0.5019638690208290 0.3672959719907850 0.3154146574183840 0.2733100640145130 0.5413688232186000 0.5279530156395120 0.4402345932395540 0.4366852410606870 0.4979773327789170 0.3437466383316600
0.02 -0.4925935193382860 -0.5849494939894080 -0.6149768931486030 -0.5994558769715950 0.2896423927820520 -0.1255022048822760 0.1913815871815020 0.3989282252665750 0.6316076153041100 -0.1329759746961010 -0.0010277552092071 -0.0000007415198554 -0.0000009243529219 0.0330191056515263 0.0184348278192339 0.0069331416349393 -1.3381199569179700 -1.4144452691294700 0.3918303510961290 0.1909212976216070 -0.0031761225955272 -0.0036500842576487 -2.5020049297189400 -0.4722757215196650 0.0649888427251637 -0.5300330753401030 -0.6092543141804070 -0.5783932279622350 -0.4567832202723850 -0.4843335992997120 0.3672096025203770 0.3193604175283950 0.2727371846461310 0.5590662841638730 0.5212490565944880 0.4457229793375830 0.4284446929672800 0.4997055429236690 0.3492753254041860
0.03 -0.4773436137435830 -0.5646500549184690 -0.5823569579995780 -0.6229871080555090 0.2895352598530250 -0.1281741601414120 0.1959394907475940 0.3700049726661150 0.5722615232020440 -0.1233348788754380 -0.0013400986538279 -0.0000008780800013 -0.0000010741358947 0.0343101384872960 0.0183116904998815 0.0075119701817267 -1.3673880371344400 -1.4049670408467200 0.4087284138519370 0.2120199290459480 -0.0031597614295051 -0.0039690305196895 -2.3679999172581600 -0.4533571902303470 0.0688570330004100 -0.4674371210038970 -0.5547847971008720 -0.5162080030607480 -0.3909967282502120 -0.4568941706767360 0.3659401986651120 0.3269487169641220 0.2754713073378610 0.5782229669599770 0.5138814813317350 0.4562412368820710 0.4231963576524820 0.5062146219159800 0.3642070292163550
0.05 -0.4384226473479580 -0.5082028496350560 -0.4996495791530560 -0.5509927916841400 0.4201424505033270 -0.1278113776092280 0.2242032272922090 0.3277716179853340 0.5335838412677030 -0.1092566090939630 -0.0009524028343619 -0.0000009362783788 -0.0000012076824503 0.0374313441023976 0.0179647463512188 0.0086002417698971 -1.4043378692826500 -1.4529353769070100 0.4227955124257500 0.2059482358996180 -0.0037038172429266 -0.0042767503271602 -2.0984569938797400 -0.4174769587709540 0.0796477449779514 -0.3278239226800660 -0.4273786543769590 -0.3669057022159870 -0.3673342531461080 -0.4926026405594960 0.3613130559351250 0.3457148557860690 0.2827051741664680 0.6026422039770350 0.5030028370059200 0.4708951658491060 0.4104373460235670 0.5195083771826150 0.4080959377619060
0.075 -0.3477680472987080 -0.3945396148772630 -0.3644851574401720 -0.3788975825498850 0.6660790354369400 -0.1257199250776420 0.2590114609066670 0.3280509470422620 0.5915580071627310 -0.1093481802115360 -0.0010601014177568 -0.0000014458228879 -0.0000014938956048 0.0400261494009523 0.0180580974419972 0.0092132504242451 -1.4072088973593200 -1.5212012494801500 0.4079055422317920 0.1599483130475640 -0.0046735359569929 -0.0044253262161005 -1.8571475913759100 -0.4031497826702400 0.0849015681692710 -0.2257128580612920 -0.3307477951183650 -0.2557559184395190 -0.4531985082804610 -0.5341761350472270 0.3646238141279680 0.3603139641158800 0.2932224947572630 0.6001445469340250 0.5039997875438060 0.4668928640936500 0.4088583646551290 0.5248133353055360 0.4440557923094290
0.1 -0.2464419641482460 -0.2774153233972800 -0.2419849681859750 -0.2159572988522690 0.8837635057027910 -0.1221833768730910 0.2890209915658740 0.3609773912176570 0.6796403235589960 -0.1203234194869740 -0.0095781938365105 -0.0091311877263691 -0.0000017618182496 0.0406923890414978 0.0187576968592212 0.0091770608487944 -1.3775350561906300 -1.5588146355752500 0.3826772642202150 0.1180456788835990 -0.0054981782655166 -0.0044752635101850 -1.6933015535378400 -0.4106809740578840 0.0822852228887146 -0.1971657286502670 -0.3034342387568920 -0.2273780092606650 -0.5595380222575010 -0.5995654008335480 0.3773149612260230 0.3622412109534710 0.3058662966967730 0.5804476608541280 0.5174927775766600 0.4518314029734340 0.4208300424568200 0.5207449309209680 0.4560381766578650
0.15 -0.0771751272296130 -0.1082252757155910 -0.0939554515669245 -0.0188559515947778 1.1045574548438600 -0.1151312333331240 0.3489251001067520 0.4435666368994170 0.8206717947215570 -0.1478533042267330 -0.0797000195466235 -0.1061400711142910 -0.0116149978331732 0.0385365803750634 0.0208403778461626 0.0084255538167330 -1.3047454734934800 -1.5546509544985100 0.3387081858027680 0.0762391834452875 -0.0060699037646678 -0.0043559591434871 -1.4739793205860400 -0.4462238803701860 0.0708425313555023 -0.2504635484625670 -0.3579852182163120 -0.2973613635520170 -0.7066557777245760 -0.6646730464270010 0.4205159985547740 0.3393429192383280 0.3335166881059750 0.5289137551348660 0.5530955106299720 0.4276458197094800 0.4552933469697380 0.5112791219012840 0.4393051343517960
0.2 0.0405594808831559 -0.0077282823725784 -0.0329357162076816 0.0977204826995843 1.1425790790134700 -0.1057191168540270 0.3722539227241170 0.5259387014440060 0.8944652896530820 -0.1753118327644590 -0.1628405724059960 -0.1905540130924890 -0.0703516281536629 0.0344218267917848 0.0220145357833909 0.0074084568455730 -1.2525154396822100 -1.5299381829848600 0.2988014581902580 0.0598123873775724 -0.0057279870130134 -0.0038467366062087 -1.3537154633193600 -0.4806650787981650 0.0627269858251427 -0.3514329644238130 -0.4494836594136780 -0.4211846625506190 -0.7761270389945640 -0.6765718066660800 0.4710484094826400 0.3078985636442060 0.3678152527072530 0.4963277349205770 0.5816461579655670 0.4175140424711400 0.4781484644913840 0.5035988500569350 0.4117968194252760
0.25 0.1161360079386870 0.0455512686241350 -0.0218646332100325 0.1828656137015420 1.1166678356454500 -0.0959115648679502 0.3639273275607390 0.5926458211482060 0.9514471984717970 -0.1975481854813300 -0.2376907309394700 -0.2386263420394340 -0.1392336794544470 0.0301984485118963 0.0220498416898711 0.0063660608238311 -1.2210171934017700 -1.5075909330134600 0.2681747226996620 0.0472484189561765 -0.0050865192380324 -0.0032636166820230 -1.3112990269528600 -0.5135409274151990 0.0616544496255378 -0.4563389214185420 -0.5390065111345010 -0.5398009092490380 -0.8288006277909410 -0.6846682992304260 0.5148599316146770 0.2855216261744740 0.3995944962541640 0.4770587925609880 0.5994129051899660 0.4166683191773280 0.4900244567390270 0.4964417374025240 0.3893046381000030
0.3 0.1659191261450740 0.0725370613365805 -0.0359674153322261 0.2295701498524820 1.0576588366467200 -0.0882656506919790 0.3427750060884890 0.6483788027762600 0.9819984405493800 -0.2161260130183380 -0.2965674398979590 -0.2665884284153660 -0.2169703936280970 0.0263787728828427 0.0216264161548529 0.0053861646702039 -1.2047472906024600 -1.4854043484828200 0.2441324298126210 0.0419492390586564 -0.0043698926044844 -0.0027135380939124 -1.3252507728285300 -0.5429162086543740 0.0645387790445636 -0.5550263121051320 -0.6210404997811030 -0.6445535318562390 -0.8538221721074140 -0.6735161372595090 0.5463002600989580 0.2736557189233880 0.4272231091987260 0.4656311763164020 0.6091651025639550 0.4221564137529650 0.4957367311495720 0.4906316632512320 0.3720915588780540
0.4 0.2142056666127370 0.0871536549688902 -0.0785690467168578 0.2764151479005750 0.9207449431454760 -0.0817387187650157 0.2621885450896460 0.7417540614842620 1.0112737345534200 -0.2472511509254110 -0.3436334917221890 -0.2565078736132940 -0.3586252797911450 0.0205765954005230 0.0202875364431140 0.0038382219060837 -1.1921038099281000 -1.4558697162866900 0.2098186797110940 0.0408684583105697 -0.0031642937062858 -0.0017940043857435 -1.4077075423307700 -0.5972162270181300 0.0741639723226930 -0.7281908574894840 -0.7628684799249960 -0.8199077697170760 -0.8746936616440970 -0.6381631348609450 0.5808849727025450 0.2713662162845130 0.4653458134731120 0.4672831153779370 0.6113503193815050 0.4361192706099510 0.4955634501806600 0.4867080815561310 0.3527750902276900
0.5 0.2236254270212470 0.0737703256835049 -0.1248626176144320 0.2932144086137190 0.8027962857692040 -0.0840244330603874 0.1721136232246120 0.8151053466925040 1.0356710065186700 -0.2717014152455810 -0.3293921568751970 -0.1956967186201360 -0.4758435322483390 0.0165224891710283 0.0187963908607794 0.0026597132484042 -1.1860778618169400 -1.4381584618490300 0.1912179053378480 0.0410520296595116 -0.0023448358088493 -0.0011582034067666 -1.5070859378876100 -0.6493752154999540 0.0836822599658712 -0.8748820619897430 -0.8876408712201270 -0.9615402715827100 -0.8939061858589470 -0.6160880182479380 0.5949464334180670 0.2871764340948960 0.4832505926756100 0.4803914686955640 0.6007190809790290 0.4486042327739210 0.4926763166550150 0.4858212403211350 0.3446261711175850
0.75 0.1528039303532890 -0.0248167903571809 -0.2511392119124840 0.1388909993170780 0.4519964034477110 -0.1046230174209790 0.0270194376114289 0.9406307668392510 1.0243375273572300 -0.3135419875863270 -0.2250006281710770 -0.0911523105914097 -0.6780831702704660 0.0110013901513618 0.0160522319622777 0.0012402638358105 -1.1698623108011400 -1.3625787842858000 0.1791792655901220 0.0659622332730993 -0.0013043059118461 -0.0005882173264089 -1.5844202517297500 -0.7429284095282450 0.1035767308819100 -1.1534790724423800 -1.1395651591115200 -1.2323996821315000 -0.8389026019711570 -0.5147492098368240 0.5850050231740750 0.3462884754383560 0.4785627709562630 0.5185233324163180 0.5620391824549910 0.4718500465503010 0.4894503194326150 0.4871171137374260 0.3419011444574020
1.0 0.0183554539383078 -0.1591378376284470 -0.3854397008591480 -0.0815004332093187 0.1288852589717840 -0.1246837038142780 -0.0535877846749373 1.0248278846159400 0.9984729722811390 -0.3393133894939400 -0.1276588419069730 -0.0409136585181734 -0.7992367966752370 0.0086318100105947 0.0146222483242542 0.0009003395366128 -1.1508125147275900 -1.3000691876438900 0.1832396128840250 0.0943261823256111 -0.0008735093977044 -0.0003997330115688 -1.4244083078078700 -0.7989976385952170 0.1185000096002400 -1.3487217771603600 -1.3270174440744400 -1.4337289163009600 -0.7382346855789400 -0.4287560627663270 0.5652851427812200 0.3922029871907690 0.4481274157753080 0.5644306606646860 0.5259679896173710 0.4845488048918390 0.4855760478703810 0.4913162411271670 0.3475742684982780
1.5 -0.2926406493971360 -0.4394400484356270 -0.6634745672889770 -0.5698164868777540 -0.4777414376471740 -0.1367512471546550 -0.1185422683336340 1.1535846852560400 0.9228592531769220 -0.3551593410006160 -0.0316373719436222 -0.0058305420526171 -0.9286080973093520 0.0062127909966995 0.0114205875168941 0.0006726268670384 -1.1172685240682800 -1.1760450613418900 0.1958900128843000 0.1499938137415910 -0.0005279011472397 -0.0005031399510306 -0.8544827391292060 -0.8438703395779730 0.1413533804677000 -1.5948082564095300 -1.5616885373157400 -1.6940289391677400 -0.5338216528196720 -0.2734691164270120 0.5400623156625950 0.4389989898505710 0.3998380606154830 0.6147869472762440 0.4771405443244140 0.4911661512017220 0.4858319625974600 0.4862020347407820 0.3584781550167080
2.0 -0.6164896637512180 -0.7252715132235520 -0.9386642110776790 -1.0016397597173700 -0.9827809560644520 -0.1204851699381740 -0.1574596881853990 1.2561590239982100 0.9157149198331690 -0.3487315863272320 -0.0067392342056503 -0.0008274455605290 -0.8998831651883260 0.0045185743588915 0.0076239354167913 0.0004849758370595 -1.0938451612547300 -1.0683876519211600 0.2093417950110930 0.1991110124549130 -0.0003935827881709 -0.0008887392881376 -0.4424325390151640 -0.8536333300862120 0.1558153259573340 -1.7120254817165000 -1.6704563706071200 -1.8185653745450900 -0.4237829724483130 -0.2166062958480880 0.5306044642337280 0.4525458066815850 0.3651681953582200 0.6249992145898750 0.4491015982391830 0.4851846396569770 0.4819819680840680 0.4774435589161110 0.3657798632961100
3.0 -1.2120217913721900 -1.2593110926431200 -1.4636739356095600 -1.6980520879594500 -1.7669432223057700 -0.0595654650319802 -0.2204723665783100 1.3973296744797800 0.9588403924773120 -0.3233624830738870 -0.0000028831797237 -0.0000043740923315 -0.7774992929692280 0.0001846487026116 0.0015942173971129 -0.0000443776256955 -1.0585068691241300 -0.9286291899300890 0.2337544609389410 0.2596941009305470 -0.0003265684501350 -0.0016673660346856 -0.0238666422441761 -0.8486298188632920 0.1646442443399270 -1.7746560709922100 -1.7136221908604800 -1.8823684494043700 -0.3206735394784300 -0.2094181559654280 0.5341895930662030 0.4630363429223910 0.3632239046532420 0.5759362561116940 0.4215979819838170 0.4631745228225680 0.4732577539251810 0.4497578024830470 0.3748448621655020
4.0 -1.7187620785302500 -1.7255326287093000 -1.9157987949568300 -2.2378527680411400 -2.3717405638272600 0.0060780094038531 -0.2907358910284120 1.4863934712127500 1.0614239334825600 -0.3008016678137440 -0.0000002303764802 -0.0000003167873542 -0.5992793127354700 -0.0045086409598014 -0.0033339971710007 -0.0004426514054550 -1.0347965137315500 -0.8267625726198150 0.2561912331555940 0.2946206159118700 -0.0002970204994493 -0.0024918478847597 0.0000000000000000 -0.8369401809898650 0.1609560550301920 -1.7432239926968500 -1.6657097551617700 -1.8532526872794200 -0.3155245227823960 -0.2880704899694910 0.5512683175278550 0.4723731595661930 0.3842160013347000 0.5005221059354860 0.4088763842852300 0.4389155701811710 0.4595536649184570 0.4197110255834490 0.3802459556632600
5.0 -2.2524124481564500 -2.2233337887420500 -2.3988731729506100 -2.7681880158076700 -2.9912308138027000 0.1087794828940540 -0.2475264997327470 1.5711476167331400 1.0248966641608600 -0.2757023074987770 -0.0000002893187016 -0.0000007071111743 -0.6712278770777070 -0.0080289129978441 -0.0055089260712685 0.0002598589919845 -0.9844367319831440 -0.7634431186144020 0.2732908377032170 0.3203152022108220 -0.0006897102389096 -0.0030925027294924 0.0000000000000000 -0.8223177494406110 0.1455355246584370 -1.6392650516693500 -1.5448698990426400 -1.7280816734851900 -0.1970906573510090 -0.2362019597302050 0.5684528701196870 0.4816961813462040 0.4683567199764780 0.4119013474002300 0.4034142608449920 0.4200274542874700 0.4420885624015020 0.3737143966344340 0.3884066340183610
pgv 2.9029349822540100 2.7442184267612700 2.5956072627404700 2.7208097262709800 3.2025577336977900 -0.1446177480065630 -0.0413092466691142 0.8212932944431650 0.8048031763759270 -0.2099764391081720 -0.0000106980728248 -0.0000492798570503 -0.2820776116949390 0.0155391426948740 0.0171590486230531 0.0030037011458330 -1.2265529440479100 -1.3749132391246600 0.3076583015302820 0.2104730674561660 -0.0009692157684588 -0.0006985849374855 -6.1179459855387300 -0.6707577779339960 0.0957650492780946 0.3935242034563910 0.3928190325309850 0.3150238242701770 -0.3632617170998910 -0.2432876895838630 0.4386543757769160 0.3740824694470210 0.3305136472559800 0.5673397303206320 0.5590865385354610 0.4351807257924570 0.4801642015831750 0.4853170221825470 0.2740663767048480
pgd 2.4541041890538500 2.3782401415145500 2.2914153189502800 2.0838396593163400 1.9313699400126300 -0.2352916881091410 0.0713994939700537 1.5616444489691000 1.4936921369303000 -0.1676096441841540 -0.0000019923442846 -0.0000232740338163 -0.2069439338171460 -0.0032395363349413 0.0109930765184774 0.0052177204872172 -1.0191698911307200 -1.1559670502824900 0.2068132897445940 0.1789279177790470 -0.0018437138641425 -0.0013634189684089 0.0000000000000000 -0.7422544318623790 0.1490020084340320 -0.4228777481185350 -0.3833592619351370 -0.4612451842659720 -0.3050704862339770 -0.2043152093014790 0.6449844035380140 0.4977962177812710 0.5366022406101780 0.7130676587043830 0.7016130925807040 0.4750313723101500 0.5971604738380890 0.5707298418086840 0.3229783037503560
""")
CONSTANTS = {'mag_ref': 6.5, 'n': 2, 'vs30_ref': 760, 'rrup_ref': 0}
CONST_FAULT = {'C4': 0.3, 'href': 0}
# subduction or crustal
SBCR = "_sb"
SUFFIX = "_if"
MC = 7.1
class Campbell2003MblgAB1987NSHMP2008(Campbell2003):
"""
Implement GMPE developed by Ken Campbell and described in
"Development of semi-empirical attenuation relationships for the CEUS",
U.S. Geological Survey, Award 01HQGR0011, final report.
Document available at:
http://earthquake.usgs.gov/research/external/reports/01HQGR0011.pdf
This GMPE is used by the National Seismic Hazard Mapping Project (NSHMP)
for the 2008 central and eastern US hazard model.
This class replicates the algorithm as implemented in
``subroutine getCampCEUS`` in the ``hazgridXnga2.f`` Fortran code available
at: http://earthquake.usgs.gov/hazards/products/conterminous/2008/software/
The class assumes rupture magnitude to be in Mblg scale (given that MFDs
for central and eastern US are given in this scale). Mblg is converted to
Mw using Atkinson and Boore 1987 conversion equation
Coefficients are given for the B/C (firm rock) conditions.
"""
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.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
C = self.COEFFS[imt]
mag = self._convert_magnitude(rup.mag)
mean = self._compute_mean(C, mag, dists.rrup)
mean = clip_mean(imt, mean)
stddevs = self._get_stddevs(C, stddev_types, mag, dists.rrup.size)
return mean, stddevs
def _convert_magnitude(self, mag):
"""
Convert magnitude from Mblg to Mw using Atkinson and Boore 1987
equation.
"""
return mblg_to_mw_atkinson_boore_87(mag)
def _compute_mean(self, C, mag, rrup):
"""
Compute mean value (Equation 30 in USGS report)
"""
mean = np.zeros_like(rrup)
mean += C['c1'] + C['c2'] * mag + C['c3'] * (8.5 - mag) ** 2
idx = rrup > 70.
mean[idx] += C['c7'] * (np.log(rrup[idx]) - np.log(70.))
idx = rrup > 130.
mean[idx] += C['c8'] * (np.log(rrup[idx]) - np.log(130.))
R = np.sqrt(
rrup ** 2 + (C['c5'] * np.exp(C['c6'] * mag)) ** 2
)
mean += C['c4'] * np.log(R) + (C['c9'] + C['c10'] * mag) * rrup
return mean
#: Coefficient tables extracted from ``subroutine getCampCEUS`` in
#: ``hazgridXnga2.f``
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13
pga 0.4492 0.633 -0.0427 -1.591 0.683 0.416 1.140 -0.873 -0.00428 0.000483 1.030 -0.0860 0.414
0.1 0.4064 0.613 -0.0353 -1.369 0.484 0.467 1.096 -1.284 -0.00454 0.00046 1.059 -0.0838 0.460
0.2 0.1325 0.617 -0.0586 -1.32 0.399 0.493 1.25 -0.928 -0.0046 0.000337 1.077 -0.0838 0.478
0.3 -0.1483 0.609 -0.0786 -1.28 0.349 0.502 1.241 -0.753 -0.00414 0.000263 1.081 -0.0838 0.482
0.5 -0.1333 0.534 -0.1379 -1.216 0.318 0.503 1.116 -0.606 -0.00341 0.000194 1.098 -0.0824 0.508
1.0 -0.3177 0.451 -0.2090 -1.158 0.299 0.503 1.067 -0.482 -0.00255 0.000141 1.110 -0.0793 0.543
2.0 -1.2483 0.459 -0.2552 -1.124 0.310 0.499 1.015 -0.417 -0.00187 0.000103 1.093 -0.0758 0.551
""")
class BindiEtAl2014Rjb(GMPE):
"""
Implements European GMPE:
D.Bindi, M. Massa, L.Luzi, G. Ameri, F. Pacor, R.Puglia and P. Augliera
(2014), "Pan-European ground motion prediction equations for the
average horizontal component of PGA, PGV and 5 %-damped PSA at spectral
periods of up to 3.0 s using the RESORCE dataset", Bulletin of
Earthquake Engineering, 12(1), 391 - 340
The regressions are developed considering the geometrical mean of the
as-recorded horizontal components
The printed version of the GMPE was corrected by Erratum:
D.Bindi, M. Massa, L.Luzi, G. Ameri, F. Pacor, R.Puglia and P. Augliera
(2014), "Erratum to Pan-European ground motion prediction equations for the
average horizontal component of PGA, PGV and 5 %-damped PSA at spectral
periods of up to 3.0 s using the RESORCE dataset", Bulletin of
Earthquake Engineering, 12(1), 431 - 448. The erratum notes that the
printed coefficients tables were in error. In this implementation
coefficients tables were taken from the Electronic Supplementary
material of the original paper, which are indicated as being unaffected.
"""
kind = "base"
#: Supported tectonic region type is 'active shallow crust'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Set of :mod:`intensity measure types <openquake.hazardlib.imt>`
#: this GSIM can calculate. A set should contain classes from module
#: :mod:`openquake.hazardlib.imt`.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
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 = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: Required site parameter is only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is Rjb (eq. 1).
REQUIRES_DISTANCES = {'rjb'}
sof = True
def __init__(self, adjustment_factor=1.0, **kwargs):
super().__init__(adjustment_factor=adjustment_factor, **kwargs)
self.adjustment_factor = np.log(adjustment_factor)
[self.dist_type] = self.REQUIRES_DISTANCES
def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
dists = getattr(ctx, self.dist_type)
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imean = _get_mean(self.kind, self.sof, C, ctx, dists)
if imt.string.startswith(('PGA', 'SA')):
# Convert units to g,
# but only for PGA and SA (not PGV)
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
else:
# PGV
mean[m] = np.log(10.0 ** imean)
mean[m] += self.adjustment_factor
sig[m] = np.log(10.0 ** C['sigma'])
tau[m] = np.log(10.0 ** C['tau'])
phi[m] = np.log(10.0 ** C['phi'])
#: Coefficients from Table 2
COEFFS = CoeffsTable(sa_damping=5, table="""
imt e1 c1 c2 h c3 b1 b2 b3 gamma sofN sofR sofS tau phi phis2s sigma
pgv 2.264810000 -1.224080000 0.202085000 5.061240000 0.000000000 0.162802000 -0.092632400 0.044030100 -0.529443000 -0.009476750 0.040057400 -0.030580500 0.156062000 0.277714000 0.120398000 0.318560000
pga 3.328190000 -1.239800000 0.217320000 5.264860000 0.001186240 -0.085504500 -0.092563900 0.000000000 -0.301899000 -0.039769500 0.077525300 -0.037755800 0.149977000 0.282398000 0.165611000 0.319753000
0.02 3.370530000 -1.263580000 0.220527000 5.200820000 0.001118160 -0.089055400 -0.091615200 0.000000000 -0.294021000 -0.039236000 0.081051600 -0.041815600 0.158670000 0.282356000 0.183959000 0.323885000
0.04 3.439220000 -1.310250000 0.244676000 4.916690000 0.001091830 -0.116919000 -0.078378900 0.000000000 -0.241765000 -0.037720400 0.079778300 -0.042057900 0.154621000 0.291143000 0.187409000 0.329654000
0.07 3.596510000 -1.290510000 0.231878000 5.359220000 0.001820940 -0.085012400 -0.056996800 0.000000000 -0.207629000 -0.045943700 0.087496800 -0.041553000 0.172785000 0.291499000 0.199913000 0.338860000
0.10 3.686380000 -1.281780000 0.219406000 6.121460000 0.002114430 -0.113550000 -0.075332500 0.000000000 -0.173237000 -0.038052800 0.084710300 -0.046658500 0.169691000 0.301967000 0.208178000 0.346379000
0.15 3.686320000 -1.176970000 0.182662000 5.741540000 0.002540270 -0.092872600 -0.102433000 0.073904200 -0.202492000 -0.026729300 0.067844100 -0.041114700 0.152902000 0.305804000 0.212124000 0.341900000
0.20 3.682620000 -1.103010000 0.133154000 5.319980000 0.002420890 0.010085700 -0.105184000 0.150461000 -0.291228000 -0.032653700 0.075976900 -0.043323200 0.150055000 0.300109000 0.190469000 0.335532000
0.26 3.643140000 -1.085270000 0.115603000 5.134550000 0.001964370 0.029939700 -0.127173000 0.178899000 -0.354425000 -0.033843800 0.074982000 -0.041138100 0.151209000 0.302419000 0.187037000 0.338114000
0.30 3.639850000 -1.105910000 0.108276000 5.128460000 0.001499220 0.039190400 -0.138578000 0.189682000 -0.393060000 -0.037245300 0.076701100 -0.039455900 0.157946000 0.297402000 0.174118000 0.336741000
0.36 3.574800000 -1.099550000 0.103083000 4.905570000 0.001049050 0.052103000 -0.151385000 0.216011000 -0.453905000 -0.027906700 0.069789800 -0.041883200 0.165436000 0.294395000 0.175848000 0.337694000
0.40 3.530060000 -1.095380000 0.101111000 4.953860000 0.000851474 0.045846400 -0.162090000 0.224827000 -0.492063000 -0.025630900 0.072566800 -0.046936000 0.157728000 0.296992000 0.169883000 0.336278000
0.46 3.433870000 -1.065860000 0.109066000 4.659900000 0.000868165 0.060083800 -0.165897000 0.197716000 -0.564463000 -0.018663500 0.064599300 -0.045935800 0.173005000 0.291868000 0.164162000 0.339290000
0.50 3.405540000 -1.057670000 0.112197000 4.432050000 0.000788528 0.088318900 -0.164108000 0.154750000 -0.596196000 -0.017419400 0.060282600 -0.042863200 0.180820000 0.289957000 0.165090000 0.341717000
0.60 3.304420000 -1.050140000 0.121734000 4.216570000 0.000487285 0.120182000 -0.163325000 0.117576000 -0.667824000 -0.000486417 0.044920900 -0.044434500 0.182233000 0.292223000 0.175634000 0.344388000
0.70 3.238820000 -1.050210000 0.114674000 4.171270000 0.000159408 0.166933000 -0.161112000 0.112005000 -0.738390000 0.011203300 0.028150600 -0.039353900 0.189396000 0.289307000 0.168617000 0.345788000
0.80 3.153700000 -1.046540000 0.129522000 4.200160000 0.000000000 0.193817000 -0.156553000 0.051728500 -0.794076000 0.016525800 0.020352200 -0.036878300 0.189074000 0.288815000 0.168170000 0.345200000
0.90 3.134810000 -1.046120000 0.114536000 4.480030000 0.000000000 0.247547000 -0.153819000 0.081575400 -0.821699000 0.016449300 0.021242200 -0.037691300 0.191986000 0.293264000 0.183719000 0.350517000
1.00 3.124740000 -1.052700000 0.103471000 4.416130000 0.000000000 0.306569000 -0.147558000 0.092837300 -0.826584000 0.026307100 0.018604300 -0.044911100 0.195026000 0.297907000 0.200775000 0.356067000
1.30 2.898410000 -0.973828000 0.104898000 4.258210000 0.000000000 0.349119000 -0.149483000 0.108209000 -0.845047000 0.025233900 0.022362100 -0.047595700 0.181782000 0.306676000 0.209625000 0.356504000
1.50 2.847270000 -0.983388000 0.109072000 4.566970000 0.000000000 0.384546000 -0.139867000 0.098737200 -0.823200000 0.018673800 0.023089400 -0.041763000 0.177752000 0.316312000 0.218569000 0.362835000
1.80 2.680160000 -0.983082000 0.164027000 4.680080000 0.000000000 0.343663000 -0.135933000 0.000000000 -0.778657000 0.011371300 0.016688200 -0.028059400 0.163242000 0.326484000 0.221367000 0.365020000
2.00 2.601710000 -0.979215000 0.163344000 4.581860000 0.000000000 0.331747000 -0.148282000 0.000000000 -0.769243000 0.005535450 0.019856600 -0.025392000 0.164958000 0.329916000 0.225350000 0.368857000
2.60 2.390670000 -0.977532000 0.211831000 5.395170000 0.000000000 0.357514000 -0.122539000 0.000000000 -0.769609000 0.008734600 0.023314200 -0.032048600 0.170280000 0.320626000 0.210193000 0.363037000
3.00 2.253990000 -0.940373000 0.227241000 5.741730000 0.000000000 0.385526000 -0.111445000 0.000000000 -0.732072000 0.022989300 -0.020662000 -0.002327150 0.176546000 0.314165000 0.207247000 0.360373000
""")
class McVerry2006Chch(McVerry2006AscSC):
"""
Extends McVerry2006AscSC to implement modifications required for the
Canterbury Seismic Hazard Model (CSHM).
"""
kind = "chch"
#: This implementation is non-verified because the model has not been
#: published, nor is independent code available.
non_verified = True
additional_sigma = 0
def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
# Compute SA with primed coeffs and PGA with both unprimed and
# primed coeffs
C_PGA = self.COEFFS_PRIMED[PGA()]
C_PGA_unprimed = self.COEFFS_UNPRIMED[PGA()]
for m, imt in enumerate(imts):
C = self.COEFFS_PRIMED[imt]
SC = self.COEFFS_STRESS[imt]
# Get S term to determine if consider site term is applied
S = _get_site_class(self.kind, ctx)
# Abrahamson and Silva (1997) hanging wall term. This is not used
# in the latest version of GMPE but is defined in functional form
# in the paper so we keep it here as a placeholder
f4HW = _compute_f4(C, ctx.mag, ctx.rrup)
# Flags for rake angles
CN, CR = _get_fault_mechanism_flags(ctx.rake)
# Get volcanic path distance
rvol = ctx.rrup if self.kind.startswith("vol") else 0.
# Get delta_C and delta_D terms for site class
delta_C, delta_D = _get_deltas(self.kind, ctx)
# Get Atkinson and Boore (2006) stress drop factors or additional
# standard deviation adjustment. Only apply these factors to
# sources located within the boundaries of the CSHM.
in_cshm = _check_in_cshm_polygon(ctx)
if in_cshm is True:
stress_drop_factor = _compute_stress_drop_adjustment(
self.kind, SC, ctx.mag)
additional_sigma = self.additional_sigma
else:
stress_drop_factor = 0
additional_sigma = 0
# Compute lnPGA_ABCD primed
lnPGAp_ABCD = _compute_mean(
self.kind, C_PGA, S, ctx.mag, ctx.rrup, rvol,
ctx.hypo_depth, CN, CR, f4HW, delta_C, delta_D)
# Compute lnPGA_ABCD unprimed
lnPGA_ABCD = _compute_mean(
self.kind, C_PGA_unprimed, S, ctx.mag, ctx.rrup,
rvol, ctx.hypo_depth, CN, CR, f4HW, delta_C, delta_D)
# Compute lnSA_ABCD
lnSAp_ABCD = _compute_mean(
self.kind, C, S, ctx.mag, ctx.rrup, rvol,
ctx.hypo_depth, CN, CR, f4HW, delta_C, delta_D)
# Stage 3: Equation 6 SA_ABCD(T). This is lnSA_ABCD
# need to calculate final lnSA_ABCD from non-log values
# but return log
mean[m] = np.log(np.exp(lnSAp_ABCD) *
(np.exp(lnPGA_ABCD) /
np.exp(lnPGAp_ABCD))) + stress_drop_factor
# Compute standard deviations
C_STD = self.COEFFS_STD[imt]
sig[m], tau[m], phi[m] = _get_stddevs(
self.kind, C_STD, ctx, additional_sigma)
#: Coefficient table (Atkinson and Boore, 2006, table 7, page 2201)
COEFFS_STRESS = CoeffsTable(sa_damping=5, table="""\
IMT delta M1 Mh
pga 0.15 0.50 5.50
0.025 0.15 0.00 5.00
0.031 0.15 0.00 5.00
0.04 0.15 0.00 5.00
0.05 0.15 0.00 5.00
0.063 0.15 0.17 5.17
0.079 0.15 0.34 5.34
0.1 0.15 0.50 5.50
0.126 0.15 1.15 5.67
0.158 0.15 1.85 5.84
0.199 0.15 2.50 6.00
0.251 0.15 2.90 6.12
0.315 0.15 3.30 6.25
0.397 0.15 3.65 6.37
0.5 0.15 4.00 6.50
0.629 0.15 4.17 6.70
0.794 0.15 4.34 6.95
1.00 0.15 4.50 7.20
1.25 0.15 4.67 7.45
1.587 0.15 4.84 7.70
2.0 0.15 5.00 8.00
2.5 0.15 5.25 8.12
3.125 0.15 5.50 8.25
4.0 0.15 5.75 8.37
5.0 0.15 6.00 8.50
pgv 0.11 2.00 5.50
""")
class BindiEtAl2017Rjb(GMPE):
"""
Implements the European GMPE of Bindi et al. (2017) for use in
moderate-seismicity regions:
D.Bindi, F. Cotton, S. R. Kotha, C. Bosse, D. Stromeyer and G. Gruenthal
(2017) "Application-driven ground motion prediction equation for
seismic hazard assessments in non-cratonic moderate-seismicity areas",
J. Seismology, 21(5), 1201 - 1218
Two different GMPEs are supported here
"""
#: Supported tectonic region type is 'stable shallow crust'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: GMPE is defined only for PGA and SA (PGV coefficients not made public)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, SA])
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
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.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
#: Required site parameter is only Vs30
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameter is magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is Rjb
REQUIRES_DISTANCES = {'rjb'}
def __init__(self, adjustment_factor=1.0, **kwargs):
super().__init__(adjustment_factor=adjustment_factor, **kwargs)
self.adjustment_factor = np.log(float(adjustment_factor))
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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
mean = (self._get_magnitude_scaling(C, rup.mag) +
self._get_distance_scaling(C, dists, rup.mag) +
self._get_site_term(C, sites.vs30))
# Mean is returned in terms of m/s^2. Need to convert to g
mean -= np.log(g)
stddevs = self.get_stddevs(C, sites.vs30.shape, stddev_types)
return mean + self.adjustment_factor, stddevs
def _get_magnitude_scaling(self, C, mag):
"""
Implements the magnitude scaling function F(M) presented in equation 4
"""
if mag < self.CONSTANTS["mh"]:
return C["e1"] + C["b1"] * (mag - self.CONSTANTS["mref"]) +\
C["b2"] * ((mag - self.CONSTANTS["mref"]) ** 2.)
else:
d_m = self.CONSTANTS["mh"] - self.CONSTANTS["mref"]
return C["e1"] + C["b3"] * (mag - self.CONSTANTS["mh"]) +\
(C["b1"] * d_m) + C["b2"] * (d_m ** 2.)
def _get_distance_scaling(self, C, dists, mag):
"""
Implements the distance scaling function F(M, R) presented in equations
2 and 3. In the case of Joyner-Boore distance then the fixed-depth
term h is required
"""
r_h = self._get_rh(C, dists)
return (C["c1"] + C["c2"] * (mag - self.CONSTANTS["mref"])) *\
np.log(r_h / self.CONSTANTS["rref"]) +\
C["c3"] * (r_h - self.CONSTANTS["rref"])
def _get_rh(self, C, dists):
"""
Returns the distance incorporating the fixed depth term, h
"""
return np.sqrt(dists.rjb**2. + C["h"]**2.)
def _get_site_term(self, C, vs30):
"""
Returns the linear site amplification term given in equation 5
"""
return C["sA"] * np.log(vs30 / 800.0)
def get_stddevs(self, C, n_sites, stddev_types):
"""
Returns the standard deviations
"""
tau = C["tau"] + np.zeros(n_sites)
phi = C["phi"] + np.zeros(n_sites)
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigma = np.sqrt(tau**2. + phi**2.)
stddevs.append(sigma)
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(phi)
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(tau)
return stddevs
# Joyner-Boore
COEFFS = CoeffsTable(sa_damping=5,
table="""\
imt e1 b1 b2 b3 c1 c2 c3 h sA tau phi
pga 0.635138 1.241105 -0.131810 -0.321920 -0.930850 0.143762 -0.010880 3.875582 -0.609150 0.495337 0.631336
0.0100 0.635138 1.241105 -0.131810 -0.321920 -0.930850 0.143762 -0.010880 3.875582 -0.609150 0.495337 0.631336
0.0200 0.705531 1.228780 -0.129160 -0.329230 -0.944120 0.145787 -0.010880 3.923887 -0.592970 0.502517 0.634714
0.0220 0.744105 1.219753 -0.127760 -0.332690 -0.949970 0.146859 -0.010880 3.948754 -0.583730 0.506053 0.636035
0.0250 0.835561 1.189969 -0.123500 -0.347660 -0.964520 0.150588 -0.010880 3.971356 -0.563480 0.514039 0.641710
0.0290 0.960622 1.149713 -0.120600 -0.364760 -0.981940 0.156387 -0.010980 3.932630 -0.533170 0.527573 0.649664
0.0300 0.982542 1.143429 -0.120050 -0.366740 -0.983330 0.157078 -0.011030 3.935425 -0.524880 0.530023 0.651497
0.0320 1.025696 1.136575 -0.117720 -0.379820 -0.985510 0.157380 -0.011130 4.000214 -0.510270 0.534272 0.654810
0.0350 1.098116 1.115775 -0.113590 -0.397190 -0.989340 0.159337 -0.011330 4.036096 -0.489150 0.541214 0.659647
0.0360 1.123583 1.105354 -0.111820 -0.402550 -0.990680 0.160659 -0.011410 4.016974 -0.480910 0.544125 0.661352
0.0400 1.206806 1.080443 -0.107980 -0.413370 -0.992560 0.163348 -0.011700 4.014361 -0.452990 0.556069 0.664047
0.0420 1.237455 1.078369 -0.108240 -0.415230 -0.990520 0.163407 -0.011860 4.054173 -0.445700 0.561054 0.666271
0.0440 1.251844 1.076735 -0.110540 -0.410250 -0.982740 0.163753 -0.012070 4.026577 -0.437860 0.567211 0.668650
0.0450 1.251626 1.075113 -0.111940 -0.404130 -0.976750 0.163945 -0.012200 3.970955 -0.434460 0.571350 0.670589
0.0460 1.256382 1.074434 -0.113630 -0.399360 -0.972150 0.164094 -0.012310 3.921404 -0.431610 0.575592 0.672206
0.0480 1.273180 1.070584 -0.115800 -0.404410 -0.965450 0.164738 -0.012500 3.830608 -0.425450 0.582299 0.675478
0.0500 1.268964 1.072599 -0.117110 -0.411960 -0.955390 0.164215 -0.012670 3.760774 -0.423150 0.584897 0.678273
0.0550 1.294806 1.072646 -0.116210 -0.412610 -0.941150 0.162012 -0.013000 3.652581 -0.425790 0.593588 0.681858
0.0600 1.274268 1.076568 -0.112050 -0.392960 -0.914590 0.159776 -0.013410 3.550820 -0.421100 0.598143 0.684462
0.0650 1.284592 1.080960 -0.109190 -0.373250 -0.899380 0.157293 -0.013670 3.491090 -0.415050 0.600609 0.686179
0.0670 1.270761 1.080915 -0.108790 -0.366810 -0.888570 0.156759 -0.013800 3.400139 -0.413930 0.601248 0.685822
0.0700 1.259126 1.089845 -0.108850 -0.346960 -0.874880 0.154148 -0.013970 3.355068 -0.413490 0.603364 0.684155
0.0750 1.215838 1.121748 -0.110610 -0.324150 -0.848450 0.147315 -0.014190 3.235534 -0.411620 0.602686 0.682186
0.0800 1.151986 1.159183 -0.110220 -0.308890 -0.822660 0.139166 -0.014300 3.178012 -0.414330 0.598061 0.679445
0.0850 1.078880 1.193976 -0.106640 -0.302760 -0.799970 0.131684 -0.014330 3.102177 -0.421470 0.593599 0.678927
0.0900 1.016519 1.227105 -0.104830 -0.283490 -0.782200 0.124327 -0.014290 3.023759 -0.440030 0.590472 0.677846
0.0950 0.973402 1.256189 -0.105520 -0.265790 -0.769890 0.118147 -0.014190 3.026574 -0.461320 0.582793 0.678857
0.1000 0.925401 1.287379 -0.111830 -0.231010 -0.757490 0.112731 -0.014100 2.985996 -0.486610 0.576948 0.679655
0.1100 0.875791 1.340574 -0.116550 -0.209500 -0.742660 0.103309 -0.013870 2.968454 -0.527410 0.558266 0.681101
0.1200 0.828032 1.383584 -0.119730 -0.132090 -0.732610 0.093477 -0.013580 3.122213 -0.561160 0.541827 0.683444
0.1300 0.766340 1.428531 -0.122180 -0.099120 -0.723060 0.084934 -0.013250 3.123764 -0.604790 0.522968 0.685163
0.1330 0.752926 1.440635 -0.123390 -0.090410 -0.722610 0.082770 -0.013130 3.162190 -0.617940 0.520507 0.685210
0.1400 0.737791 1.468425 -0.127720 -0.075320 -0.724260 0.077987 -0.012880 3.286426 -0.645450 0.512704 0.684238
0.1500 0.736715 1.504067 -0.130450 -0.040160 -0.733400 0.071440 -0.012490 3.554848 -0.683200 0.500299 0.686074
0.1600 0.749177 1.525331 -0.132690 -0.029340 -0.750100 0.069666 -0.012040 3.687601 -0.723930 0.488304 0.689339
0.1700 0.760213 1.540786 -0.138410 -0.015620 -0.766220 0.069663 -0.011610 3.781996 -0.760640 0.475100 0.688702
0.1800 0.739452 1.563804 -0.138710 -0.021800 -0.775680 0.068009 -0.011250 3.856147 -0.790880 0.462568 0.686140
0.1900 0.730298 1.570019 -0.144490 -0.004910 -0.787040 0.069004 -0.010850 3.868169 -0.815350 0.452189 0.680811
0.2000 0.699276 1.588260 -0.149360 0.020797 -0.791930 0.067300 -0.010520 3.870361 -0.834000 0.441413 0.676819
0.2200 0.659139 1.637386 -0.161840 0.057295 -0.809450 0.063984 -0.009850 4.011015 -0.865780 0.430961 0.665048
0.2400 0.585197 1.670581 -0.168330 0.047490 -0.816190 0.063724 -0.009460 4.030252 -0.907470 0.418078 0.657967
0.2500 0.544202 1.676278 -0.169680 0.066640 -0.819600 0.065290 -0.009280 3.969146 -0.930390 0.414367 0.656646
0.2600 0.518890 1.690318 -0.172100 0.079712 -0.827790 0.064973 -0.009020 4.004102 -0.950260 0.407553 0.654576
0.2800 0.468023 1.718140 -0.171930 0.096277 -0.843840 0.063219 -0.008490 4.088128 -0.970900 0.402642 0.655900
0.2900 0.449715 1.730149 -0.173960 0.103671 -0.852910 0.063330 -0.008210 4.161005 -0.978320 0.400506 0.654953
0.3000 0.438012 1.742259 -0.179910 0.116360 -0.861500 0.063859 -0.008000 4.217235 -0.982850 0.398426 0.654131
0.3200 0.435852 1.767679 -0.189340 0.128703 -0.883920 0.064745 -0.007540 4.439888 -0.987550 0.393950 0.650810
0.3400 0.404536 1.797985 -0.195110 0.115054 -0.899800 0.064053 -0.007100 4.399340 -0.993250 0.384897 0.649751
0.3500 0.382972 1.810384 -0.197220 0.099968 -0.906200 0.064678 -0.006920 4.368682 -0.999760 0.384327 0.649189
0.3600 0.349214 1.821998 -0.198100 0.084615 -0.908870 0.065198 -0.006770 4.366836 -1.006870 0.385376 0.648155
0.3800 0.280029 1.840613 -0.202330 0.060432 -0.910860 0.067799 -0.006580 4.269163 -1.013800 0.384998 0.647082
0.4000 0.216017 1.862263 -0.206160 0.067862 -0.915170 0.068428 -0.006360 4.254286 -1.016590 0.383209 0.648535
0.4200 0.172509 1.879301 -0.212120 0.083118 -0.924180 0.070022 -0.006110 4.267693 -1.014390 0.380057 0.646898
0.4400 0.139057 1.894512 -0.220880 0.096344 -0.933450 0.072375 -0.005880 4.267138 -1.008760 0.378131 0.645543
0.4500 0.123479 1.903496 -0.223920 0.098657 -0.938110 0.072849 -0.005780 4.314011 -1.007770 0.377127 0.645109
0.4600 0.092663 1.914621 -0.226230 0.113557 -0.939190 0.072457 -0.005700 4.373658 -1.006970 0.374313 0.644466
0.4800 0.064142 1.925415 -0.231520 0.119283 -0.950590 0.074303 -0.005460 4.503590 -1.004980 0.376973 0.642511
0.5000 0.015134 1.933643 -0.229620 0.126283 -0.957250 0.074768 -0.005220 4.570597 -1.004220 0.378237 0.639470
0.5500 -0.107970 1.951700 -0.239610 0.164680 -0.971840 0.078830 -0.004640 4.510815 -1.006060 0.383912 0.635885
0.6000 -0.210030 1.967164 -0.235140 0.136069 -0.988640 0.082926 -0.004190 4.583048 -1.003190 0.397759 0.634794
0.6500 -0.318340 1.994321 -0.231640 0.106534 -0.998240 0.085986 -0.003910 4.624840 -0.997570 0.410119 0.631284
0.6670 -0.377670 1.999595 -0.227650 0.094506 -0.995190 0.087318 -0.003870 4.550387 -0.994190 0.415335 0.630272
0.7000 -0.461320 2.010666 -0.224060 0.086120 -0.997760 0.089917 -0.003720 4.398042 -0.984550 0.421072 0.626758
0.7500 -0.602990 2.023635 -0.222370 0.039362 -0.994020 0.095549 -0.003580 4.174297 -0.964820 0.430431 0.623797
0.8000 -0.737520 2.041943 -0.218890 0.054982 -0.990400 0.097224 -0.003500 4.062969 -0.942860 0.437310 0.622591
0.8500 -0.833250 2.058361 -0.213530 0.031862 -0.997750 0.099138 -0.003280 4.055099 -0.929260 0.442478 0.625612
0.9000 -0.913750 2.082115 -0.206790 -0.001830 -1.006360 0.098959 -0.003070 4.199566 -0.928390 0.455462 0.624580
0.9500 -1.027550 2.107107 -0.200650 -0.029910 -1.003330 0.097355 -0.002960 4.189130 -0.924830 0.471674 0.622931
1.0000 -1.116170 2.130210 -0.201780 -0.017300 -1.006680 0.096426 -0.002820 4.231572 -0.915310 0.479707 0.620973
1.1000 -1.281600 2.155173 -0.200600 -0.030950 -1.013040 0.100472 -0.002480 4.180282 -0.892360 0.490696 0.618982
1.2000 -1.541750 2.181763 -0.180260 -0.031330 -0.995630 0.098812 -0.002330 4.022894 -0.881650 0.502163 0.615611
1.3000 -1.695110 2.211878 -0.169820 -0.049360 -0.999650 0.098186 -0.002050 4.073868 -0.868980 0.520770 0.609101
1.4000 -1.843290 2.235781 -0.158540 -0.008240 -1.008190 0.095328 -0.001720 4.219321 -0.867660 0.529452 0.604887
1.5000 -1.901680 2.229950 -0.155900 0.012115 -1.032620 0.100703 -0.001370 4.401009 -0.852200 0.540605 0.604146
1.6000 -2.008610 2.256904 -0.159130 0.035439 -1.040790 0.100755 -0.001170 4.443051 -0.831210 0.544404 0.600164
1.7000 -2.131090 2.258859 -0.146030 0.043698 -1.043480 0.098506 -0.001000 4.642552 -0.809230 0.550368 0.599125
1.8000 -2.212390 2.282670 -0.148270 0.043236 -1.051520 0.098118 -0.000850 4.880542 -0.796600 0.556535 0.598574
1.9000 -2.293230 2.330732 -0.162870 0.083305 -1.059710 0.094681 -0.000660 5.151302 -0.795890 0.550160 0.597577
2.0000 -2.335640 2.339893 -0.153660 0.062914 -1.081170 0.095849 -0.000450 5.404803 -0.782790 0.548455 0.594664
2.2000 -2.583710 2.328118 -0.106080 0.085979 -1.070680 0.090160 -0.000490 5.458659 -0.769760 0.555283 0.596546
2.4000 -2.757660 2.366893 -0.099200 0.137943 -1.065930 0.082511 -0.000430 5.577205 -0.759120 0.555954 0.590970
2.5000 -2.911190 2.389345 -0.094020 0.174453 -1.039020 0.077098 -0.000670 5.662470 -0.738660 0.558695 0.589879
2.6000 -2.980700 2.436770 -0.110630 0.259638 -1.035520 0.070752 -0.000670 5.977967 -0.728720 0.558466 0.587132
2.8000 -2.985610 2.403452 -0.093490 0.313060 -1.067010 0.072788 -0.000570 6.541798 -0.685760 0.523922 0.589979
3.0000 -3.118900 2.396847 -0.081150 0.381270 -1.063110 0.070630 -0.000670 6.815989 -0.676270 0.524274 0.591716
3.2000 -3.296140 2.418203 -0.071370 0.439181 -1.046650 0.065154 -0.000810 7.011276 -0.663990 0.515799 0.592432
3.4000 -3.296240 2.441129 -0.094510 0.479797 -1.057270 0.067191 -0.000870 7.209539 -0.651160 0.522075 0.588690
3.5000 -3.327090 2.441528 -0.090670 0.504891 -1.062860 0.068069 -0.000870 7.507757 -0.643560 0.523420 0.584815
3.6000 -3.476920 2.457411 -0.074510 0.540008 -1.039050 0.062581 -0.001010 7.768941 -0.632120 0.534581 0.581911
3.8000 -3.568780 2.414174 -0.066080 0.556090 -1.035910 0.071428 -0.001140 7.884801 -0.631060 0.538444 0.573748
4.0000 -3.719730 2.410756 -0.062210 0.581531 -1.020870 0.075380 -0.001280 7.944414 -0.617710 0.530623 0.568737
""")
CONSTANTS = {"mref": 4.5, "mh": 6.5, "rref": 1.0}
class SharmaEtAl2009(GMPE):
# pylint: disable=no-init
"""
Implements GMPE of Sharma et al. (2009). This GMPE is intended for the
Indian Himalayas but is based on data from both Zagros in Iran and the
Himalayas. The combination of these two regions is motivated by the
sparsity of near field data. Seismotectonic similarity is supposed
based on both regions being continental collision zones, and in spite
of the lack of subduction in Zagros.
Note that Figure 7-9 of Sharma et al. (2009) are in error (Sharma,
personal communication). This implementation is verified against test
vector obtained from lead author.
Support for PGA has been added by assuming it to be equal to the spectral
acceleration at 0.04 s. This is assumed by the authors in the captions for
Figures 11-13 anyway.
Reference:
Sharma, M. L., Douglas, J., Bungum, H., and Kotadia, J. (2009).
Ground-motion prediction equations based on data from the Himalayan and
Zagros regions. *Journal of Earthquake Engineering*, 13(8):1191–1210.
"""
#: Supported tectonic region type is 'active shallow crust'
#: however as inndicated the introduction the tectonics of the
#: Himalayas have a "great range of focal depths" (Sharma et
#: al., 2009, p. 1192).
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Set of :mod:`intensity measure types <openquake.hazardlib.imt>`
#: this GSIM can calculate. A set should contain classes from module
#: :mod:`openquake.hazardlib.imt`.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, SA])
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
#: :attr:`~openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
#: see p. 1200.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Only total standard deviation is supported, see Table 2, p. 1202.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([const.StdDev.TOTAL])
#: Required site parameter Vs30 is used to set binary rock/soil
#: classification dummy variable, see equation (1) on p. 1200.
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake, see
#: equation (1) on p. 1200. Rake is used to distinguish between
#: reverse and strike-slip faulting, and to detect mis-application
#: of GMPE to normal faulting.
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is Joyner-Boore distance, see p. 1200
REQUIRES_DISTANCES = {'rjb'}
ALREADY_WARNED = False # warn the first time only
def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
# pylint: disable=too-many-arguments
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for specification of input and result values.
"""
# extract dictionary of coefficients specific to required
# intensity measure type
coeffs = self.COEFFS[imt]
# equation (1) is in terms of common logarithm
log_mean = (self._compute_magnitude(rup, coeffs) +
self._compute_distance(dists, coeffs) +
self._get_site_amplification(sites, coeffs) +
self._get_mechanism(rup, coeffs))
# so convert to g and thence to the natural logarithm
mean = log_mean * np.log(10.0) - np.log(g)
# convert standard deviations from common to natural logarithm
log_stddevs = self._get_stddevs(coeffs, stddev_types, len(sites.vs30))
stddevs = log_stddevs * np.log(10.0)
return mean, stddevs
def _get_stddevs(self, coeffs, stddev_types, num_sites):
"""
Return total sigma as reported in Table 2, p. 1202.
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
stddevs.append(coeffs['sigma'] + np.zeros(num_sites))
return np.array(stddevs)
@classmethod
def _compute_magnitude(cls, rup, coeffs):
"""
Compute first two terms of equation (1) on p. 1200:
``b1 + b2 * M``
"""
return coeffs['b1'] + coeffs['b2'] * rup.mag
@classmethod
def _compute_distance(cls, dists, coeffs):
"""
Compute third term of equation (1) on p. 1200:
``b3 * log(sqrt(Rjb ** 2 + b4 ** 2))``
"""
return coeffs['b3'] * np.log10(
np.sqrt(dists.rjb**2. + coeffs['b4']**2.))
def _get_site_amplification(self, sites, coeffs):
"""
Compute fourth term of equation (1) on p. 1200:
``b5 * S``
"""
is_rock = self.get_site_type_dummy_variables(sites)
return coeffs['b5'] * is_rock
def _get_mechanism(self, rup, coeffs):
"""
Compute fifth term of equation (1) on p. 1200:
``b6 * H``
"""
is_strike_slip = self.get_fault_type_dummy_variables(rup)
return coeffs['b6'] * is_strike_slip
def get_site_type_dummy_variables(self, sites):
"""
Binary rock/soil classification dummy variable based on sites.vs30.
"``S`` is 1 for a rock site and 0 otherwise" (p. 1201).
"""
is_rock = np.array(sites.vs30 > self.NEHRP_BC_BOUNDARY)
return is_rock
def get_fault_type_dummy_variables(self, rup):
"""
Fault-type classification dummy variable based on rup.rake.
"``H`` is 1 for a strike-slip mechanism and 0 for a reverse mechanism"
(p. 1201).
Note:
UserWarning is raised if mechanism is determined to be normal
faulting, since as summarized in Table 2 on p. 1197 the data used
for regression included only reverse and stike-slip events.
"""
# normal faulting
is_normal = np.array(
self.RAKE_THRESH < -rup.rake < (180. - self.RAKE_THRESH))
# reverse raulting
is_reverse = np.array(
self.RAKE_THRESH < rup.rake < (180. - self.RAKE_THRESH))
if not self.ALREADY_WARNED and is_normal.any():
# make sure that the warning is printed only once to avoid
# flooding the terminal
msg = ('Normal faulting not supported by %s; '
'treating as strike-slip' % type(self).__name__)
warnings.warn(msg, UserWarning)
self.ALREADY_WARNED = True
is_strike_slip = ~is_reverse | is_normal
is_strike_slip = is_strike_slip.astype(float)
return is_strike_slip
#: Coefficients taken from Table 2, p. 1202. Note that "In
#: this article, only the coefficients for a subset of these
#: periods [between 0.04 and 2.5 s] are reported" and the damping
#: is 5% (Sharma et al., 2009, p. 1200). "After trials with
#: different values b4 was fixed to be 15km for all periods."
#: (Sharma et al., 2009, p. 1201)
COEFFS = CoeffsTable(sa_damping=5.,
table="""\
IMT b1 b2 b3 b4 b5 b6 sigma
pga 1.0170 0.1046 -1.0070 15.0 -0.0735 -0.3068 0.3227
0.04 1.0170 0.1046 -1.0070 15.0 -0.0735 -0.3068 0.3227
0.05 1.0280 0.1245 -1.0550 15.0 -0.0775 -0.3246 0.3350
0.10 1.3820 0.1041 -1.0620 15.0 -0.1358 -0.3326 0.3427
0.20 1.3820 0.1041 -1.0620 15.0 -0.1358 -0.3326 0.3596
0.30 1.3680 0.0684 -0.9139 15.0 -0.0972 -0.3011 0.3651
0.40 0.9747 0.1009 -0.8886 15.0 -0.0552 -0.2639 0.3613
0.50 0.5295 0.1513 -0.8601 15.0 -0.0693 -0.2533 0.3654
0.75 -0.5790 0.3147 -0.9064 15.0 -0.0111 -0.2394 0.3770
1.00 -1.6120 0.4673 -0.9278 15.0 -0.0203 -0.2355 0.3949
1.25 -1.7160 0.4763 -0.9482 15.0 -0.0200 -0.2921 0.4190
1.50 -2.1380 0.5222 -0.9333 15.0 0.0284 -0.3197 0.4251
2.00 -2.6900 0.5707 -0.9082 15.0 0.0400 -0.2770 0.4077
2.50 -2.9420 0.5671 -0.8270 15.0 0.0054 -0.2710 0.3959
""")
#: Sharma et al. (2009) does not use VS30 so no threshhold is given.
#: A value of 760 m/s was selected. This is consistent with
#: :mod:`openquake.hazardlib.gsim.atkinson_boore_2003`,
#: corresponds to NEHRP class A/B, and is close to the
#: threshhold for Eurocode 8 Class 8 (800 m/s).
NEHRP_BC_BOUNDARY = 760.
#: Rake threshhold of 30 degrees was selected, same as
#: :mod:`openquake.hazardlib.gsim.boore_atkinson_2008` and
#: :mod:`openquake.hazardlib.gsim.campbell_bozorgnia_2008`.
#: Contrast with 45 degree threshhold used by 30 degree
#: threshhold used in :mod:`openquake.hazardlib.gsim.zhao_2006`.
RAKE_THRESH = 30.
class TravasarouEtAl2003(GMPE):
"""
Implements the ground motion prediction equation for Arias Intensity
given by Travasarou et al., (2003):
Travasarou, T., Bray, J. D. and Abrahamson, N. A. (2003) "Emprical
Attenuation Relationship for Arias Intensity", Earthquake Engineering
and Structural Dynamics, 32: 1133 - 1155
Ground motion records are generally taken from active shallow crustal
regions
"""
#: Supported tectonic region type is 'active shallow crust'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Set of :mod:`intensity measure types <openquake.hazardlib.imt>`
#: this GSIM can calculate. A set should contain classes from module
#: :mod:`openquake.hazardlib.imt`.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
IA,
])
#: Supported intensity measure component is actually the arithmetic mean of
#: two horizontal components - we find this to be equivalent to
#: :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, see equations 13 - 15
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
#: Required site parameter is only Vs30 (used to distinguish rock
#: and stiff and soft soil).
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
#: Required rupture parameters are magnitude and rake (eq. 1, page 199).
REQUIRES_RUPTURE_PARAMETERS = set(('rake', 'mag'))
#: Required distance measure is RRup (eq. 1, page 199).
REQUIRES_DISTANCES = set(('rrup', ))
#: No independent tests - verification against paper
non_verified = True
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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
# Implements mean model (equation 12)
mean = (self._compute_magnitude(rup, C) +
self._compute_distance(dists, C) +
self._get_site_amplification(sites, rup, C) +
self._get_mechanism(rup, C))
stddevs = self._get_stddevs(rup, np.exp(mean), stddev_types, sites)
return mean, stddevs
def _get_stddevs(self, rup, arias, stddev_types, sites):
"""
Return standard deviations as defined in table 1, p. 200.
"""
stddevs = []
# Magnitude dependent inter-event term (Eq. 13)
if rup.mag < 4.7:
tau = 0.611
elif rup.mag > 7.6:
tau = 0.475
else:
tau = 0.611 - 0.047 * (rup.mag - 4.7)
# Retrieve site-class dependent sigma
sigma1, sigma2 = self._get_intra_event_sigmas(sites)
sigma = np.copy(sigma1)
# Implements the nonlinear intra-event sigma (Eq. 14)
idx = arias >= 0.125
sigma[idx] = sigma2[idx]
idx = np.logical_and(arias > 0.013, arias < 0.125)
sigma[idx] = sigma1[idx] - 0.106 * (np.log(arias[idx]) -
np.log(0.0132))
sigma_total = np.sqrt(tau**2. + sigma**2.)
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
stddevs.append(sigma_total)
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(sigma)
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(tau * np.ones_like(sites.vs30))
return stddevs
def _get_intra_event_sigmas(self, sites):
"""
The intra-event term nonlinear and dependent on both the site class
and the expected ground motion. In this case the sigma coefficients
are determined from the site class as described below Eq. 14
"""
sigma1 = 1.18 * np.ones_like(sites.vs30)
sigma2 = 0.94 * np.ones_like(sites.vs30)
idx1 = np.logical_and(sites.vs30 >= 360.0, sites.vs30 < 760.0)
idx2 = sites.vs30 < 360.0
sigma1[idx1] = 1.17
sigma2[idx1] = 0.93
sigma1[idx2] = 0.96
sigma2[idx2] = 0.73
return sigma1, sigma2
def _compute_magnitude(self, rup, C):
"""
Compute the first term of the equation described on p. 1144:
``c1 + c2 * (M - 6) + c3 * log(M / 6)``
"""
return C['c1'] + C['c2'] * (rup.mag - 6.0) +\
(C['c3'] * np.log(rup.mag / 6.0))
def _compute_distance(self, dists, C):
"""
Compute the second term of the equation described on p. 1144:
`` c4 * np.log(sqrt(R ** 2. + h ** 2.)
"""
return C["c4"] * np.log(np.sqrt(dists.rrup**2. + C["h"]**2.))
def _get_site_amplification(self, sites, rup, C):
"""
Compute the third term of the equation described on p. 1144:
``(s11 + s12 * (M - 6)) * Sc + (s21 + s22 * (M - 6)) * Sd`
"""
Sc, Sd = self._get_site_type_dummy_variables(sites)
return (C["s11"] + C["s12"] * (rup.mag - 6.0)) * Sc +\
(C["s21"] + C["s22"] * (rup.mag - 6.0)) * Sd
def _get_site_type_dummy_variables(self, sites):
"""
Get site type dummy variables, ``Sc`` (for soft and stiff soil sites)
and ``Sd`` (for rock sites).
"""
Sc = np.zeros_like(sites.vs30)
Sd = np.zeros_like(sites.vs30)
# Soft soil; Vs30 < 360 m/s. Page 199.
Sd[sites.vs30 < 360.0] = 1
# Stiff soil 360 <= Vs30 < 760
Sc[np.logical_and(sites.vs30 >= 360.0, sites.vs30 < 760.0)] = 1
return Sc, Sd
def _get_mechanism(self, rup, C):
"""
Compute the fourth term of the equation described on p. 199:
``f1 * Fn + f2 * Fr``
"""
Fn, Fr = self._get_fault_type_dummy_variables(rup)
return (C['f1'] * Fn) + (C['f2'] * Fr)
def _get_fault_type_dummy_variables(self, rup):
"""
The original classification considers four style of faulting categories
(normal, strike-slip, reverse-oblique and reverse).
"""
Fn, Fr = 0, 0
if rup.rake >= -112.5 and rup.rake <= -67.5:
# normal
Fn = 1
elif rup.rake >= 22.5 and rup.rake <= 157.5:
# Joins both the reverse and reverse-oblique categories
Fr = 1
return Fn, Fr
#: For Ia, coefficients are taken from table 3,
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT c1 c2 c3 c4 h s11 s12 s21 s22 f1 f2
ia 2.800 -1.981 20.72 -1.703 8.78 0.454 0.101 0.479 0.334 -0.166 0.512
""")
class BindiEtAl2017Rhypo(BindiEtAl2017Rjb):
"""
Version of the Bindi et al. (2017) GMPE using hypocentral distance.
"""
#: Required distance measure is Rhypo (eq. 1).
REQUIRES_DISTANCES = set(('rhypo', ))
def _get_rh(self, C, dists):
"""
In this case only the hypocentral distance is needed - return this
directly
"""
return dists.rhypo
# Hypocentral
COEFFS = CoeffsTable(sa_damping=5,
table="""\
imt e1 b1 b2 b3 c1 c2 c3 sA tau phi
pga 1.494544 1.514441 -0.09357000 0.33240700 -1.15213 0.09175100 -0.00930000 -0.61492 0.50156400 0.63757400
0.0100 1.494544 1.514441 -0.09357000 0.33240700 -1.15213 0.09175100 -0.00930000 -0.61492 0.50156400 0.63757400
0.0200 1.570345 1.503896 -0.09074000 0.32841500 -1.16673 0.09346100 -0.00929000 -0.59877 0.50877700 0.64092400
0.0220 1.610601 1.494865 -0.08933000 0.32517400 -1.17294 0.09459200 -0.00929000 -0.58954 0.51221500 0.64221300
0.0250 1.715268 1.466781 -0.08502000 0.31234200 -1.19098 0.09800100 -0.00927000 -0.56930 0.52020600 0.64762700
0.0290 1.861380 1.428625 -0.08179000 0.29794300 -1.21392 0.10342500 -0.00933000 -0.53904 0.53402200 0.65550100
0.0300 1.886291 1.421821 -0.08125000 0.29616200 -1.21608 0.10426900 -0.00937000 -0.53074 0.53642400 0.65719700
0.0320 1.923407 1.413206 -0.07893000 0.28318900 -1.21652 0.10507100 -0.00949000 -0.51611 0.54071300 0.66029500
0.0350 1.998679 1.392584 -0.07470000 0.26943700 -1.22112 0.10705800 -0.00968000 -0.49500 0.54785700 0.66475400
0.0360 2.028152 1.381789 -0.07285000 0.26414200 -1.22348 0.10849800 -0.00975000 -0.48678 0.55085900 0.66638200
0.0400 2.109385 1.353035 -0.06875000 0.25141800 -1.22451 0.11223800 -0.01006000 -0.45885 0.56311600 0.66891400
0.0420 2.130849 1.348203 -0.06893000 0.24849100 -1.21988 0.11301400 -0.01024000 -0.45157 0.56809300 0.67111500
0.0440 2.139374 1.342776 -0.07114000 0.25033600 -1.21041 0.11427900 -0.01046000 -0.44371 0.57433300 0.67347500
0.0450 2.139921 1.339719 -0.07243000 0.25529700 -1.20457 0.11480000 -0.01059000 -0.44030 0.57857200 0.67536700
0.0460 2.145808 1.338217 -0.07400000 0.25986500 -1.20022 0.11514700 -0.01070000 -0.43746 0.58288600 0.67695800
0.0480 2.164007 1.332446 -0.07590000 0.25331300 -1.19373 0.11626200 -0.01088000 -0.43129 0.58957800 0.68023800
0.0500 2.158757 1.332431 -0.07709000 0.24452000 -1.18335 0.11620700 -0.01106000 -0.42897 0.59230900 0.68296200
0.0550 2.192883 1.332603 -0.07585000 0.25047800 -1.17146 0.11400500 -0.01137000 -0.43164 0.60146300 0.68639100
0.0600 2.164618 1.329451 -0.07168000 0.26589700 -1.14287 0.11339100 -0.01179000 -0.42686 0.60562500 0.68874400
0.0650 2.169851 1.332136 -0.06863000 0.28788100 -1.12631 0.11130800 -0.01205000 -0.42078 0.60763400 0.69027700
0.0670 2.159330 1.331516 -0.06817000 0.29447400 -1.11649 0.11084400 -0.01218000 -0.41964 0.60815200 0.68978000
0.0700 2.138568 1.336694 -0.06819000 0.31214000 -1.10021 0.10913800 -0.01237000 -0.41914 0.61004800 0.68803200
0.0750 2.088161 1.370326 -0.06962000 0.34301300 -1.07214 0.10181800 -0.01259000 -0.41729 0.60913500 0.68604000
0.0800 2.013020 1.409712 -0.06915000 0.36648400 -1.04365 0.09311800 -0.01272000 -0.42000 0.60454300 0.68316700
0.0850 1.926213 1.447195 -0.06540000 0.37911800 -1.01749 0.08490100 -0.01277000 -0.42717 0.59996000 0.68264100
0.0900 1.863184 1.490262 -0.06411000 0.41339200 -1.00019 0.07517100 -0.01271000 -0.44537 0.59525600 0.68178700
0.0950 1.816356 1.524769 -0.06400000 0.44298200 -0.98736 0.06745900 -0.01261000 -0.46721 0.58942800 0.68276300
0.1000 1.769731 1.561097 -0.07001000 0.48625300 -0.97568 0.06073600 -0.01250000 -0.49272 0.58237600 0.68358000
0.1100 1.713437 1.627587 -0.07485000 0.52838300 -0.95971 0.04800300 -0.01228000 -0.53342 0.56406700 0.68482000
0.1200 1.650659 1.679477 -0.07830000 0.62138000 -0.94611 0.03595100 -0.01200000 -0.56717 0.54751100 0.68670900
0.1300 1.587248 1.736100 -0.08075000 0.67076800 -0.93659 0.02452600 -0.01167000 -0.61086 0.52868700 0.68824800
0.1303 1.572885 1.750059 -0.08207000 0.68211600 -0.93605 0.02189100 -0.01155000 -0.62402 0.52600300 0.68838000
0.1400 1.552383 1.779373 -0.08622000 0.69997700 -0.93656 0.01664200 -0.01130000 -0.65256 0.51624500 0.68789600
0.1500 1.542832 1.822970 -0.08971000 0.74863400 -0.94369 0.00828200 -0.01093000 -0.68928 0.50509700 0.68942400
0.1600 1.560224 1.853572 -0.09209000 0.76894100 -0.96193 0.00426100 -0.01046000 -0.73004 0.49248800 0.69259000
0.1700 1.579203 1.874846 -0.09809000 0.78589400 -0.98040 0.00282000 -0.01001000 -0.76676 0.47859900 0.69214900
0.1800 1.560126 1.900628 -0.09861000 0.78013100 -0.99052 0.00046300 -0.00964000 -0.79702 0.46530800 0.69022300
0.1900 1.561523 1.913600 -0.10464000 0.79985100 -1.00487 -0.00025000 -0.00923000 -0.82148 0.45437400 0.68465600
0.2000 1.534762 1.937215 -0.10968000 0.82878000 -1.01098 -0.00329000 -0.00888000 -0.84010 0.44301400 0.68059700
0.2200 1.486267 1.990180 -0.12257000 0.86321000 -1.02611 -0.00754000 -0.00824000 -0.87190 0.43256700 0.66935000
0.2400 1.407764 2.026004 -0.12928000 0.84990100 -1.03164 -0.00851000 -0.00786000 -0.91362 0.41991800 0.66273500
0.2500 1.375784 2.032175 -0.13109000 0.86268700 -1.03746 -0.00701000 -0.00766000 -0.93658 0.41548000 0.66200600
0.2600 1.352420 2.047970 -0.13334000 0.87710100 -1.04635 -0.00787000 -0.00740000 -0.95647 0.40921100 0.66013800
0.2800 1.310876 2.087583 -0.13339000 0.90472700 -1.06524 -0.01251000 -0.00685000 -0.97718 0.40352100 0.66127700
0.2900 1.288881 2.100521 -0.13569000 0.90948300 -1.07335 -0.01267000 -0.00658000 -0.98462 0.40096600 0.66060000
0.3000 1.275442 2.114611 -0.14176000 0.92162200 -1.08149 -0.01264000 -0.00637000 -0.98919 0.39883000 0.65986500
0.3200 1.255382 2.138187 -0.15163000 0.92530000 -1.09884 -0.01132000 -0.00595000 -0.99388 0.39422400 0.65689500
0.3400 1.234872 2.175803 -0.15724000 0.91628300 -1.11747 -0.01372000 -0.00551000 -0.99965 0.38489700 0.65633800
0.3500 1.214958 2.188117 -0.15939000 0.89716700 -1.12411 -0.01305000 -0.00532000 -1.00617 0.38438500 0.65620900
0.3600 1.178177 2.198759 -0.16041000 0.87692100 -1.12582 -0.01232000 -0.00519000 -1.01325 0.38563900 0.65527800
0.3800 1.117221 2.213072 -0.16498000 0.83988600 -1.12981 -0.00874000 -0.00498000 -1.02015 0.38538000 0.65455800
0.4000 1.053371 2.231908 -0.16904000 0.83842700 -1.13403 -0.00745000 -0.00477000 -1.02292 0.38398900 0.65644500
0.4200 1.014572 2.248211 -0.17528000 0.84750800 -1.14429 -0.00570000 -0.00452000 -1.02071 0.38116300 0.65503100
0.4400 0.988765 2.263190 -0.18432000 0.85492200 -1.15559 -0.00333000 -0.00427000 -1.01503 0.37938500 0.65371600
0.4500 0.971080 2.271611 -0.18755000 0.85507600 -1.15965 -0.00273000 -0.00418000 -1.01402 0.37821100 0.65322600
0.4600 0.934947 2.278561 -0.18987000 0.86410300 -1.15919 -0.00227000 -0.00411000 -1.01319 0.37542700 0.65263700
0.4800 0.890134 2.282694 -0.19561000 0.85586000 -1.16594 0.00115000 -0.00392000 -1.01115 0.37804600 0.65100100
0.5000 0.837695 2.288490 -0.19402000 0.85597200 -1.17172 0.00211100 -0.00369000 -1.01039 0.37890200 0.64813900
0.5500 0.730056 2.304199 -0.20478000 0.87788100 -1.19033 0.00661400 -0.00308000 -1.01218 0.38382600 0.64484800
0.6000 0.620431 2.321087 -0.20035000 0.84052000 -1.20522 0.01013500 -0.00265000 -1.00922 0.39717400 0.64339000
0.6500 0.515740 2.346797 -0.19738000 0.79998800 -1.21571 0.01357000 -0.00237000 -1.00356 0.40864100 0.63980100
0.6670 0.464230 2.351350 -0.19355000 0.78406800 -1.21478 0.01501100 -0.00231000 -1.00016 0.41360900 0.63869800
0.7000 0.400679 2.363368 -0.18899000 0.77142200 -1.22305 0.01705500 -0.00211000 -0.99075 0.41944700 0.63539300
0.7500 0.263690 2.363957 -0.18745000 0.69625900 -1.22008 0.02550900 -0.00197000 -0.97102 0.42917900 0.63348100
0.8000 0.129816 2.375162 -0.18395000 0.69659900 -1.21642 0.02879900 -0.00189000 -0.94913 0.43599900 0.63299400
0.8500 0.025422 2.392046 -0.17872000 0.66186200 -1.22113 0.03092100 -0.00170000 -0.93538 0.44140600 0.63645800
0.9000 -0.069930 2.411239 -0.17222000 0.62036500 -1.22569 0.03175500 -0.00153000 -0.93452 0.45399700 0.63563800
0.9500 -0.169440 2.440097 -0.16570000 0.59649300 -1.22731 0.02900700 -0.00136000 -0.93139 0.47009100 0.63398700
1.0000 -0.265860 2.458374 -0.16692000 0.60123700 -1.22842 0.02921500 -0.00125000 -0.92189 0.47768700 0.63264900
1.1000 -0.416510 2.470917 -0.16339000 0.55695800 -1.23923 0.03553300 -0.00087000 -0.89927 0.48787700 0.63147600
1.2000 -0.676110 2.489858 -0.14316000 0.54136400 -1.22206 0.03537000 -0.00072000 -0.88874 0.49853000 0.62884300
1.3000 -0.852810 2.521182 -0.13235000 0.51865900 -1.21955 0.03436000 -0.00051000 -0.87598 0.51607900 0.62246900
1.4000 -1.027320 2.541416 -0.11945000 0.55094900 -1.22072 0.03196700 -0.00025000 -0.87443 0.52496000 0.61893700
1.5000 -1.091190 2.533838 -0.11504000 0.56338100 -1.24382 0.03696100 0.00008140 -0.85909 0.53547200 0.61796200
1.6000 -1.203170 2.569142 -0.12202000 0.59349300 -1.25013 0.03601600 0.00027400 -0.83843 0.53827100 0.61437200
1.7000 -1.342010 2.567601 -0.10904000 0.59760200 -1.24860 0.03440000 0.00041600 -0.81596 0.54366400 0.61391700
1.8000 -1.464790 2.583144 -0.11012000 0.58584200 -1.24529 0.03546200 0.00047500 -0.80287 0.54944500 0.61386400
1.9000 -1.588030 2.626960 -0.12239000 0.62424800 -1.24246 0.03210200 0.00058900 -0.80291 0.54388400 0.61357700
2.0000 -1.665130 2.630186 -0.11339000 0.59597700 -1.25353 0.03463800 0.00068900 -0.78964 0.54160400 0.61145600
2.2000 -1.963860 2.603575 -0.06043000 0.61244200 -1.22940 0.03030700 0.00054700 -0.77741 0.54894500 0.61511200
2.4000 -2.200470 2.650725 -0.05391000 0.67350500 -1.20835 0.02147900 0.00048400 -0.76743 0.55054600 0.61181100
2.5000 -2.394560 2.662607 -0.05076000 0.69011300 -1.16970 0.01964100 0.00014000 -0.74665 0.55237900 0.61151800
2.6000 -2.518890 2.699475 -0.06517000 0.76896700 -1.15124 0.01503400 0.00001320 -0.73657 0.55053000 0.60974800
2.8000 -2.632480 2.659062 -0.04832000 0.80778700 -1.15291 0.01954700 -0.00013000 -0.69291 0.51851600 0.61430300
3.0000 -2.841610 2.639776 -0.03570000 0.85876400 -1.12781 0.02050000 -0.00043000 -0.68331 0.51793400 0.61678100
3.2000 -3.079350 2.656785 -0.02557000 0.91052300 -1.09559 0.01631800 -0.00069000 -0.66901 0.51229200 0.61741600
3.4000 -3.053530 2.708866 -0.05286000 0.94438500 -1.11408 0.01575500 -0.00066000 -0.65883 0.51883900 0.61307300
3.5000 -3.123440 2.700877 -0.04946000 0.96057000 -1.10921 0.01845800 -0.00074000 -0.65059 0.51995800 0.60896600
3.6000 -3.315890 2.703451 -0.03308000 0.98451700 -1.07375 0.01543600 -0.00097000 -0.63882 0.53285400 0.60589900
3.8000 -3.428990 2.646549 -0.02495000 0.97546100 -1.06479 0.02724100 -0.00115000 -0.63825 0.53727300 0.59715100
4.0000 -3.599560 2.629226 -0.02208000 0.97803700 -1.04398 0.03440400 -0.00134000 -0.62463 0.52996100 0.59149600
""")
class FukushimaTanaka1990(GMPE):
"""
Implements the PGA GMPE of Fukushima and Tanaka (1990)
Fukushima, Y. and Tanaka, T. (1990) A New Attenuation Relation for Peak
Horizontal Acceleration of Strong Earthquake Ground Motion in Japan.
Bulletin of the Seismological Society of America, 80(4), 757 - 783
"""
#: The GMPE is derived from shallow earthquakes in California and Japan
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
])
#: Supported intensity measure component is the average horizontal
#: component
#: :attr:`openquake.hazardlib.const.IMC.AVERAGE_HORIZONTAL`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types is total.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: Required site parameters. The GMPE was developed for an ''average''
#: site conditions. The authors specify that for rock sites the
#: values should be lowered by 40 % and for soil site they should be
#: raised by 40 %. For greatest consistencty the site condition is
#: neglected currently but a site-dependent GMPE may be implemented
#: inside a subclass.
REQUIRES_SITES_PARAMETERS = set(())
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is rupture distance
REQUIRES_DISTANCES = set(('rrup',))
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.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
C = self.COEFFS[imt]
imean = (self._compute_magnitude_scaling(C, rup.mag) +
self._compute_distance_scaling(C, dists.rrup, rup.mag))
# Original GMPE returns log10 acceleration in cm/s/s
# Converts to natural logarithm of g
mean = np.log((10.0 ** (imean - 2.0)) / g)
istddevs = self._compute_stddevs(
C, dists.rrup.shape, stddev_types
)
# Convert from common logarithm to natural logarithm
stddevs = np.log(10 ** np.array(istddevs))
return mean, stddevs
def _compute_magnitude_scaling(self, C, mag):
"""
Returns the magnitude scaling term
"""
return C["c1"] * mag + C["c5"]
def _compute_distance_scaling(self, C, rrup, mag):
"""
Returns the distance scaling term
"""
rscale1 = rrup + C["c2"] * (10.0 ** (C["c3"] * mag))
return -np.log10(rscale1) - (C["c4"] * rrup)
def _compute_stddevs(self, C, num_sites, stddev_types):
"""
Return total standard deviation.
"""
std_total = C['sigma']
stddevs = []
for _ in stddev_types:
stddevs.append(np.zeros(num_sites) + std_total)
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c1 c2 c3 c4 c5 sigma
pga 0.41 0.032 0.41 0.0034 1.30 0.21
""")
class FaccioliCauzzi2006(GMPE):
"""
Implements "Macroseismic Intensities for seismic scenarios estimated from
instrumentally based correlations" by E. Faccioli and C. Cauzzi
First European Conference on Earthquake Engineering and Seismology
Geneva, Switzerland, 3-8 September 2006
Paper Number: 569
Implemented by [email protected]
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {MMI}
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
REQUIRES_SITES_PARAMETERS = set()
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
REQUIRES_DISTANCES = {'repi'}
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)
stddevs = self._get_stddevs(C,
stddev_types,
num_sites=dists.repi.shape)
return mean, stddevs
def _compute_mean(self, C, rup, dists):
"""
Compute mean value defined by equation 1/page 414
no amplification factor is applied to the equation
hence the S-factor = 0
"""
d = np.sqrt(dists.repi**2 + C['h']**2)
term01 = C['c3'] * (np.log(d))
mean = C['c1'] + C['c2'] * rup.mag + term01
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((C['sigma']) + np.zeros(num_sites))
return stddevs
#: Coefficient table constructed from the electronic suplements of the
#: original paper - coeff in the same order as in Table 4/page 703
#: for Maw only (read last paragraph on page 701 -
#: expains what Maw should be used)
COEFFS = CoeffsTable(table="""\
IMT c1 c2 c3 h sigma
MMI 1.0157 1.2566 -0.6547 2 0.5344
""")
class ChiouYoungs2008(GMPE):
"""
Implements GMPE developed by Brian S.-J. Chiou and Robert R. Youngs
and published as "An NGA Model for the Average Horizontal Component
of Peak Ground Motion and Response Spectra" (2008, Earthquake Spectra,
Volume 24, No. 1, pages 173-215).
"""
#: Supported tectonic region type is active shallow crust, see page 174.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: peak ground velocity and peak ground acceleration, see tables
#: at pages 198 and 199.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV, SA])
#: Supported intensity measure component is orientation-independent
#: measure :attr:`~openquake.hazardlib.const.IMC.GMRotI50`, see page 174.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.GMRotI50
#: Supported standard deviation types are inter-event, intra-event
#: and total, see chapter "Variance model".
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
DEFINED_FOR_REFERENCE_VELOCITY = 1130.
#: Required site parameters are Vs30 (eq. 13b), Vs30 measured flag (eq. 20)
#: and Z1.0 (eq. 13b).
REQUIRES_SITES_PARAMETERS = {'vs30', 'vs30measured', 'z1pt0'}
#: Required rupture parameters are magnitude, rake (eq. 13a and 13b),
#: dip (eq. 13a) and ztor (eq. 13a).
REQUIRES_RUPTURE_PARAMETERS = {'dip', 'rake', 'mag', 'ztor'}
#: Required distance measures are RRup, Rjb and Rx (all are in eq. 13a).
REQUIRES_DISTANCES = {'rrup', 'rjb', 'rx'}
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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
# intensity on a reference soil is used for both mean
# and stddev calculations.
ln_y_ref = self._get_ln_y_ref(rup, dists, C)
# exp1 and exp2 are parts of eq. 10 and eq. 13b,
# calculate it once for both.
exp1 = np.exp(C['phi3'] * (sites.vs30.clip(-np.inf, 1130) - 360))
exp2 = np.exp(C['phi3'] * (1130 - 360))
mean = self._get_mean(sites, C, ln_y_ref, exp1, exp2)
stddevs = self._get_stddevs(sites, rup, C, stddev_types, ln_y_ref,
exp1, exp2)
return mean, stddevs
def _get_mean(self, sites, C, ln_y_ref, exp1, exp2):
"""
Add site effects to an intensity.
Implements eq. 13b.
"""
# we do not support estimating of basin depth and instead
# rely on it being available (since we require it).
z1pt0 = sites.z1pt0
# we consider random variables being zero since we want
# to find the exact mean value.
eta = epsilon = 0
ln_y = (
# first line of eq. 13b
ln_y_ref + C['phi1'] * np.log(sites.vs30 / 1130).clip(-np.inf, 0)
# second line
+ C['phi2'] * (exp1 - exp2) * np.log(
(np.exp(ln_y_ref) + C['phi4']) / C['phi4'])
# third line
+ C['phi5'] *
(1.0 - 1.0 / np.cosh(C['phi6'] *
(z1pt0 - C['phi7']).clip(0, np.inf))) +
C['phi8'] / np.cosh(0.15 * (z1pt0 - 15).clip(0, np.inf))
# fourth line
+ eta + epsilon)
return ln_y
def _get_stddevs(self, sites, rup, C, stddev_types, ln_y_ref, exp1, exp2):
"""
Get standard deviation for a given intensity on reference soil.
Implements equations 19, 20 and 21 for inter-event, intra-event
and total standard deviations respectively.
"""
# aftershock flag is zero, we consider only main shock.
AS = 0
Fmeasured = sites.vs30measured
Finferred = 1 - sites.vs30measured
# eq. 19 to calculate inter-event standard error
mag_test = min(max(rup.mag, 5.0), 7.0) - 5.0
tau = C['tau1'] + (C['tau2'] - C['tau1']) / 2 * mag_test
# b and c coeffs from eq. 10
b = C['phi2'] * (exp1 - exp2)
c = C['phi4']
y_ref = np.exp(ln_y_ref)
# eq. 20
NL = b * y_ref / (y_ref + c)
sigma = (
# first line of eq. 20
(C['sig1'] + 0.5 *
(C['sig2'] - C['sig1']) * mag_test + C['sig4'] * AS)
# second line
* np.sqrt((C['sig3'] * Finferred + 0.7 * Fmeasured) + (1 + NL)**2))
ret = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
# eq. 21
ret += [np.sqrt(((1 + NL)**2) * (tau**2) + (sigma**2))]
elif stddev_type == const.StdDev.INTRA_EVENT:
ret.append(sigma)
elif stddev_type == const.StdDev.INTER_EVENT:
# this is implied in eq. 21
ret.append(np.abs((1 + NL) * tau))
return ret
def _get_ln_y_ref(self, rup, dists, C):
"""
Get an intensity on a reference soil.
Implements eq. 13a.
"""
# reverse faulting flag
Frv = 1 if 30 <= rup.rake <= 150 else 0
# normal faulting flag
Fnm = 1 if -120 <= rup.rake <= -60 else 0
# hanging wall flag
Fhw = (dists.rx >= 0)
# aftershock flag. always zero since we only consider main shock
AS = 0
ln_y_ref = (
# first line of eq. 13a
C['c1'] + (C['c1a'] * Frv + C['c1b'] * Fnm + C['c7'] *
(rup.ztor - 4)) * (1 - AS) + (C['c10'] + C['c7a'] *
(rup.ztor - 4)) * AS
# second line
+ C['c2'] * (rup.mag - 6) + ((C['c2'] - C['c3']) / C['cn']) *
np.log(1 + np.exp(C['cn'] * (C['cm'] - rup.mag)))
# third line
+ C['c4'] * np.log(dists.rrup + C['c5'] *
np.cosh(C['c6'] * max(rup.mag - C['chm'], 0)))
# fourth line
+
(C['c4a'] - C['c4']) * np.log(np.sqrt(dists.rrup**2 + C['crb']**2))
# fifth line
+ (C['cg1'] + C['cg2'] /
(np.cosh(max(rup.mag - C['cg3'], 0)))) * dists.rrup
# sixth line
+ C['c9'] * Fhw *
np.tanh(dists.rx * (np.cos(np.radians(rup.dip))**2) / C['c9a']) *
(1 - np.sqrt(dists.rjb**2 + rup.ztor**2) / (dists.rrup + 0.001)))
return ln_y_ref
#: Coefficient tables are constructed from values in tables 1, 2 and 3
#: (pages 197, 198 and 199). Spectral acceleration is defined for damping
#: of 5%, see page 208.
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT c2 c3 c4 c4a crb chm cg3 c1 c1a c1b cn cm c5 c6 c7 c7a c9 c9a c10 cg1 cg2 phi1 phi2 phi3 phi4 phi5 phi6 phi7 phi8 tau1 tau2 sig1 sig2 sig3 sig4
pga 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.2687 0.1000 -0.2550 2.996 4.1840 6.1600 0.4893 0.0512 0.0860 0.7900 1.5005 -0.3218 -0.00804 -0.00785 -0.4417 -0.1417 -0.007010 0.102151 0.2289 0.014996 580.0 0.0700 0.3437 0.2637 0.4458 0.3459 0.8000 0.0663
pgv 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 2.2884 0.1094 -0.0626 1.648 4.2979 5.1700 0.4407 0.0207 0.0437 0.3079 2.6690 -0.1166 -0.00275 -0.00625 -0.7861 -0.0699 -0.008444 5.410000 0.2899 0.006718 459.0 0.1138 0.2539 0.2381 0.4496 0.3554 0.7504 0.0133
0.010 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.2687 0.1000 -0.2550 2.996 4.1840 6.1600 0.4893 0.0512 0.0860 0.7900 1.5005 -0.3218 -0.00804 -0.00785 -0.4417 -0.1417 -0.007010 0.102151 0.2289 0.014996 580.0 0.0700 0.3437 0.2637 0.4458 0.3459 0.8000 0.0663
0.020 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.2515 0.1000 -0.2550 3.292 4.1879 6.1580 0.4892 0.0512 0.0860 0.8129 1.5028 -0.3323 -0.00811 -0.00792 -0.4340 -0.1364 -0.007279 0.108360 0.2289 0.014996 580.0 0.0699 0.3471 0.2671 0.4458 0.3459 0.8000 0.0663
0.030 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.1744 0.1000 -0.2550 3.514 4.1556 6.1550 0.4890 0.0511 0.0860 0.8439 1.5071 -0.3394 -0.00839 -0.00819 -0.4177 -0.1403 -0.007354 0.119888 0.2289 0.014996 580.0 0.0701 0.3603 0.2803 0.4535 0.3537 0.8000 0.0663
0.040 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.0671 0.1000 -0.2550 3.563 4.1226 6.1508 0.4888 0.0508 0.0860 0.8740 1.5138 -0.3453 -0.00875 -0.00855 -0.4000 -0.1591 -0.006977 0.133641 0.2289 0.014996 579.9 0.0702 0.3718 0.2918 0.4589 0.3592 0.8000 0.0663
0.050 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -0.9464 0.1000 -0.2550 3.547 4.1011 6.1441 0.4884 0.0504 0.0860 0.8996 1.5230 -0.3502 -0.00912 -0.00891 -0.3903 -0.1862 -0.006467 0.148927 0.2290 0.014996 579.9 0.0701 0.3848 0.3048 0.4630 0.3635 0.8000 0.0663
0.075 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -0.7051 0.1000 -0.2540 3.448 4.0860 6.1200 0.4872 0.0495 0.0860 0.9442 1.5597 -0.3579 -0.00973 -0.00950 -0.4040 -0.2538 -0.005734 0.190596 0.2292 0.014996 579.6 0.0686 0.3878 0.3129 0.4702 0.3713 0.8000 0.0663
0.10 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -0.5747 0.1000 -0.2530 3.312 4.1030 6.0850 0.4854 0.0489 0.0860 0.9677 1.6104 -0.3604 -0.00975 -0.00952 -0.4423 -0.2943 -0.005604 0.230662 0.2297 0.014996 579.2 0.0646 0.3835 0.3152 0.4747 0.3769 0.8000 0.0663
0.15 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -0.5309 0.1000 -0.2500 3.044 4.1717 5.9871 0.4808 0.0479 0.0860 0.9660 1.7549 -0.3565 -0.00883 -0.00862 -0.5162 -0.3113 -0.005845 0.266468 0.2326 0.014988 577.2 0.0494 0.3719 0.3128 0.4798 0.3847 0.8000 0.0612
0.20 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -0.6352 0.1000 -0.2449 2.831 4.2476 5.8699 0.4755 0.0471 0.0860 0.9334 1.9157 -0.3470 -0.00778 -0.00759 -0.5697 -0.2927 -0.006141 0.255253 0.2386 0.014964 573.9 -0.0019 0.3601 0.3076 0.4816 0.3902 0.8000 0.0530
0.25 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -0.7766 0.1000 -0.2382 2.658 4.3184 5.7547 0.4706 0.0464 0.0860 0.8946 2.0709 -0.3379 -0.00688 -0.00671 -0.6109 -0.2662 -0.006439 0.231541 0.2497 0.014881 568.5 -0.0479 0.3522 0.3047 0.4815 0.3946 0.7999 0.0457
0.30 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -0.9278 0.0999 -0.2313 2.505 4.3844 5.6527 0.4665 0.0458 0.0860 0.8590 2.2005 -0.3314 -0.00612 -0.00598 -0.6444 -0.2405 -0.006704 0.207277 0.2674 0.014639 560.5 -0.0756 0.3438 0.3005 0.4801 0.3981 0.7997 0.0398
0.40 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.2176 0.0997 -0.2146 2.261 4.4979 5.4997 0.4607 0.0445 0.0850 0.8019 2.3886 -0.3256 -0.00498 -0.00486 -0.6931 -0.1975 -0.007125 0.165464 0.3120 0.013493 540.0 -0.0960 0.3351 0.2984 0.4758 0.4036 0.7988 0.0312
0.50 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.4695 0.0991 -0.1972 2.087 4.5881 5.4029 0.4571 0.0429 0.0830 0.7578 2.5000 -0.3189 -0.00420 -0.00410 -0.7246 -0.1633 -0.007435 0.133828 0.3610 0.011133 512.9 -0.0998 0.3353 0.3036 0.4710 0.4079 0.7966 0.0255
0.75 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -1.9278 0.0936 -0.1620 1.812 4.7571 5.2900 0.4531 0.0387 0.0690 0.6788 2.6224 -0.2702 -0.00308 -0.00301 -0.7708 -0.1028 -0.008120 0.085153 0.4353 0.006739 441.9 -0.0765 0.3429 0.3205 0.4621 0.4157 0.7792 0.0175
1.0 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -2.2453 0.0766 -0.1400 1.648 4.8820 5.2480 0.4517 0.0350 0.0450 0.6196 2.6690 -0.2059 -0.00246 -0.00241 -0.7990 -0.0699 -0.008444 0.058595 0.4629 0.005749 391.8 -0.0412 0.3577 0.3419 0.4581 0.4213 0.7504 0.0133
1.5 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -2.7307 0.0022 -0.1184 1.511 5.0697 5.2194 0.4507 0.0280 0.0134 0.5101 2.6985 -0.0852 -0.00180 -0.00176 -0.8382 -0.0425 -0.007707 0.031787 0.4756 0.005544 348.1 0.0140 0.3769 0.3703 0.4493 0.4213 0.7136 0.0090
2.0 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -3.1413 -0.0591 -0.1100 1.470 5.2173 5.2099 0.4504 0.0213 0.0040 0.3917 2.7085 0.0160 -0.00147 -0.00143 -0.8663 -0.0302 -0.004792 0.019716 0.4785 0.005521 332.5 0.0544 0.4023 0.4023 0.4459 0.4213 0.7035 0.0068
3.0 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -3.7413 -0.0931 -0.1040 1.456 5.4385 5.2040 0.4501 0.0106 0.0010 0.1244 2.7145 0.1876 -0.00117 -0.00115 -0.9032 -0.0129 -0.001828 0.009643 0.4796 0.005517 324.1 0.1232 0.4406 0.4406 0.4433 0.4213 0.7006 0.0045
4.0 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -4.1814 -0.0982 -0.1020 1.465 5.5977 5.2020 0.4501 0.0041 0.0000 0.0086 2.7164 0.3378 -0.00107 -0.00104 -0.9231 -0.0016 -0.001523 0.005379 0.4799 0.005517 321.7 0.1859 0.4784 0.4784 0.4424 0.4213 0.7001 0.0034
5.0 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -4.5187 -0.0994 -0.1010 1.478 5.7276 5.2010 0.4500 0.0010 0.0000 0.0000 2.7172 0.4579 -0.00102 -0.00099 -0.9222 0.0000 -0.001440 0.003223 0.4799 0.005517 320.9 0.2295 0.5074 0.5074 0.4420 0.4213 0.7000 0.0027
7.5 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -5.1224 -0.0999 -0.1010 1.498 5.9891 5.2000 0.4500 0.0000 0.0000 0.0000 2.7177 0.7514 -0.00096 -0.00094 -0.8346 0.0000 -0.001369 0.001134 0.4800 0.005517 320.3 0.2660 0.5328 0.5328 0.4416 0.4213 0.7000 0.0018
10.0 1.06 3.45 -2.1 -0.5 50.0 3.0 4.0 -5.5872 -0.1000 -0.1000 1.502 6.1930 5.2000 0.4500 0.0000 0.0000 0.0000 2.7180 1.1856 -0.00094 -0.00091 -0.7332 0.0000 -0.001361 0.000515 0.4800 0.005517 320.1 0.2682 0.5542 0.5542 0.4414 0.4213 0.7000 0.0014
""")
class SomervilleEtAl2009NonCratonic(GMPE):
"""
Implements GMPE developed by P. Somerville, R. Graves, N. Collins, S. G.
Song, S. Ni, and P. Cummins for Non-Cratonic Australia published in "Source
and Ground Motion Models for Australian Earthquakes", Report to Geoscience
Australia (2009). Document available at:
http://www.ga.gov.au/cedda/publications/193?yp=2009
"""
#: The supported tectonic region type is stable continental region
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: The supported intensity measure types are PGA, PGV, and SA, see table
#: 3
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV, SA])
#: The supported intensity measure component is set to 'average
#: horizontal', however the original paper does not report this information
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: The supported standard deviations is total, see tables 3
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([const.StdDev.TOTAL])
#: no site parameters are defined, the GMPE is calibrated for Vs30 = 865
#: m/s
REQUIRES_SITES_PARAMETERS = set()
#: The required rupture parameter is magnitude, see table 2
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: The required distance parameter is 'Joyner-Boore' distance, see table 2
REQUIRES_DISTANCES = set(('rjb', ))
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.
Implement equations as defined in table 2.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
C = self.COEFFS[imt]
mean = self._compute_mean(C, rup.mag, dists.rjb)
stddevs = self._get_stddevs(C, stddev_types, dists.rjb.shape[0])
return mean, stddevs
def _compute_mean(self, C, mag, rjb):
"""
Compute mean value, see table 2.
"""
m1 = 6.4
r1 = 50.
h = 6.
R = np.sqrt(rjb**2 + h**2)
R1 = np.sqrt(r1**2 + h**2)
less_r1 = rjb < r1
ge_r1 = rjb >= r1
mean = (C['c1'] + C['c4'] * (mag - m1) * np.log(R) + C['c5'] * rjb +
C['c8'] * (8.5 - mag)**2)
mean[less_r1] += C['c3'] * np.log(R[less_r1])
mean[ge_r1] += (C['c3'] * np.log(R1) + C['c6'] *
(np.log(R[ge_r1]) - np.log(R1)))
if mag < m1:
mean += C['c2'] * (mag - m1)
else:
mean += C['c7'] * (mag - m1)
return mean
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return total standard deviation.
"""
stddevs = []
for _ in stddev_types:
stddevs.append(np.zeros(num_sites) + C['sigma'])
return stddevs
#: Coefficients taken from table 3
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 sigma
pgv 5.07090 0.52780 -0.85740 0.17700 -0.00501 -0.61190 0.80660 -0.03800 0.6417
pga 1.03780 -0.03970 -0.79430 0.14450 -0.00618 -0.72540 -0.03590 -0.09730 0.5685
0.010 1.05360 -0.04190 -0.79390 0.14450 -0.00619 -0.72660 -0.03940 -0.09740 0.5684
0.020 1.05680 -0.03920 -0.79680 0.14550 -0.00617 -0.73230 -0.03930 -0.09600 0.5684
0.030 1.13530 -0.04790 -0.80920 0.15000 -0.00610 -0.76410 -0.05710 -0.09210 0.5681
0.040 1.30000 -0.07020 -0.83150 0.15920 -0.00599 -0.82850 -0.09810 -0.08530 0.5676
0.050 1.47680 -0.09310 -0.83330 0.15600 -0.00606 -0.86740 -0.12740 -0.09130 0.5670
0.075 1.70220 -0.05160 -0.80720 0.14560 -0.00655 -0.87690 -0.10970 -0.08690 0.5663
0.100 1.65720 0.15080 -0.77590 0.13100 -0.00708 -0.77830 0.01690 -0.05980 0.5659
0.150 1.94440 -0.09620 -0.75000 0.11670 -0.00698 -0.69490 -0.13320 -0.12530 0.5659
0.200 1.82720 -0.06230 -0.73430 0.11940 -0.00677 -0.64380 -0.09570 -0.11920 0.5669
0.250 1.74380 -0.02530 -0.72480 0.11950 -0.00646 -0.63740 -0.06250 -0.11650 0.5678
0.3003 1.80560 -0.27020 -0.73190 0.13490 -0.00606 -0.66440 -0.17470 -0.14340 0.5708
0.400 1.88750 -0.37820 -0.70580 0.09960 -0.00589 -0.58770 -0.24420 -0.21890 0.5697
0.500 2.03760 -0.79590 -0.69730 0.11470 -0.00565 -0.59990 -0.48670 -0.29690 0.5739
0.750 1.93060 -0.80280 -0.74510 0.11220 -0.00503 -0.59460 -0.50120 -0.34990 0.5876
1.000 1.60380 -0.47800 -0.86950 0.07320 -0.00569 -0.41590 0.06360 -0.33730 0.6269
1.4993 0.47740 0.90960 -1.02440 0.11060 -0.00652 -0.19000 1.09610 -0.10660 0.7517
2.000 -0.25810 1.37770 -1.01000 0.10310 -0.00539 -0.27340 1.50330 -0.04530 0.8036
3.0003 -0.96360 1.14690 -0.88530 0.10380 -0.00478 -0.40420 1.54130 -0.11020 0.8219
4.000 -1.46140 1.07950 -0.80490 0.10960 -0.00395 -0.46040 1.41960 -0.14700 0.8212
5.000 -1.61160 0.74860 -0.78100 0.09650 -0.00307 -0.46490 1.24090 -0.22170 0.8240
7.5019 -2.35310 0.35190 -0.64340 0.09590 -0.00138 -0.68260 0.92880 -0.31230 0.7957
10.000 -3.26140 0.69730 -0.62760 0.12920 -0.00155 -0.61980 1.01050 -0.24550 0.7602
""")
class NullGMPE(GMPE):
"""
This is a GMPE for testing. It returns the mean and stddevs
specified in the constructor.
"""
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV, SA])
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = \
const.IMC.GREATER_OF_TWO_HORIZONTAL
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
REQUIRES_SITES_PARAMETERS = set(('vs30', ))
REQUIRES_RUPTURE_PARAMETERS = set(())
REQUIRES_DISTANCES = set(('rjb', ))
def __init__(self, mean=0, phi=0.8, tau=0.6):
"""
The default constructor takes three named arguments:
Args:
mean (float): the mean value returned by the GMPE (default=0).
This value is returned for all locations, regardles of
the IMT or the contents of sites, rupture and distance
contexts.
phi (float): the within-event standard deviation returned by the
GMPE (default=0.8)
tau (float): the between-event standard deviation returned by the
GMPE (default=0.6)
The total standard deviation returned will be ``sqrt(phi^2 + tau^2)``.
"""
self.mean = mean
self.phi = phi
self.tau = tau
self.sigma = np.sqrt(phi**2 + tau**2)
def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
Implements the OpenQuake GroundShakingIntensityModel
get_mean_and_stddevs interface. See superclass
`method <http://docs.openquake.org/oq-hazardlib/master/gsim/index.html#openquake.hazardlib.gsim.base.GroundShakingIntensityModel.get_mean_and_stddevs>`__.
Returns a constant values for all locations specified in
the dists.rbj array, regardless of the contents of that array or
any of the other contexts. The imt is also ignored.
""" # noqa
mean = np.full_like(dists.rjb, self.mean)
stddevs = []
for stddev_type in stddev_types:
if stddev_type == const.StdDev.TOTAL:
stddevs.append(
np.full_like(dists.rjb,
np.sqrt(self.phi**2 + self.tau**2)))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.full_like(dists.rjb, self.phi))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.full_like(dists.rjb, self.tau))
return mean, stddevs
#
# Dummy COEFFS table so MultiGMPE won't complain
#
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT c1
pga 0.
pgv 0.
0.01 0.
10 0.
""")
class GulerceEtAl2017(GMPE):
"""
Implements the GKAS16 GMPE by Gulerce et al. (2017) for vertical-component
ground motions from the PEER NGA-West2 Project.
This model follows the same functional form as in ASK14 by Abrahamson et
al. (2014) with minor modifications to the underlying parameters.
Note that this is a more updated version than the GMPE described in the
original PEER Report 2013/24.
**Reference:**
Gulerce, Z., Kamai, R., Abrahamson, N., & Silva, W. (2017). Ground Motion
Prediction Equations for the Vertical Ground Motion Component Based on the
NGA-W2 Database. *Earthquake Spectra*, *33*(2), 499-528.
"""
#: Supported tectonic region type is active shallow crust, as part of the
#: NGA-West2 Database; re-defined here for clarity.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure type is spectral acceleration
#: at T=0.01 to 10.0 s; see Tables 1a and 1b.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {SA}
#: Supported intensity measure component is the
#: :attr:`~openquake.hazardlib.const.IMC.Vertical` direction component;
#: see title.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.VERTICAL
#: Supported standard deviation types are inter-event, intra-event
#: and total; see the section for "Equations for Standard Deviation".
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
#: Required site parameter is Vs30 only. Unlike in ASK14, the nonlinear
#: site response and Z1.0 scaling is not incorporated; see the section
#: for "Site Amplification Effects".
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude, rake, dip, ztor, and width;
#: see the section for "Functional Form of the Model".
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'dip', 'ztor', 'width'}
#: Required distance measures are Rrup, Rjb, Ry0 and Rx;
#: see the section for "Functional Form of the Model".
REQUIRES_DISTANCES = {'rrup', 'rjb', 'rx', 'ry0'}
def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
"""
See :meth:`superclass method
for spec of input and result values.
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
"""
# get the necessary set of coefficients
C = self.COEFFS[imt]
# get the mean value
mean = (self._get_basic_term(C, rup, dists) +
self._get_faulting_style_term(C, rup) +
self._get_site_response_term(C, imt, sites.vs30) +
self._get_hanging_wall_term(C, dists, rup) +
self._get_top_of_rupture_depth_term(C, imt, rup))
mean += self._get_regional_term(C, imt, sites.vs30, dists.rrup)
# get standard deviations
stddevs = self._get_stddevs(C, imt, rup, sites, stddev_types, dists)
return mean, stddevs
def _get_basic_term(self, C, rup, dists):
"""
Compute and return basic form, see Equation 11 to 13.
"""
# Fictitious depth calculation, Equation 13. Unlike ASK14, the break in
# the c4m function is shifted to M6.0.
# The equation for c4m for M4.0-6.0 is different from GKAS16 EQS paper,
# but used the supplementary material instead after code verification.
if rup.mag > 6.:
c4m = C['c4']
elif rup.mag > 4.:
c4m = C['c4'] - ((C['c4'] - 1.) * (6. - rup.mag) / (6. - 4.))
else:
c4m = 1.
# Equation 12
R = np.sqrt(dists.rrup**2. + c4m**2.)
# basic form, Equation 11
base_term = C['a1'] * np.ones_like(dists.rrup) + C['a17'] * dists.rrup
if rup.mag >= self.CONSTS['m1']:
base_term += (C['a5'] * (rup.mag - self.CONSTS['m1']) + C['a8'] *
(8.5 - rup.mag)**2. +
(C['a2'] + C['a3'] *
(rup.mag - self.CONSTS['m1'])) * np.log(R))
elif rup.mag >= self.CONSTS['m2']:
base_term += (C['a4'] * (rup.mag - self.CONSTS['m1']) + C['a8'] *
(8.5 - rup.mag)**2. +
(C['a2'] + C['a3'] *
(rup.mag - self.CONSTS['m1'])) * np.log(R))
else:
base_term += (
C['a4'] * (self.CONSTS['m2'] - self.CONSTS['m1']) + C['a8'] *
(8.5 - self.CONSTS['m2'])**2. + C['a6'] *
(rup.mag - self.CONSTS['m2']) +
(C['a2'] + C['a3'] *
(self.CONSTS['m2'] - self.CONSTS['m1'])) * np.log(R))
return base_term
def _get_faulting_style_term(self, C, rup):
"""
Compute and return faulting style term, that is the sum of the second
and third terms in Equation 1.
"""
# this implements Equations 3 and 4;
# f7 is the term for reverse fault mechanisms;
# f8 is the term for normal fault mechanisms.
if rup.mag > 5.:
f7 = C['a11']
f8 = C['a12']
elif rup.mag >= 4.:
f7 = C['a11'] * (rup.mag - 4.)
f8 = C['a12'] * (rup.mag - 4.)
else:
f7 = 0.0
f8 = 0.0
# ranges of rake values for each faulting mechanism are same with ASK14
return (f7 * float(rup.rake > 30 and rup.rake < 150) +
f8 * float(rup.rake > -150 and rup.rake < -30))
def _get_vs30star(self, vs30, imt):
"""
This computes and returns the tapered Vs30, in Equations 15 and 16.
"""
# compute the limiting v1 value, see Equation 16.
t = imt.period
if t <= 0.50:
v1 = 1500.0
elif t < 3.0:
# changed to -0.351 for additional significant figures
v1 = np.exp(-0.351 * np.log(t / 0.5) + np.log(1500.))
else:
v1 = 800.0
# set the vs30 star value, see Equation 15.
vs30_star = np.ones_like(vs30) * vs30
vs30_star[vs30 >= v1] = v1
return vs30_star
def _get_site_response_term(self, C, imt, vs30):
"""
Compute and return site response model term; see section
"Site Amplification Effects".
"""
# vs30 star, Equation 15
vs30_star = self._get_vs30star(vs30, imt)
# compute the site term
site_resp_term = np.zeros_like(vs30)
# Unlike ASK14, the site term here is independent of nonlinear response
# parameters b, c, and n.
vs30_rat = vs30_star / C['vlin']
site_resp_term = C['a10'] * np.log(vs30_rat)
return site_resp_term
def _get_hanging_wall_term(self, C, dists, rup):
"""
Compute and return hanging wall model term, see section on
"Hanging Wall Effects".
"""
if rup.dip == 90.0:
return np.zeros_like(dists.rx)
else:
Fhw = np.zeros_like(dists.rx)
Fhw[dists.rx > 0] = 1.
# Compute dip taper t1, Equation 6
T1 = np.ones_like(dists.rx)
T1 *= 60. / 45. if rup.dip <= 30. else (90. - rup.dip) / 45.0
# Compute magnitude taper t2, Equation 7, with a2hw set to 0.2.
T2 = np.zeros_like(dists.rx)
a2hw = 0.2
if rup.mag >= 6.5:
T2 += (1. + a2hw * (rup.mag - 6.5))
elif rup.mag > 5.5:
T2 += (1. + a2hw * (rup.mag - 6.5) - (1. - a2hw) *
(rup.mag - 6.5)**2)
else:
T2 *= 0.
# Compute distance taper t3, Equation 8
T3 = np.zeros_like(dists.rx)
r1 = rup.width * np.cos(np.radians(rup.dip))
# The r2 term is different here from ASK14 where r2 = 3*r1.
r2 = 4. * r1
#
idx = dists.rx < r1
T3[idx] = (np.ones_like(dists.rx)[idx] * self.CONSTS['h1'] +
self.CONSTS['h2'] * (dists.rx[idx] / r1) +
self.CONSTS['h3'] * (dists.rx[idx] / r1)**2)
#
idx = ((dists.rx >= r1) & (dists.rx <= r2))
T3[idx] = 1. - (dists.rx[idx] - r1) / (r2 - r1)
# Compute depth taper t4, Equation 9
T4 = np.zeros_like(dists.rx)
#
if rup.ztor <= 10.:
T4 += (1. - rup.ztor**2. / 100.)
# Compute off-edge distance taper T5, Equation 10
# ry1 computed same as in ASK14
T5 = np.zeros_like(dists.rx)
ry1 = dists.rx * np.tan(np.radians(20.))
#
idx = (dists.ry0 - ry1) <= 0.0
T5[idx] = 1.
#
idx = (((dists.ry0 - ry1) > 0.0) & ((dists.ry0 - ry1) < 5.0))
T5[idx] = 1. - (dists.ry0[idx] - ry1[idx]) / 5.0
# Finally, compute the hanging wall term, Equation 5
return Fhw * C['a13'] * T1 * T2 * T3 * T4 * T5
def _get_top_of_rupture_depth_term(self, C, imt, rup):
"""
Compute and return top-of-rupture depth term, see section
"Deph Scaling Effects".
"""
if rup.ztor >= 20.0:
return C['a15']
else:
return C['a15'] * rup.ztor / 20.0
def _get_regional_term(self, C, imt, vs30, rrup):
"""
As with ASK14, we assume California as the default region,
hence here the regional term is assumed = 0.
"""
return 0.
def _get_stddevs(self, C, imt, rup, sites, stddev_types, dists):
"""
Return standard deviations as described in section "Equations for
Standard Deviation".
"""
std_intra = self._get_intra_event_std(C, rup.mag)
std_inter = self._get_inter_event_std(C, rup.mag)
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.sqrt(std_intra**2 + std_inter**2))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(std_intra)
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(std_inter)
return stddevs
def _get_intra_event_std(self, C, mag):
"""
Returns intra-event std dev, Phi, Equation 19.
"""
# Intra-event standard deviation model is simplified since the effect
# of nonlinearity of the rock motion is not incorporated
# (Equations 27-30 in ASK14 are not used).
phi = self._get_phi_regional(C, mag)
return phi
def _get_phi_regional(self, C, mag):
"""
Returns regional (default) intra-event standard deviation
"""
if mag < 4:
phi_reg = C['s1']
elif mag <= 6:
phi_reg = C['s1'] + (C['s2_noJP'] - C['s1']) / 2. * (mag - 4.)
else:
phi_reg = C['s2_noJP']
return phi_reg
def _get_inter_event_std(self, C, mag):
"""
Returns inter-event standard deviation, Tau, Equation 20
"""
tau = self._get_tau_regional(C, mag)
return tau
def _get_tau_regional(self, C, mag):
"""
Returns regional (default) inter-event standard deviation
"""
if mag < 5:
tau_reg = C['s3']
elif mag <= 7:
tau_reg = C['s3'] + (C['s4_noJP'] - C['s3']) / 2. * (mag - 5.)
else:
tau_reg = C['s4_noJP']
return tau_reg
#: Coefficients obtained from Tables 1a, 1b, 2, and 3 in
#: Gulerce et al. (2017). This coefficient table is also provided in a free
#: supplementary material distributed by the authors.
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT vlin c c4 a1 a2 a3 a4 a5 a6 a8 a10 a11 a12 a13 a14 a15 a17 a25 a26 a27 a28 a29 a31 a35 s1 s2_all s3 s4_all s2_noJP s4_noJP
0.01 660 2.4 8.6 1.3504 -1.087 0.275 0.121 -0.592 1.78 0 -0.397 -0.2 -0.12 0.67 -0.168 1.1 -0.0062 0.0015 -0.0007 0.0031 0.0035 -0.001 0.252 0.38 0.734 0.52 0.4402 0.3501 0.45 0.3219
0.02 680 2.4 8.6 1.4832 -1.106 0.275 0.111 -0.592 1.78 0 -0.36 -0.2 -0.12 0.67 -0.165 1.1 -0.0064 0.0017 -0.0007 0.0031 0.0035 -0.0009 0.215 0.343 0.734 0.5396 0.4546 0.3586 0.473 0.3328
0.03 770 2.4 8.6 1.7798 -1.15 0.275 0.105 -0.592 1.759 0 -0.34 -0.2 -0.12 0.67 -0.18 1.1 -0.0069 0.0016 -0.0008 0.0032 0.0037 -0.001 0.195 0.323 0.734 0.551 0.4958 0.3904 0.4865 0.3613
0.05 915 2.4 8.6 1.9652 -1.108 0.26 0.148 -0.559 1.708 0 -0.405 -0.2 -0.12 0.67 -0.212 1.1 -0.0092 0.0013 -0.0011 0.003 0.0047 -0.0006 0.26 0.388 0.734 0.5654 0.5365 0.4604 0.5035 0.4108
0.075 960 2.4 8.6 1.7821 -1.006 0.247 0.202 -0.531 1.689 0 -0.46 -0.2 -0.12 0.67 -0.112 1.1 -0.0102 -0.0009 -0.0021 0.003 0.0054 -0.0009 0.315 0.443 0.734 0.5769 0.5078 0.468 0.504 0.3945
0.1 910 2.4 8.6 1.6862 -0.952 0.239 0.258 -0.514 1.742 0 -0.474 -0.2 -0.12 0.67 -0.09 1.1 -0.0097 -0.0014 -0.0035 0.0026 0.0051 -0.0014 0.329 0.457 0.734 0.585 0.4714 0.4165 0.504 0.3621
0.15 740 2.4 8.6 1.6087 -0.94 0.227 0.309 -0.488 1.831 0 -0.474 -0.159 -0.12 0.67 -0.075 1.1 -0.0075 -0.0014 -0.0045 0.002 0.0041 -0.0024 0.329 0.457 0.734 0.585 0.4189 0.3713 0.504 0.3283
0.2 590 2.4 8.6 1.4836 -0.928 0.218 0.346 -0.469 1.937 0 -0.474 -0.129 -0.12 0.67 -0.075 1.1 -0.006 -0.0012 -0.0045 0.002 0.0038 -0.0029 0.329 0.457 0.7098 0.585 0.3955 0.3389 0.504 0.3058
0.25 495 2.4 8.6 1.3777 -0.928 0.211 0.374 -0.454 2.032 0 -0.474 -0.106 -0.12 0.62 -0.075 1.1 -0.0045 -0.0015 -0.0047 0.0015 0.0029 -0.0037 0.329 0.457 0.6909 0.585 0.3819 0.3138 0.504 0.2884
0.3 430 1.8 8.6 1.3091 -0.928 0.206 0.397 -0.443 2.109 0 -0.474 -0.088 -0.12 0.579 -0.075 1.031 -0.0036 -0.0015 -0.0044 0.0013 0.0025 -0.004 0.329 0.457 0.6756 0.585 0.3835 0.2932 0.504 0.2741
0.4 360 1.8 8.6 1.1237 -0.928 0.197 0.434 -0.352 2.227 0 -0.474 -0.059 -0.12 0.515 -0.075 0.922 -0.0024 -0.0015 -0.0034 0.0011 0.0016 -0.0041 0.329 0.457 0.6513 0.585 0.4 0.2608 0.504 0.2516
0.5 340 1.8 8.6 0.961 -0.928 0.19 0.462 -0.281 2.351 0 -0.49 -0.036 -0.12 0.465 -0.075 0.837 -0.0017 -0.0012 -0.0025 0.0007 0.0011 -0.0041 0.345 0.473 0.6325 0.585 0.4277 0.2357 0.5249 0.2342
0.75 330 1.8 8.6 0.6477 -0.928 0.178 0.513 -0.152 2.577 0 -0.575 0.006 -0.12 0.374 -0.06 0.683 -0.001 -0.0002 -0.0006 0 0.0004 -0.0038 0.43 0.558 0.5983 0.611 0.4686 0.19 0.563 0.2025
1 330 1.8 8.6 0.4024 -0.928 0.169 0.6 -0.061 2.7 0 -0.626 0.035 -0.12 0.31 0.017 0.574 -0.001 0 0 0 0.0004 -0.0031 0.481 0.609 0.5741 0.6295 0.5 0.19 0.59 0.18
1.5 330 1.8 8.6 0.0656 -0.928 0.157 0.838 0.068 2.821 0 -0.721 0.076 -0.12 0.219 0.147 0.42 -0.001 0 0 0 0.0004 -0.0023 0.576 0.704 0.5399 0.6555 0.5337 0.19 0.628 0.184
2 330 1.8 8.6 -0.2475 -0.928 0.148 1.006 0.159 2.869 0 -0.73 0.106 -0.12 0.155 0.246 0.311 -0.001 0 0 0 0.0004 -0.0018 0.585 0.713 0.5157 0.674 0.5337 0.19 0.655 0.184
3 330 1.8 8.6 -0.7131 -0.928 0.136 1.244 0.288 2.92 0 -0.649 0.147 -0.12 0.064 0.385 0.157 -0.001 0 0 0 0.0004 -0.0018 0.504 0.632 0.4815 0.7 0.5337 0.19 0.693 0.184
4 330 1.8 8.6 -1.0571 -0.928 0.128 1.413 0.494 2.95 0 -0.575 0.176 -0.12 0 0.484 0.048 -0.001 0 0 0 0.0004 -0.0018 0.43 0.558 0.4572 0.7 0.5337 0.19 0.72 0.184
5 330 1.8 8.6 -1.7084 -0.848 0.121 1.544 0.654 2.95 0 -0.5 0.199 -0.12 0 0.561 -0.037 -0.001 0 0 0 0.0004 -0.0018 0.355 0.483 0.4384 0.7 0.5337 0.19 0.72 0.184
6 330 1.8 8.6 -2.2393 -0.783 0.115 1.651 0.784 2.95 0 -0.427 0.218 -0.12 0 0.624 -0.106 -0.001 0 0 0 0.0004 -0.0018 0.282 0.41 0.4231 0.7 0.5337 0.19 0.72 0.184
7.5 330 1.8 8.6 -2.9456 -0.704 0.109 1.78 0.9425 2.95 0 -0.3185 0.2405 -0.12 0 0.7 -0.19 -0.001 0 0 0 0.0004 -0.0018 0.1735 0.3015 0.4044 0.7 0.5337 0.19 0.72 0.184
10 330 1.8 8.6 -4.0143 -0.6 0.1 1.95 1.15 2.95 0 -0.209 0.27 -0.12 0 0.8 -0.3 -0.001 0 0 0 0.0004 -0.0018 0.064 0.192 0.38 0.7 0.5337 0.19 0.72 0.184
""")
#: equation constants (that are IMT independent)
CONSTS = {
# m1, m2 specified at section "Moderate-to-Large Magnitude Scaling"
'm1': 6.75,
'm2': 5.50,
# h1, h2, h3 specified at section "Hanging Wall Effects"
'h1': +0.25,
'h2': +1.50,
'h3': -0.75,
}
class RietbrockEtAl2013SelfSimilar(GMPE):
"""
Implements the ground motion prediction equation of Rietbrock et al
(2013):
Rietbrock, A., Strasser, F., Edwards, B. (2013) A Stochastic Earthquake
Ground-Motion Prediction Model for the United Kingdom. Bulletin of the
Seismological Society of America, 103(1), 57 -77
The GMPE is derived for the United Kingdom, a low seismicity region.
Consequently ground motions are generated via numerical simulations using
a stochastic point-source model, calibrated with parameters derived from
local weak-motion data. This implementation applies to the case
when stress drop is considered to be self-similar (i.e. independent
of magnitude).
"""
#: Supported tectonic region type is stabe continental crust,
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are spectral acceleration, peak
#: ground acceleration and peak ground velocity.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV, SA])
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
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
])
#: No site parameter is required
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is Rjb
REQUIRES_DISTANCES = set(('rjb', ))
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]
imean = (self._get_magnitude_scaling_term(C, rup.mag) +
self._get_distance_scaling_term(C, dists.rjb, rup.mag))
# 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 imt.name in "SA PGA":
mean = np.log((10.0**(imean - 2.0)) / g)
else:
mean = np.log(10**imean)
stddevs = self._get_stddevs(C, stddev_types, dists.rjb.shape[0])
return mean, stddevs
def _get_magnitude_scaling_term(self, C, mag):
"""
Returns the magnitude scaling component of the model
Equation 10, Page 63
"""
return C["c1"] + (C["c2"] * mag) + (C["c3"] * (mag**2.0))
def _get_distance_scaling_term(self, C, rjb, mag):
"""
Returns the distance scaling component of the model
Equation 10, Page 63
"""
# Depth adjusted distance, equation 11 (Page 63)
rval = np.sqrt(rjb**2.0 + C["c11"]**2.0)
f_0, f_1, f_2 = self._get_distance_segment_coefficients(rval)
return ((C["c4"] + C["c5"] * mag) * f_0 +
(C["c6"] + C["c7"] * mag) * f_1 +
(C["c8"] + C["c9"] * mag) * f_2 + (C["c10"] * rval))
def _get_distance_segment_coefficients(self, rval):
"""
Returns the coefficients describing the distance attenuation shape
for three different distance bins, equations 12a - 12c
"""
# Get distance segment ends
nsites = len(rval)
# Equation 12a
f_0 = np.log10(self.CONSTS["r0"] / rval)
f_0[rval > self.CONSTS["r0"]] = 0.0
# Equation 12b
f_1 = np.log10(rval)
f_1[rval > self.CONSTS["r1"]] = np.log10(self.CONSTS["r1"])
# Equation 12c
f_2 = np.log10(rval / self.CONSTS["r2"])
f_2[rval <= self.CONSTS["r2"]] = 0.0
return f_0, f_1, f_2
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Returns the standard deviation. Original standard deviations are in
logarithms of base 10. Converts to natural logarithm.
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigma = np.sqrt(C["tau"]**2.0 + C["phi"]**2.0)
stddevs.append(np.log(10.0**(sigma + np.zeros(num_sites))))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0**(C["phi"] + np.zeros(num_sites))))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0**(C["tau"] + np.zeros(num_sites))))
return stddevs
# Coefficients from Table 5, Page 64
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 sigma tau phi
pgv -2.9598 0.9039 -0.0434 -1.6243 0.1987 -1.6511 0.1654 -2.4308 0.0851 -0.001472 1.7736 0.347 0.311 0.153
pga -0.0135 0.6889 -0.0488 -1.8987 0.2151 -1.9063 0.1740 -2.0131 0.0887 -0.002747 1.5473 0.436 0.409 0.153
0.03 0.8282 0.5976 -0.0418 -2.1321 0.2159 -2.0530 0.1676 -1.5148 0.1163 -0.004463 1.1096 0.449 0.417 0.167
0.04 0.4622 0.6273 -0.0391 -1.7242 0.1644 -1.6849 0.1270 -1.4513 0.0910 -0.004355 1.1344 0.445 0.417 0.155
0.05 0.2734 0.6531 -0.0397 -1.5932 0.1501 -1.5698 0.1161 -1.5350 0.0766 -0.003939 1.1493 0.442 0.416 0.149
0.06 0.0488 0.6945 -0.0420 -1.4913 0.1405 -1.4807 0.1084 -1.6563 0.0657 -0.003449 1.2154 0.438 0.414 0.143
0.08 -0.2112 0.7517 -0.0460 -1.4151 0.1340 -1.4130 0.1027 -1.7821 0.0582 -0.002987 1.2858 0.433 0.410 0.140
0.10 -0.5363 0.8319 -0.0521 -1.3558 0.1296 -1.3579 0.0985 -1.8953 0.0520 -0.002569 1.3574 0.428 0.405 0.138
0.12 -0.9086 0.9300 -0.0597 -1.3090 0.1264 -1.3120 0.0948 -1.9863 0.0475 -0.002234 1.4260 0.422 0.399 0.138
0.16 -1.3733 1.0572 -0.0698 -1.2677 0.1237 -1.2684 0.0910 -2.0621 0.0434 -0.001944 1.4925 0.416 0.392 0.139
0.20 -1.9180 1.2094 -0.0819 -1.2315 0.1213 -1.2270 0.0872 -2.1196 0.0396 -0.001708 1.5582 0.409 0.384 0.141
0.25 -2.5107 1.3755 -0.0949 -1.1992 0.1189 -1.1881 0.0833 -2.1598 0.0361 -0.001522 1.6049 0.402 0.376 0.144
0.31 -3.1571 1.5549 -0.1087 -1.1677 0.1160 -1.1494 0.0791 -2.1879 0.0328 -0.001369 1.6232 0.395 0.366 0.148
0.40 -3.8516 1.7429 -0.1228 -1.1354 0.1126 -1.1099 0.0746 -2.2064 0.0294 -0.001240 1.6320 0.387 0.356 0.152
0.50 -4.5556 1.9258 -0.1360 -1.1015 0.1084 -1.0708 0.0700 -2.2171 0.0261 -0.001129 1.6109 0.378 0.345 0.156
0.63 -5.2405 2.0926 -0.1471 -1.0659 0.1035 -1.0328 0.0655 -2.2220 0.0229 -0.001033 1.5735 0.369 0.333 0.160
0.79 -5.8909 2.2357 -0.1557 -1.0279 0.0981 -0.9969 0.0612 -2.2229 0.0197 -0.000945 1.5262 0.360 0.320 0.164
1.00 -6.4633 2.3419 -0.1605 -0.9895 0.0925 -0.9665 0.0577 -2.2211 0.0167 -0.000863 1.4809 0.350 0.307 0.168
1.25 -6.9250 2.4037 -0.1612 -0.9545 0.0879 -0.9462 0.0558 -2.2178 0.0139 -0.000785 1.4710 0.341 0.294 0.172
1.59 -7.2960 2.4189 -0.1573 -0.9247 0.0848 -0.9421 0.0567 -2.2137 0.0111 -0.000701 1.5183 0.331 0.280 0.177
2.00 -7.5053 2.3805 -0.1492 -0.9128 0.0855 -0.9658 0.0619 -2.2110 0.0086 -0.000618 1.6365 0.323 0.267 0.181
2.50 -7.5569 2.2933 -0.1376 -0.9285 0.0915 -1.0264 0.0729 -2.2108 0.0067 -0.000535 1.8421 0.315 0.254 0.186
3.13 -7.4510 2.1598 -0.1228 -0.9872 0.1050 -1.1349 0.0914 -2.2141 0.0060 -0.000458 2.1028 0.308 0.242 0.190
4.00 -7.1688 1.9738 -0.1048 -1.1274 0.1325 -1.3132 0.1207 -2.2224 0.0079 -0.000397 2.4336 0.299 0.227 0.195
5.00 -6.8063 1.7848 -0.0879 -1.3324 0.1691 -1.5158 0.1533 -2.2374 0.0142 -0.000387 2.6686 0.291 0.214 0.198
""")
CONSTS = {"r0": 10.0, "r1": 50.0, "r2": 100.0}
class McVerry2006Asc(GMPE):
"""
Implements GMPE developed by G. McVerry, J. Zhao, N.A. Abrahamson,
P. Somerville published as "New Zealand Acceleration Response Spectrum
Attenuation Relations for Crustal and Subduction Zone Earthquakes",
Bulletin of the New Zealand Society for Earthquake Engineering, v.39,
no. 1, p. 1-58, March 2006.
URL: http://www.nzsee.org.nz/db/Bulletin/Archive/39(1)0001.pdf
Last accessed 10 September 2014.
This class implements the GMPE for Active Shallow Crust
earthquakes (Asc suffix).
The GMPE distinguishes between rock, stiff soil and soft soil
which respectively equate to the New Zealand site class combined A/B
C, and D. No model is provided for New Zealand site class E
The rake angle is also taken into account to
distinguish between faulting mechanisms. A hanging-wall term is noted in
the functional form of the model in the paper but is not used at present.
Furthermore, a Rvolc (volcanic path distance) is noted in the functional
form but this is not implemented in the McVerry2006Asc model, it is
implemented in a seperate GMPE McVerry2006Volc where Rvol=Rrup as this
is how it is implemented in Stirling et al. 2012.
This is a legacy class based on the original implementation of McVerry
et al. (2006), where the site terms are incorrectly implemented as
functions of Vs30. The New Zealand site classification boundaries do not
depend on Vs30 and so this class will yield erroneous results for some
site locations. Instead, calling `McVerry2006AscSC` and specifying site
class values in the .ini file will give the correct results.
"""
kind = "asc"
#: Supported tectonic region type for base class is 'active shallow crust'
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are PGA and SA. PGA is assumed to
#: have same coefficients as SA(0.00)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is the stronger of two
#: horizontal components (see Section 6 paragraph 2, page 21)
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = \
const.IMC.GREATER_OF_TWO_HORIZONTAL
#: Supported standard deviation types are Inter, Intra and Total
# (see equations 8-9 page 29)
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT}
#: The legacy implementation of the McVerry model takes vs30 and maps
# to New Zealand's categorical site classification scheme
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude, and rake and hypocentral
# depth rake is for determining fault style flags. Hypo depth is for
# subduction GMPEs
REQUIRES_RUPTURE_PARAMETERS = {'mag', 'rake', 'hypo_depth'}
#: Required distance measure is RRup (paragraphy 3, page 26) which is
# defined as nearest distance to the source.
REQUIRES_DISTANCES = {'rrup'}
def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
# Compute SA with primed coeffs and PGA with both unprimed and
# primed coeffs
C_PGA = self.COEFFS_PRIMED[PGA()]
C_PGA_unprimed = self.COEFFS_UNPRIMED[PGA()]
for m, imt in enumerate(imts):
C = self.COEFFS_PRIMED[imt]
# Get S term to determine if consider site term is applied
S = _get_site_class(self.kind, ctx)
# Abrahamson and Silva (1997) hanging wall term. This is not used
# in the latest version of GMPE but is defined in functional form
# in the paper so we keep it here as a placeholder
f4HW = _compute_f4(C, ctx.mag, ctx.rrup)
# Flags for rake angles
CN, CR = _get_fault_mechanism_flags(ctx.rake)
# Get volcanic path distance
rvol = ctx.rrup if self.kind.startswith("vol") else 0.
# Get delta_C and delta_D terms for site class
delta_C, delta_D = _get_deltas(self.kind, ctx)
# Compute lnPGA_ABCD primed
lnPGAp_ABCD = _compute_mean(
self.kind, C_PGA, S, ctx.mag, ctx.rrup, rvol,
ctx.hypo_depth, CN, CR, f4HW, delta_C, delta_D)
# Compute lnPGA_ABCD unprimed
lnPGA_ABCD = _compute_mean(
self.kind, C_PGA_unprimed, S, ctx.mag, ctx.rrup,
rvol, ctx.hypo_depth, CN, CR, f4HW, delta_C, delta_D)
# Compute lnSA_ABCD
lnSAp_ABCD = _compute_mean(
self.kind, C, S, ctx.mag, ctx.rrup, rvol,
ctx.hypo_depth, CN, CR, f4HW, delta_C, delta_D)
# Stage 3: Equation 6 SA_ABCD(T). This is lnSA_ABCD
# need to calculate final lnSA_ABCD from non-log values but
# return log
mean[m] = np.log(np.exp(lnSAp_ABCD) *
(np.exp(lnPGA_ABCD) / np.exp(lnPGAp_ABCD)))
# Compute standard deviations
C_STD = self.COEFFS_STD[imt]
sig[m], tau[m], phi[m] = _get_stddevs(self.kind, C_STD, ctx)
#: Coefficient table (table 3, page 108)
COEFFS_PRIMED = CoeffsTable(sa_damping=5, table="""\
imt c1 c3as c4as c5 c6as c8 ca9 c10as c11 c12y c13y c15 c17 c18y c19y c20 c24 c29 c30as c32 c33as c43 c46
pga 0.18130 0.00000 -0.14400 -0.00846 0.17000 -0.75519 0.37000 5.60000 8.10697 1.41400 0.00000 -2.55200 -2.48795 1.78180 0.55400 0.01622 -0.41369 0.44307 -0.23000 0.20000 0.26000 -0.29648 -0.03301
0.075 1.36561 0.03000 -0.14400 -0.00889 0.17000 -0.94568 0.37000 5.58000 8.68782 1.41400 0.00000 -2.70700 -2.54215 1.78180 0.55400 0.01850 -0.48652 0.31139 -0.28000 0.20000 0.26000 -0.48366 -0.03452
0.10 1.77717 0.02800 -0.14400 -0.00837 0.17000 -1.01852 0.37000 5.50000 9.37929 1.41400 -0.00110 -2.65500 -2.60945 1.78180 0.55400 0.01740 -0.61973 0.34059 -0.28000 0.20000 0.26000 -0.43854 -0.03595
0.20 1.39535 -0.01380 -0.14400 -0.00940 0.17000 -0.78199 0.37000 5.10000 10.6148 1.41400 -0.00270 -2.52800 -2.70851 1.78180 0.55400 0.01542 -0.67672 0.37235 -0.24500 0.20000 0.26000 -0.29906 -0.03853
0.30 0.44591 -0.03600 -0.14400 -0.00987 0.17000 -0.56098 0.37000 4.80000 9.40776 1.41400 -0.00360 -2.45400 -2.47668 1.78180 0.55400 0.01278 -0.59339 0.56648 -0.19500 0.20000 0.19800 -0.05184 -0.03604
0.40 0.01645 -0.05180 -0.14400 -0.00923 0.17000 -0.51281 0.37000 4.52000 8.50343 1.41400 -0.00430 -2.40100 -2.36895 1.78180 0.55400 0.01426 -0.30579 0.69911 -0.16000 0.20000 0.15400 0.20301 -0.03364
0.50 0.14826 -0.06350 -0.14400 -0.00823 0.17000 -0.56716 0.37000 4.30000 8.46463 1.41400 -0.00480 -2.36000 -2.40630 1.78180 0.55400 0.01287 -0.24839 0.63188 -0.12100 0.20000 0.11900 0.37026 -0.03260
0.75 -0.21246 -0.08620 -0.14400 -0.00738 0.17000 -0.55384 0.33100 3.90000 7.30176 1.41400 -0.00570 -2.28600 -2.26512 1.78180 0.55400 0.01080 -0.01298 0.51577 -0.05000 0.20000 0.05700 0.73517 -0.02877
1.00 -0.10451 -0.10200 -0.14400 -0.00588 0.17000 -0.65892 0.28100 3.70000 7.08727 1.41400 -0.00640 -2.23400 -2.27668 1.78180 0.55400 0.00946 0.06672 0.34048 0.00000 0.20000 0.01300 0.87764 -0.02561
1.50 -0.48665 -0.12000 -0.14400 -0.00630 0.17000 -0.58222 0.21000 3.55000 6.93264 1.41400 -0.00730 -2.16000 -2.28347 1.78180 0.55400 0.00788 -0.02289 0.12468 0.04000 0.20000 -0.04900 0.75438 -0.02034
2.00 -0.77433 -0.12000 -0.14400 -0.00630 0.17000 -0.58222 0.16000 3.55000 6.64496 1.41400 -0.00730 -2.16000 -2.28347 1.78180 0.55400 0.00788 -0.02289 0.12468 0.04000 0.20000 -0.04900 0.75438 -0.02034
3.00 -1.30916 -0.17260 -0.14400 -0.00553 0.17000 -0.57009 0.08900 3.50000 5.05488 1.41400 -0.00890 -2.03300 -2.03050 1.78180 0.55400 -0.00265 -0.20537 0.14593 0.04000 0.20000 -0.15600 0.61545 -0.01673
""")
COEFFS_UNPRIMED = CoeffsTable(sa_damping=5, table="""\
imt c1 c3as c4as c5 c6as c8 ca9 c10as c11 c12y c13y c15 c17 c18y c19y c20 c24 c29 c30as c32 c33as c43 c46
pga 0.28815 0.00000 -0.14400 -0.00967 0.17000 -0.70494 0.37000 5.60000 8.68354 1.41400 0.00000 -2.55200 -2.56727 1.78180 0.55400 0.01550 -0.50962 0.30206 -0.23000 0.20000 0.26000 -0.31769 -0.03279
0.075 1.36561 0.03000 -0.14400 -0.00889 0.17000 -0.94568 0.37000 5.58000 8.68782 1.41400 0.00000 -2.70700 -2.54215 1.78180 0.55400 0.01850 -0.48652 0.31139 -0.28000 0.20000 0.26000 -0.48366 -0.03452
0.10 1.77717 0.02800 -0.14400 -0.00837 0.17000 -1.01852 0.37000 5.50000 9.37929 1.41400 -0.00110 -2.65500 -2.60945 1.78180 0.55400 0.01740 -0.61973 0.34059 -0.28000 0.20000 0.26000 -0.43854 -0.03595
0.20 1.39535 -0.01380 -0.14400 -0.00940 0.17000 -0.78199 0.37000 5.10000 10.6148 1.41400 -0.00270 -2.52800 -2.70851 1.78180 0.55400 0.01542 -0.67672 0.37235 -0.24500 0.20000 0.26000 -0.29906 -0.03853
0.30 0.44591 -0.03600 -0.14400 -0.00987 0.17000 -0.56098 0.37000 4.80000 9.40776 1.41400 -0.00360 -2.45400 -2.47668 1.78180 0.55400 0.01278 -0.59339 0.56648 -0.19500 0.20000 0.19800 -0.05184 -0.03604
0.40 0.01645 -0.05180 -0.14400 -0.00923 0.17000 -0.51281 0.37000 4.52000 8.50343 1.41400 -0.00430 -2.40100 -2.36895 1.78180 0.55400 0.01426 -0.30579 0.69911 -0.16000 0.20000 0.15400 0.20301 -0.03364
0.50 0.14826 -0.06350 -0.14400 -0.00823 0.17000 -0.56716 0.37000 4.30000 8.46463 1.41400 -0.00480 -2.36000 -2.40630 1.78180 0.55400 0.01287 -0.24839 0.63188 -0.12100 0.20000 0.11900 0.37026 -0.03260
0.75 -0.21246 -0.08620 -0.14400 -0.00738 0.17000 -0.55384 0.33100 3.90000 7.30176 1.41400 -0.00570 -2.28600 -2.26512 1.78180 0.55400 0.01080 -0.01298 0.51577 -0.05000 0.20000 0.05700 0.73517 -0.02877
1.00 -0.10451 -0.10200 -0.14400 -0.00588 0.17000 -0.65892 0.28100 3.70000 7.08727 1.41400 -0.00640 -2.23400 -2.27668 1.78180 0.55400 0.00946 0.06672 0.34048 0.00000 0.20000 0.01300 0.87764 -0.02561
1.50 -0.48665 -0.12000 -0.14400 -0.00630 0.17000 -0.58222 0.21000 3.55000 6.93264 1.41400 -0.00730 -2.16000 -2.28347 1.78180 0.55400 0.00788 -0.02289 0.12468 0.04000 0.20000 -0.04900 0.75438 -0.02034
2.00 -0.77433 -0.12000 -0.14400 -0.00630 0.17000 -0.58222 0.16000 3.55000 6.64496 1.41400 -0.00730 -2.16000 -2.28347 1.78180 0.55400 0.00788 -0.02289 0.12468 0.04000 0.20000 -0.04900 0.75438 -0.02034
3.00 -1.30916 -0.17260 -0.14400 -0.00553 0.17000 -0.57009 0.08900 3.50000 5.05488 1.41400 -0.00890 -2.03300 -2.03050 1.78180 0.55400 -0.00265 -0.20537 0.14593 0.04000 0.20000 -0.15600 0.61545 -0.01673
""")
#: Coefficient table for standard deviation calculation (table 4, page 109)
COEFFS_STD = CoeffsTable(sa_damping=5, table="""\
imt sigmaM6 sigSlope tau
pga 0.4865 -0.1261 0.2687
0.075 0.5281 -0.0970 0.3217
0.10 0.5398 -0.0673 0.3088
0.20 0.5703 -0.0243 0.2726
0.30 0.5505 -0.0861 0.2112
0.40 0.5627 -0.1405 0.2005
0.50 0.5680 -0.1444 0.1476
0.75 0.5562 -0.0932 0.1794
1.00 0.5629 -0.0749 0.2053
1.50 0.5394 -0.0056 0.2411
2.00 0.5394 -0.0056 0.2411
3.00 0.5701 0.0934 0.2406
""")
class AllenEtAl2012(IPE):
"""
Implements the Intensity Prediction Equation of Allen, Wald and Worden
(2012) for Modified Mercalli Intensity in Active Crustal Regions
Allen, T. I., Wald, D. J. and Worden, C. B. (2012) Intensity attenuation
in active crustal regions, J. Seismology, 16: 409 - 433
This class implements the version using rupture distance, neglecting
site amplification
"""
#: The GMPE is derived from induced earthquakes
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are peak ground acceleration
#: and peak ground velocity
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
MMI,
])
#: Supported intensity measure component is not considered for IPEs, so
#: we assume equivalent to 'average horizontal'
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types is total.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([const.StdDev.TOTAL])
#: No required site parameters (in the present version)
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude (ML is used)
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is rupture distance
REQUIRES_DISTANCES = set(('rrup', ))
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.
"""
C = self.COEFFS[imt]
mean = (self._compute_magnitude_term(C, rup.mag) +
self._compute_distance_term(C, dists.rrup, rup.mag))
stddevs = self._get_stddevs(C, dists.rrup, stddev_types)
return mean, stddevs
def _compute_magnitude_term(self, C, mag):
"""
Returns the magnitude scaling term
"""
return C["c0"] + (C["c1"] * mag)
def _compute_distance_term(self, C, rrup, mag):
"""
Returns the distance scaling term
"""
exponent_term = (1.0 + C["c3"] * np.exp(mag - 5.))**2.
return C["c2"] * np.log(np.sqrt(rrup**2. + exponent_term))
def _get_stddevs(self, C, distance, stddev_types):
"""
Returns the total standard deviation, which is a function of distance
"""
stddevs = []
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev_type == const.StdDev.TOTAL:
sigma = C["s1"] + (C["s2"] / (1.0 +
((distance / C["s3"])**2.)))
stddevs.append(sigma + np.zeros_like(distance))
return stddevs
COEFFS = CoeffsTable(sa_damping=5,
table="""
IMT c0 c1 c2 c3 s1 s2 s3
mmi 3.950 0.913 -1.107 0.813 0.72 0.23 44.7
""")
class AtkinsonBoore1995GSCBest(GMPE):
"""
Implement equation used by the Geological Survey of Canada (GSC) for
the 2010 Eastern Canada National Seismic Hazard Model. The equation fits
the table values defined by Gail M. Atkinson and David M. Boore in
"Ground-Motion Relations for Eastern North America", Bullettin of the
Seismological Society of America, Vol. 85, No. 1, pp. 17-30, February 1995.
Table of coefficients were provided by GSC and are associated to the 'Best'
case (that is mean value unaffected).
The class assumes magnitude to be in Mblg scale. The Atkinson 1993
conversion equation is used to obtain Mw values.
"""
#: Supported tectonic region type is stable continental, given
#: that the equations have been derived for Eastern North America
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, SA])
#: Supported intensity measure component is random horizontal
#: :attr:`~openquake.hazardlib.const.IMC.RANDOM_HORIZONTAL`,
#: see page 22 in Atkinson and Boore's manuscript
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RANDOM_HORIZONTAL
#: Supported standard deviation type is total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([const.StdDev.TOTAL])
#: site params are not required
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameter is magnitude
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is hypocentral distance
#: see page 18 in Atkinson and Boore's manuscript
REQUIRES_DISTANCES = set(('rhypo', ))
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.
"""
C = self.COEFFS[imt]
# clip rhypo at 10 (this is the minimum distance used in
# deriving the equation), see page 22, this avoids singularity
# in mean value equation
rhypo = dists.rhypo.copy()
rhypo[rhypo < 10] = 10
# convert magnitude from Mblg to Mw
mag = rup.mag * 0.98 - 0.39 if rup.mag <= 5.5 else \
2.715 - 0.277 * rup.mag + 0.127 * rup.mag * rup.mag
# functional form as explained in 'Youngs_fit_to_AB95lookup.doc'
f1 = np.minimum(np.log(rhypo), np.log(70.))
f2 = np.maximum(np.log(rhypo / 130.), 0)
mean = (C['c1'] + C['c2'] * mag + C['c3'] * mag**2 +
(C['c4'] + C['c5'] * mag) * f1 +
(C['c6'] + C['c7'] * mag) * f2 + C['c8'] * rhypo)
stddevs = self._get_stddevs(stddev_types, dists.rhypo.shape[0])
return mean, stddevs
def _get_stddevs(self, stddev_types, num_sites):
"""
Return total standard deviation.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
stddevs = [np.zeros(num_sites) + 0.69 for _ in stddev_types]
return stddevs
#: coefficient table provided by GSC
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8
pga -1.329 1.272 -0.08240 -2.556 0.17220 -1.9600 0.17460 -0.0045350
0.1 -2.907 1.522 -0.08528 -2.052 0.12484 -1.4224 0.07965 -0.0043090
0.2 -5.487 1.932 -0.10290 -1.818 0.09797 -1.0760 0.06075 -0.0033250
0.3 -7.567 2.284 -0.11930 -1.734 0.08814 -0.9551 0.04392 -0.0025700
0.5 -9.476 2.503 -0.12310 -1.631 0.07610 -1.0490 0.06224 -0.0019590
1.0 -11.134 2.470 -0.10569 -1.520 0.06165 -0.9106 0.05248 -0.001497
2.0 -13.210 2.945 -0.15670 -1.864 0.11620 -0.7653 0.02729 -0.0009921
""")
class Kanno2006Shallow(GMPE):
# pylint: disable=too-few-public-methods
"""
Implements GMPE of Kanno et al. (2006) for shallow events based on data
predominantly from Japan.
Note that "both crustal and subduction interface events fall into the
category of shallow events" (p. 883) where "shallow" is defined as "focal
depth of 30 km or less" (p. 895).
Verification of mean value data was performed against a test vector kindly
provided by the lead author.
**Reference**
Page number citations in this documentation refer to:
Kanno, T., Narita, A., Morikawa, N., Fujiwara, H., and Fukushima, Y.
(2006). A new attenuation relation for strong ground motion in Japan based
on recorded data. *Bull. Seism. Soc. Am.* 96(3):879–897.
"""
#: This model is generally considered to be intended for subduction
#: regions, but the authors do not constrain the type of event, only the
#: depth: "both crustal and subduction interface events fall into the
#: category of shallow events." (p. 883)
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTERFACE
#: "regression coefficients for the base model in equations (5) and (6)
#: for PGA , PGV , and 5% damped response spectral acceleration are given"
#: (p. 883)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([PGA, PGV, SA])
#: "The peak value is the peak square root of the sum of squares
#: of two orthogonal horizontal components in the time domain" (p. 880)
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.PEAK_SRSS_HORIZONTAL
#: Although interevent and intraevent residuals are separately discussed
#: in the context of focal depth and site conditions, only the total
#: standard deviation is tabulated.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([const.StdDev.TOTAL])
#: "Coefficients p and q were derived by regression analysis on the
#: residuals averaged at intervals of every 100 m/sec in AVS30." (p. 884)
REQUIRES_SITES_PARAMETERS = set(('vs30',))
#: Sole required rupture parameter is magnitude; faulting style is not
#: addressed.
REQUIRES_RUPTURE_PARAMETERS = set(('mag',))
#: "The source distance is the closest distance from a fault plane to the
#: observation site and is the hypocentral distance in the case of
#: earthquakes for which the fault model is not available." (p. 880)
REQUIRES_DISTANCES = set(('rrup',))
def get_mean_and_stddevs(self, sites, rup, dists, imt, stddev_types):
# pylint: disable=too-many-arguments
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.get_mean_and_stddevs>`
for specification of input and result values.
Implements the following equations:
Equation (5) on p. 881 predicts ground motion for shallow events
(depth <= 30 km):
``log(pre) = a*M + b*X - log(X + d*10^(e*M)) + c + epsilon``
"where pre is the predicted PGA (cm/sec^2), PGV (cm/sec), or 5%
damped response spectral acceleration (cm/sec^2)" (p. 883) and a,
b, c and d are tabulated regression coefficients. Note that
subscripts on the regression coeffients have been dropped -
subscript `1` denoted "shallow" while subscript `2` denoted "deep"
- so that the "deep" model of equation (6) can be implemented trivally
by changing coefficients and setting d = 0.
Equation (8) on p. 883 gives the model used for site amplitfication:
``G = p*log(VS30) + q``
Where p and q are tabulated regression coefficients.
Equation (9) on p. 884 for the ground motion at a given site:
``log(pre_G) = log(pre) + G``
No adjustment of epsilon is made as a function of VS30.
Note finally that "log represents log_10 in the present study"
(p. 880).
"""
# obtain coefficients for required intensity measure type (IMT)
coeffs = self.COEFFS_BASE[imt].copy()
coeffs.update(self.COEFFS_SITE[imt])
# obtain IMT-independent coefficients
coeffs.update(self.CONSTS)
# compute bedrock motion, equation (5)
log_mean = self._compute_mag_dist_terms(rup, dists, coeffs)
# make site corrections, equation (9)
log_mean += self._compute_site_amplification(sites, coeffs)
# retrieve standard deviations
log_stddevs = self._get_stddevs(coeffs, stddev_types)
# convert from common to natural logarithm
ln_mean = log_mean*np.log(10)
ln_stddevs = log_stddevs*np.log(10)
# convert accelerations from cm/s^2 to g
if not isinstance(imt, PGV):
ln_mean -= np.log(100*g)
return ln_mean, [ln_stddevs]
@classmethod
def _compute_mag_dist_terms(cls, rup, dists, coeffs):
"""
Compute equation (5) and implcitly equation (6):
``log(pre) = c + a*M + b*X - log(X + d*10^(e*M)) + epsilon``
"""
log_pre = coeffs['c'] + coeffs['a']*rup.mag + coeffs['b']*dists.rrup \
- np.log10(dists.rrup + coeffs['d']*10**(coeffs['e']*rup.mag))
return log_pre
@classmethod
def _compute_site_amplification(cls, sites, coeffs):
"""
Compute equation (8):
``G = p*log(VS30) + q``
"""
return coeffs['p']*np.log10(sites.vs30) + coeffs['q']
def _get_stddevs(self, coeffs, stddev_types):
"""
Only total error is reported so this is a simple lookup.
"""
for stddev_type in stddev_types:
assert stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
return coeffs['epsilon']
#: Coefficients obtained from author via personal communcation with
#: slightly more precision than Table 3, p. 884.
COEFFS_BASE = CoeffsTable(sa_damping=5., table="""\
IMT a b c d epsilon
pga 0.556 -0.003070 0.2560 0.00547 0.366
0.05 0.540 -0.003540 0.4790 0.00611 0.374
0.06 0.536 -0.003720 0.5660 0.00648 0.379
0.07 0.528 -0.003850 0.6690 0.00664 0.384
0.08 0.524 -0.003970 0.7470 0.00687 0.393
0.09 0.523 -0.004050 0.7950 0.00710 0.399
0.1 0.520 -0.004090 0.8470 0.00732 0.404
0.11 0.501 -0.003990 0.9600 0.00607 0.404
0.12 0.510 -0.003970 0.9280 0.00619 0.404
0.13 0.514 -0.003930 0.9140 0.00616 0.403
0.15 0.518 -0.003800 0.8920 0.00595 0.405
0.17 0.525 -0.003650 0.8440 0.00557 0.406
0.2 0.535 -0.003390 0.7610 0.00525 0.401
0.22 0.535 -0.003190 0.7340 0.00482 0.399
0.25 0.541 -0.002930 0.6590 0.00436 0.399
0.3 0.556 -0.002580 0.5050 0.00389 0.392
0.35 0.561 -0.002370 0.4210 0.00359 0.398
0.4 0.577 -0.002120 0.2620 0.00329 0.404
0.45 0.589 -0.001890 0.1290 0.00297 0.405
0.5 0.593 -0.001610 0.0375 0.00216 0.405
0.6 0.623 -0.001390 -0.2220 0.00250 0.409
0.7 0.634 -0.001180 -0.3700 0.00215 0.413
0.8 0.651 -0.001070 -0.5440 0.00197 0.408
0.9 0.681 -0.000942 -0.8030 0.00187 0.407
1 0.710 -0.000878 -1.0400 0.00208 0.406
1.1 0.722 -0.000737 -1.1900 0.00176 0.405
1.2 0.732 -0.000614 -1.3200 0.00142 0.405
1.3 0.742 -0.000554 -1.4400 0.00140 0.405
1.5 0.773 -0.000518 -1.7000 0.00167 0.398
1.7 0.791 -0.000464 -1.8900 0.00194 0.391
2 0.804 -0.000356 -2.0800 0.00195 0.387
2.2 0.821 -0.000372 -2.2400 0.00216 0.384
2.5 0.844 -0.000308 -2.4600 0.00228 0.382
3 0.862 -0.000197 -2.7200 0.00207 0.378
3.5 0.895 -0.000348 -2.9900 0.00322 0.374
4 0.921 -0.000512 -3.2100 0.00446 0.375
4.5 0.944 -0.000703 -3.3900 0.00639 0.377
5 0.916 -0.000360 -3.3500 0.00303 0.377
pgv 0.702 -0.000925 -1.9300 0.00217 0.321
""")
#: Coefficients obtained from author via personal communcation with
#: slightly more precision Table 5, p. 888.
COEFFS_SITE = CoeffsTable(sa_damping=5., table="""\
IMT p q
pga -0.5514 1.3490
0.05 -0.3244 0.7962
0.06 -0.2614 0.6450
0.07 -0.2418 0.5974
0.08 -0.2616 0.6417
0.09 -0.2929 0.7154
0.1 -0.3199 0.7776
0.11 -0.3477 0.8406
0.12 -0.3900 0.9399
0.13 -0.4307 1.0350
0.15 -0.5308 1.2760
0.17 -0.6113 1.4680
0.2 -0.6831 1.6470
0.22 -0.7184 1.7370
0.25 -0.7499 1.8200
0.3 -0.8045 1.9630
0.35 -0.8518 2.0870
0.4 -0.8676 2.1310
0.45 -0.8851 2.1760
0.5 -0.9094 2.2470
0.6 -0.9238 2.2970
0.7 -0.9622 2.4070
0.8 -0.9759 2.4570
0.9 -0.9685 2.4390
1 -0.9264 2.3220
1.1 -0.9176 2.2960
1.2 -0.9062 2.2630
1.3 -0.8825 2.2020
1.5 -0.8531 2.1210
1.7 -0.8294 2.0590
2 -0.7756 1.9210
2.2 -0.7567 1.8750
2.5 -0.7244 1.7960
3 -0.6845 1.6990
3.5 -0.6597 1.6390
4 -0.6182 1.5370
4.5 -0.6035 1.4990
5 -0.5861 1.4560
pgv -0.7057 1.7650
""")
#: "coefficient e_1 = 0.5 was selected for all periods in the present
#: study." (p. 881)
CONSTS = {
'e': 0.5,
}
class AfshariStewart2016(GMPE):
"""
Implements the GMPE of Afshari & Stewart (2016) for relative significant
duration for 5 - 75 %, 5 - 95 % and 20 - 80 % Arias Intensity.
Afshari, K. and Stewart, J. P. (2016) "Physically Parameterized Prediction
Equations for Signficant Duration in Active Crustal Regions", Earthquake
Spectra, 32(4), 2057 - 2081
"""
#: Supported tectonic region type is active shallow crust
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are 5 - 95 % Arias and 5 - 75 % Arias
#: significant duration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([RSD595, RSD575, RSD2080])
#: Supported intensity measure component is the geometric mean horizontal
#: component
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation type is only total, see table 7, page 35
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
#: Requires vs30
REQUIRES_SITES_PARAMETERS = set(('vs30', 'z1pt0'))
#: Required rupture parameters are magnitude and top of rupture depth
REQUIRES_RUPTURE_PARAMETERS = set(('mag', 'rake'))
#: Required distance measure is closest distance to rupture
REQUIRES_DISTANCES = set(('rrup', ))
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.
"""
C = self.COEFFS[imt]
mean = (np.log(
self.get_magnitude_term(C, rup) +
self.get_distance_term(C, dists.rrup)) +
self.get_site_amplification(C, sites))
stddevs = self.get_stddevs(C, sites.vs30.shape, rup.mag, stddev_types)
return mean, stddevs
def get_magnitude_term(self, C, rup):
"""
Returns the magnitude scaling term in equation 3
"""
b0, stress_drop = self._get_sof_terms(C, rup.rake)
if rup.mag <= C["m1"]:
return b0
else:
# Calculate moment (equation 5)
m_0 = 10.0**(1.5 * rup.mag + 16.05)
# Get stress-drop scaling (equation 6)
if rup.mag > C["m2"]:
stress_drop += (C["b2"] * (C["m2"] - self.CONSTANTS["mstar"]) +
(C["b3"] * (rup.mag - C["m2"])))
else:
stress_drop += (C["b2"] * (rup.mag - self.CONSTANTS["mstar"]))
stress_drop = np.exp(stress_drop)
# Get corner frequency (equation 4)
f0 = 4.9 * 1.0E6 * 3.2 * ((stress_drop / m_0)**(1. / 3.))
return 1. / f0
def get_distance_term(self, C, rrup):
"""
Returns the distance scaling term in equation 7
"""
f_p = C["c1"] * rrup
idx = np.logical_and(rrup > self.CONSTANTS["r1"],
rrup <= self.CONSTANTS["r2"])
f_p[idx] = (C["c1"] * self.CONSTANTS["r1"]) +\
C["c2"] * (rrup[idx] - self.CONSTANTS["r1"])
idx = rrup > self.CONSTANTS["r2"]
f_p[idx] = C["c1"] * self.CONSTANTS["r1"] +\
C["c2"] * (self.CONSTANTS["r2"] - self.CONSTANTS["r1"]) +\
C["c3"] * (rrup[idx] - self.CONSTANTS["r2"])
return f_p
def _get_sof_terms(self, C, rake):
"""
Returns the style-of-faulting scaling parameters
"""
if rake >= 45.0 and rake <= 135.0:
# Reverse faulting
return C["b0R"], C["b1R"]
elif rake <= -45. and rake >= -135.0:
# Normal faulting
return C["b0N"], C["b1N"]
else:
# Strike slip
return C["b0SS"], C["b1SS"]
def _get_lnmu_z1(self, vs30):
"""
Returns the z1.0 normalisation term for California (equation 11)
"""
return (-7.15 / 4.) * np.log(
(vs30 ** 4. + 570.94 ** 4) / (1360.0 ** 4. + 570.94 ** 4.)) -\
np.log(1000.0)
def get_site_amplification(self, C, sites):
"""
Returns the site amplification term
"""
# Gets delta normalised z1
dz1 = sites.z1pt0 - np.exp(self._get_lnmu_z1(sites.vs30))
f_s = C["c5"] * dz1
# Calculates site amplification term
f_s[dz1 > self.CONSTANTS["dz1ref"]] = (C["c5"] *
self.CONSTANTS["dz1ref"])
idx = sites.vs30 > self.CONSTANTS["v1"]
f_s[idx] += (C["c4"] * np.log(self.CONSTANTS["v1"] / C["vref"]))
idx = np.logical_not(idx)
f_s[idx] += (C["c4"] * np.log(sites.vs30[idx] / C["vref"]))
return f_s
def get_stddevs(self, C, nsites, mag, stddev_types):
"""
Returns the standard deviations
"""
tau = self._get_tau(C, mag) + np.zeros(nsites)
phi = self._get_phi(C, mag) + np.zeros(nsites)
stddevs = []
for stddev in stddev_types:
assert stddev in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
if stddev == const.StdDev.TOTAL:
stddevs.append(np.sqrt(tau**2. + phi**2.))
elif stddev == const.StdDev.INTER_EVENT:
stddevs.append(tau)
elif stddev == const.StdDev.INTRA_EVENT:
stddevs.append(phi)
return stddevs
def _get_tau(self, C, mag):
"""
Returns magnitude dependent inter-event standard deviation (tau)
(equation 14)
"""
if mag < 6.5:
return C["tau1"]
elif mag < 7.:
return C["tau1"] + (C["tau2"] - C["tau1"]) * ((mag - 6.5) / 0.5)
else:
return C["tau2"]
def _get_phi(self, C, mag):
"""
Returns the magnitude dependent intra-event standard deviation (phi)
(equation 15)
"""
if mag < 5.5:
return C["phi1"]
elif mag < 5.75:
return C["phi1"] + (C["phi2"] - C["phi1"]) * ((mag - 5.5) / 0.25)
else:
return C["phi2"]
COEFFS = CoeffsTable(sa_damping=5,
table="""\
imt m1 m2 b0N b0R b0SS b0U b1N b1R b1SS b1U b2 b3 c1 c2 c3 c4 c5 vref tau1 tau2 phi1 phi2
rsd575 5.35 7.15 1.555 0.7806 1.2790 1.280 4.992 7.061 5.578 5.576 0.9011 -1.684 0.1159 0.1065 0.0682 -0.2246 0.0006 368.2 0.28 0.25 0.54 0.41
rsd595 5.2 7.40 2.541 1.6120 2.3020 2.182 3.170 4.536 3.467 3.628 0.9443 -3.911 0.3165 0.2539 0.0932 -0.3183 0.0006 369.9 0.25 0.19 0.43 0.35
rsd2080 5.2 7.40 1.409 0.7729 0.8804 0.8822 4.778 6.579 6.188 6.182 0.7414 -3.164 0.0646 0.0865 0.0373 -0.4237 0.0005 369.6 0.30 0.19 0.56 0.45
""")
CONSTANTS = {
"mstar": 6.0,
"r1": 10.0,
"r2": 50.0,
"v1": 600.0,
"dz1ref": 200.0
}
class RietbrockEtAl2013SelfSimilar(GMPE):
"""
Implements the ground motion prediction equation of Rietbrock et al
(2013):
Rietbrock, A., Strasser, F., Edwards, B. (2013) A Stochastic Earthquake
Ground-Motion Prediction Model for the United Kingdom. Bulletin of the
Seismological Society of America, 103(1), 57 -77
The GMPE is derived for the United Kingdom, a low seismicity region.
Consequently ground motions are generated via numerical simulations using
a stochastic point-source model, calibrated with parameters derived from
local weak-motion data. This implementation applies to the case
when stress drop is considered to be self-similar (i.e. independent
of magnitude).
"""
#: Supported tectonic region type is stabe continental crust,
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are spectral acceleration, peak
#: ground acceleration and peak ground velocity.
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, PGV, SA}
#: Supported intensity measure component is the geometric mean of two
#: horizontal components
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 = {
const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT, const.StdDev.TOTAL}
#: No site parameter is required
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is Rjb
REQUIRES_DISTANCES = {'rjb'}
def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
imean = (_get_magnitude_scaling_term(C, ctx.mag) +
_get_distance_scaling_term(C, ctx.rjb, ctx.mag))
# 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 imt.string.startswith(('PGA', 'SA')):
mean[m] = np.log((10.0 ** (imean - 2.0)) / g)
else:
mean[m] = np.log(10 ** imean)
# Original standard deviations are in
# logarithms of base 10. Converts to natural logarithm.
sig[m] = np.log(10.0 ** np.sqrt(C["tau"]**2 + C["phi"]**2))
tau[m] = np.log(10.0 ** C["tau"])
phi[m] = np.log(10.0 ** C["phi"])
# Coefficients from Table 5, Page 64
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 sigma tau phi
pgv -2.9598 0.9039 -0.0434 -1.6243 0.1987 -1.6511 0.1654 -2.4308 0.0851 -0.001472 1.7736 0.347 0.311 0.153
pga -0.0135 0.6889 -0.0488 -1.8987 0.2151 -1.9063 0.1740 -2.0131 0.0887 -0.002747 1.5473 0.436 0.409 0.153
0.03 0.8282 0.5976 -0.0418 -2.1321 0.2159 -2.0530 0.1676 -1.5148 0.1163 -0.004463 1.1096 0.449 0.417 0.167
0.04 0.4622 0.6273 -0.0391 -1.7242 0.1644 -1.6849 0.1270 -1.4513 0.0910 -0.004355 1.1344 0.445 0.417 0.155
0.05 0.2734 0.6531 -0.0397 -1.5932 0.1501 -1.5698 0.1161 -1.5350 0.0766 -0.003939 1.1493 0.442 0.416 0.149
0.06 0.0488 0.6945 -0.0420 -1.4913 0.1405 -1.4807 0.1084 -1.6563 0.0657 -0.003449 1.2154 0.438 0.414 0.143
0.08 -0.2112 0.7517 -0.0460 -1.4151 0.1340 -1.4130 0.1027 -1.7821 0.0582 -0.002987 1.2858 0.433 0.410 0.140
0.10 -0.5363 0.8319 -0.0521 -1.3558 0.1296 -1.3579 0.0985 -1.8953 0.0520 -0.002569 1.3574 0.428 0.405 0.138
0.12 -0.9086 0.9300 -0.0597 -1.3090 0.1264 -1.3120 0.0948 -1.9863 0.0475 -0.002234 1.4260 0.422 0.399 0.138
0.16 -1.3733 1.0572 -0.0698 -1.2677 0.1237 -1.2684 0.0910 -2.0621 0.0434 -0.001944 1.4925 0.416 0.392 0.139
0.20 -1.9180 1.2094 -0.0819 -1.2315 0.1213 -1.2270 0.0872 -2.1196 0.0396 -0.001708 1.5582 0.409 0.384 0.141
0.25 -2.5107 1.3755 -0.0949 -1.1992 0.1189 -1.1881 0.0833 -2.1598 0.0361 -0.001522 1.6049 0.402 0.376 0.144
0.31 -3.1571 1.5549 -0.1087 -1.1677 0.1160 -1.1494 0.0791 -2.1879 0.0328 -0.001369 1.6232 0.395 0.366 0.148
0.40 -3.8516 1.7429 -0.1228 -1.1354 0.1126 -1.1099 0.0746 -2.2064 0.0294 -0.001240 1.6320 0.387 0.356 0.152
0.50 -4.5556 1.9258 -0.1360 -1.1015 0.1084 -1.0708 0.0700 -2.2171 0.0261 -0.001129 1.6109 0.378 0.345 0.156
0.63 -5.2405 2.0926 -0.1471 -1.0659 0.1035 -1.0328 0.0655 -2.2220 0.0229 -0.001033 1.5735 0.369 0.333 0.160
0.79 -5.8909 2.2357 -0.1557 -1.0279 0.0981 -0.9969 0.0612 -2.2229 0.0197 -0.000945 1.5262 0.360 0.320 0.164
1.00 -6.4633 2.3419 -0.1605 -0.9895 0.0925 -0.9665 0.0577 -2.2211 0.0167 -0.000863 1.4809 0.350 0.307 0.168
1.25 -6.9250 2.4037 -0.1612 -0.9545 0.0879 -0.9462 0.0558 -2.2178 0.0139 -0.000785 1.4710 0.341 0.294 0.172
1.59 -7.2960 2.4189 -0.1573 -0.9247 0.0848 -0.9421 0.0567 -2.2137 0.0111 -0.000701 1.5183 0.331 0.280 0.177
2.00 -7.5053 2.3805 -0.1492 -0.9128 0.0855 -0.9658 0.0619 -2.2110 0.0086 -0.000618 1.6365 0.323 0.267 0.181
2.50 -7.5569 2.2933 -0.1376 -0.9285 0.0915 -1.0264 0.0729 -2.2108 0.0067 -0.000535 1.8421 0.315 0.254 0.186
3.13 -7.4510 2.1598 -0.1228 -0.9872 0.1050 -1.1349 0.0914 -2.2141 0.0060 -0.000458 2.1028 0.308 0.242 0.190
4.00 -7.1688 1.9738 -0.1048 -1.1274 0.1325 -1.3132 0.1207 -2.2224 0.0079 -0.000397 2.4336 0.299 0.227 0.195
5.00 -6.8063 1.7848 -0.0879 -1.3324 0.1691 -1.5158 0.1533 -2.2374 0.0142 -0.000387 2.6686 0.291 0.214 0.198
""")
class Campbell2003(GMPE):
"""
Implements GMPE developed by K.W Campbell and published as "Prediction of
Strong Ground Motion Using the Hybrid Empirical Method and Its Use in the
Development of Ground Motion (Attenuation) Relations in Eastern North
America" (Bulletting of the Seismological Society of America, Volume 93,
Number 3, pages 1012-1033, 2003). The class implements also the corrections
given in the erratum (2004).
"""
#: Supported tectonic region type is stable continental crust given that
#: the equations have been derived for Eastern North America.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration, see table 6, page 1022 (PGA is assumed
#: to be equal to SA at 0.01 s)
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
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 type is only total, see equation 35, page
#: 1021
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL
])
#: No site parameters are needed
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameter is only magnitude, see equation 30 page
#: 1021.
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance measure is closest distance to rupture, see equation
#: 30 page 1021.
REQUIRES_DISTANCES = set(('rrup', ))
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.
"""
assert all(stddev_type in self.DEFINED_FOR_STANDARD_DEVIATION_TYPES
for stddev_type in stddev_types)
C = self.COEFFS[imt]
mean = self._compute_mean(C, rup.mag, dists.rrup)
stddevs = self._get_stddevs(C, stddev_types, rup.mag,
dists.rrup.shape[0])
return mean, stddevs
def _compute_mean(self, C, mag, rrup):
"""
Compute mean value according to equation 30, page 1021.
"""
mean = (C['c1'] +
self._compute_term1(C, mag) +
self._compute_term2(C, mag, rrup) +
self._compute_term3(C, rrup))
return mean
def _get_stddevs(self, C, stddev_types, mag, num_sites):
"""
Return total standard deviation as for equation 35, page 1021.
"""
stddevs = []
for _ in stddev_types:
if mag < 7.16:
sigma = C['c11'] + C['c12'] * mag
elif mag >= 7.16:
sigma = C['c13']
stddevs.append(np.zeros(num_sites) + sigma)
return stddevs
def _compute_term1(self, C, mag):
"""
This computes the term f1 in equation 31, page 1021
"""
return (C['c2'] * mag) + C['c3'] * (8.5 - mag) ** 2
def _compute_term2(self, C, mag, rrup):
"""
This computes the term f2 in equation 32, page 1021
"""
c78_factor = (C['c7'] * np.exp(C['c8'] * mag)) ** 2
R = np.sqrt(rrup ** 2 + c78_factor)
return C['c4'] * np.log(R) + (C['c5'] + C['c6'] * mag) * rrup
def _compute_term3(self, C, rrup):
"""
This computes the term f3 in equation 34, page 1021 but corrected
according to the erratum.
"""
f3 = np.zeros_like(rrup)
idx_between_70_130 = (rrup > 70) & (rrup <= 130)
idx_greater_130 = rrup > 130
f3[idx_between_70_130] = (
C['c9'] * (np.log(rrup[idx_between_70_130]) - np.log(70))
)
f3[idx_greater_130] = (
C['c9'] * (np.log(rrup[idx_greater_130]) - np.log(70)) +
C['c10'] * (np.log(rrup[idx_greater_130]) - np.log(130))
)
return f3
#: Coefficient tables are constructed from the electronic suplements of
#: the original paper.
COEFFS = CoeffsTable(sa_damping=5, table="""\
IMT c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13
pga 0.0305 0.633 -0.0427 -1.591 -0.00428 0.000483 0.683 0.416 1.140 -0.873 1.030 -0.0860 0.414
0.020 1.3535 0.630 -0.0404 -1.787 -0.00388 0.000497 1.020 0.363 0.851 -0.715 1.030 -0.0860 0.414
0.030 1.1860 0.622 -0.0362 -1.691 -0.00367 0.000501 0.922 0.376 0.759 -0.922 1.030 -0.0860 0.414
0.050 0.3736 0.616 -0.0353 -1.469 -0.00378 0.000500 0.630 0.423 0.771 -1.239 1.042 -0.0838 0.443
0.075 -0.0395 0.615 -0.0353 -1.383 -0.00421 0.000486 0.491 0.463 0.955 -1.349 1.052 -0.0838 0.453
0.100 -0.1475 0.613 -0.0353 -1.369 -0.00454 0.000460 0.484 0.467 1.096 -1.284 1.059 -0.0838 0.460
0.150 -0.1901 0.616 -0.0478 -1.368 -0.00473 0.000393 0.461 0.478 1.239 -1.079 1.068 -0.0838 0.469
0.200 -0.4328 0.617 -0.0586 -1.320 -0.00460 0.000337 0.399 0.493 1.250 -0.928 1.077 -0.0838 0.478
0.300 -0.6906 0.609 -0.0786 -1.280 -0.00414 0.000263 0.349 0.502 1.241 -0.753 1.081 -0.0838 0.482
0.500 -0.5907 0.534 -0.1379 -1.216 -0.00341 0.000194 0.318 0.503 1.166 -0.606 1.098 -0.0824 0.508
0.750 -0.5429 0.480 -0.1806 -1.184 -0.00288 0.000160 0.304 0.504 1.110 -0.526 1.105 -0.0806 0.528
1.000 -0.6104 0.451 -0.2090 -1.158 -0.00255 0.000141 0.299 0.503 1.067 -0.482 1.110 -0.0793 0.543
1.500 -0.9666 0.441 -0.2405 -1.135 -0.00213 0.000119 0.304 0.500 1.029 -0.438 1.099 -0.0771 0.547
2.000 -1.4306 0.459 -0.2552 -1.124 -0.00187 0.000103 0.310 0.499 1.015 -0.417 1.093 -0.0758 0.551
3.000 -2.2331 0.492 -0.2646 -1.121 -0.00154 0.000084 0.310 0.499 1.014 -0.393 1.090 -0.0737 0.562
4.000 -2.7975 0.507 -0.2738 -1.119 -0.00135 0.000074 0.294 0.506 1.018 -0.386 1.092 -0.0722 0.575
""")
class Atkinson2015(GMPE):
"""
Implements the Induced Seismicity GMPE of Atkinson (2015)
Atkinson, G. A. (2015) Ground-Motion Prediction Equation for Small-to-
Moderate Events at Short Hypocentral Distances, with Application to
Induced-Seismicity Hazards. Bulletin of the Seismological Society of
America. 105(2).
"""
#: The GMPE is derived from induced earthquakes
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.INDUCED
#: Supported intensity measure types are peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set([
PGA,
PGV,
SA
])
#: Supported intensity measure component is the larger of two components
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RotD50
#: Supported standard deviation types is total.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL,
const.StdDev.INTER_EVENT,
const.StdDev.INTRA_EVENT
])
#: No required site parameters, the GMPE is derived for B/C site
#: amplification factors
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameters are magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is hypocentral distance
REQUIRES_DISTANCES = {'rhypo'}
#: GMPE not tested against independent implementation so raise
#: not verified warning
non_verified = True
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.
"""
C = self.COEFFS[imt]
imean = (self._get_magnitude_term(C, rup.mag) +
self._get_distance_term(C, dists.rhypo, rup.mag))
# Convert mean from cm/s and cm/s/s
if imt.name in "SA PGA":
mean = np.log((10.0 ** (imean - 2.0)) / g)
else:
mean = np.log(10.0 ** imean)
stddevs = self._get_stddevs(C, len(dists.rhypo), stddev_types)
return mean, stddevs
def _get_magnitude_term(self, C, mag):
"""
Returns the magnitude scaling term
"""
return C["c0"] + (C["c1"] * mag) + (C["c2"] * (mag ** 2.0))
def _get_distance_term(self, C, rhypo, mag):
"""
Returns the distance scaling term
"""
h_eff = self._get_effective_distance(mag)
r_val = np.sqrt(rhypo ** 2.0 + h_eff ** 2.0)
return C["c3"] * np.log10(r_val)
def _get_effective_distance(self, mag):
"""
Returns the effective distance term in equation 3. This may be
overwritten in sub-classes
"""
h_eff = 10.0 ** (-1.72 + 0.43 * mag)
if h_eff > 1.0:
return h_eff
else:
return 1.0
def _get_stddevs(self, C, num_sites, stddev_types):
"""
Return standard deviations, converting from log10 to log
"""
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["sigma"]) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(np.log(10.0 ** C["tau"]) + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(np.log(10.0 ** C["phi"]) + np.zeros(num_sites))
return stddevs
COEFFS = CoeffsTable(sa_damping=5, table="""
IMT c0 c1 c2 c3 phi tau sigma
pgv -4.151 1.762 -0.09509 -1.669 0.27 0.19 0.33
pga -2.376 1.818 -0.1153 -1.752 0.28 0.24 0.37
0.0303 -2.283 1.842 -0.1189 -1.785 0.28 0.27 0.39
0.0500 -2.018 1.826 -0.1192 -1.831 0.28 0.30 0.41
0.1000 -1.954 1.830 -0.1185 -1.774 0.29 0.25 0.39
0.2000 -2.266 1.785 -0.1061 -1.657 0.30 0.21 0.37
0.3000 -2.794 1.852 -0.1078 -1.608 0.30 0.19 0.36
0.5000 -3.873 2.060 -0.1212 -1.544 0.29 0.20 0.35
1.0000 -4.081 1.742 -0.07381 -1.481 0.26 0.22 0.34
2.0000 -4.462 1.485 -0.03815 -1.361 0.24 0.23 0.33
3.0303 -3.827 1.060 0.009086 -1.398 0.24 0.22 0.32
5.0000 -4.321 1.080 0.009376 -1.378 0.25 0.18 0.31
""")
class AkkarBommer2010(GMPE):
"""
Implements GMPE developed by Sinan Akkar and Julian J. Bommer
and published as "Empirical Equations for the Prediction of PGA, PGV,
and Spectral Accelerations in Europe, the Mediterranean Region, and
the Middle East", Seismological Research Letters, 81(2), 195-206.
SA at 4 s (not supported by the original equations) has been added in the
context of the SHARE project and assumed to be equal to SA at 3 s but
scaled with proper factor.
Equation coefficients for PGA and SA periods up to 0.05 seconds have been
taken from updated model as described in 'Extending ground-motion
prediction equations for spectral accelerations to higher response
frequencies',Julian J. Bommer, Sinan Akkar, Stephane Drouet,
Bull. Earthquake Eng. (2012) volume 10, pages 379 - 399.
Coefficients for PGV and SA above 0.05 seconds are taken from the
original 2010 publication.
"""
#: Supported tectonic region type is 'active shallow crust' because the
#: equations have been derived from data from Southern Europe, North
#: Africa, and active areas of the Middle East, as explained in the
# 'Introduction', page 195.
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Set of :mod:`intensity measure types <openquake.hazardlib.imt>`
#: this GSIM can calculate. A set should contain classes from module
#: :mod:`openquake.hazardlib.imt`.
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 page 196.
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL
#: Supported standard deviation types are inter-event, intra-event
#: and total, see equation 2, page 199.
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([
const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT
])
#: Required site parameter is only Vs30 (used to distinguish rock
#: and stiff and soft soil).
REQUIRES_SITES_PARAMETERS = {'vs30'}
#: Required rupture parameters are magnitude and rake (eq. 1, page 199).
REQUIRES_RUPTURE_PARAMETERS = {'rake', 'mag'}
#: Required distance measure is RRup (eq. 1, page 199).
REQUIRES_DISTANCES = {'rjb'}
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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS[imt]
imean = (self._compute_magnitude(rup, C) +
self._compute_distance(rup, dists, imt, C) +
self._get_site_amplification(sites, imt, C) +
self._get_mechanism(sites, rup, imt, C))
# Convert units to g,
# but only for PGA and SA (not PGV):
if imt.name in 'PGA SA':
mean = np.log((10.0**(imean - 2.0)) / g)
else:
# PGV:
mean = np.log(10.0**imean)
# apply scaling factor for SA at 4 s
if imt.name == 'SA' and imt.period == 4.0:
mean /= 0.8
istddevs = self._get_stddevs(C,
stddev_types,
num_sites=len(sites.vs30))
stddevs = np.log(10**np.array(istddevs))
return mean, stddevs
def _get_stddevs(self, C, stddev_types, num_sites):
"""
Return standard deviations as defined in table 1, p. 200.
"""
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(C['SigmaTot'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(C['Sigma1'] + np.zeros(num_sites))
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(C['tau'] + np.zeros(num_sites))
return stddevs
def _compute_magnitude(self, rup, C):
"""
Compute the first term of the equation described on p. 199:
``b1 + b2 * M + b3 * M**2``
"""
return C['b1'] + (C['b2'] * rup.mag) + (C['b3'] * (rup.mag**2))
def _compute_distance(self, rup, dists, imt, C):
"""
Compute the second term of the equation described on p. 199:
``(b4 + b5 * M) * log(sqrt(Rjb ** 2 + b6 ** 2))``
"""
return (((C['b4'] + C['b5'] * rup.mag) * np.log10(
(np.sqrt(dists.rjb**2.0 + C['b6']**2.0)))))
def _get_site_amplification(self, sites, imt, C):
"""
Compute the third term of the equation described on p. 199:
``b7 * Ss + b8 * Sa``
"""
Ss, Sa = self._get_site_type_dummy_variables(sites)
return (C['b7'] * Ss) + (C['b8'] * Sa)
def _get_site_type_dummy_variables(self, sites):
"""
Get site type dummy variables, ``Ss`` (for soft and stiff soil sites)
and ``Sa`` (for rock sites).
"""
Ss = np.zeros((len(sites.vs30), ))
Sa = np.zeros((len(sites.vs30), ))
# Soft soil; Vs30 < 360 m/s. Page 199.
idxSs = (sites.vs30 < 360.0)
# Stiff soil Class A; 360 m/s <= Vs30 <= 750 m/s. Page 199.
idxSa = (sites.vs30 >= 360.0) & (sites.vs30 <= 750.0)
Ss[idxSs] = 1
Sa[idxSa] = 1
return Ss, Sa
def _get_mechanism(self, sites, rup, imt, C):
"""
Compute the fourth term of the equation described on p. 199:
``b9 * Fn + b10 * Fr``
"""
Fn, Fr = self._get_fault_type_dummy_variables(sites, rup, imt)
return (C['b9'] * Fn) + (C['b10'] * Fr)
def _get_fault_type_dummy_variables(self, sites, rup, imt):
"""
Same classification of SadighEtAl1997. Akkar and Bommer 2010 is based
on Akkar and Bommer 2007b; read Strong-Motion Dataset and Record
Processing on p. 514 (Akkar and Bommer 2007b).
"""
Fn, Fr = 0, 0
if rup.rake >= -135 and rup.rake <= -45:
# normal
Fn = 1
elif rup.rake >= 45 and rup.rake <= 135:
# reverse
Fr = 1
return Fn, Fr
#: For PGA and SA up to 0.05 seconds, coefficients are taken from table 5,
#: page 385 of 'Extending ground-motion prediction equations for spectral
#: accelerations to higher response frequencies', while for PGV and SA with
#: periods greater than 0.05 coefficients are taken from table 1, pages
#: 200-201 of 'Empirical Equations for the Prediction of PGA, PGV,
#: and Spectral Accelerations in Europe, the Mediterranean Region, and
#: the Middle East'
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 Sigma1 tau SigmaTot
pga 1.43525 0.74866 -0.06520 -2.72950 0.25139 7.74959 0.08320 0.00766 -0.05823 0.07087 0.2611 0.1056 0.281646179
0.01 1.43153 0.75258 -0.06557 -2.73290 0.25170 7.73304 0.08105 0.00745 -0.05886 0.07169 0.2616 0.1051 0.281922986
0.02 1.48690 0.75966 -0.06767 -2.82146 0.26510 7.20661 0.07825 0.00618 -0.06111 0.06756 0.2635 0.1114 0.286080775
0.03 1.64821 0.73507 -0.06700 -2.89764 0.27607 6.87179 0.06376 -0.00528 -0.06189 0.06529 0.2675 0.1137 0.290661212
0.04 2.08925 0.65032 -0.06218 -3.02618 0.28999 7.42328 0.05045 -0.02091 -0.06278 0.05935 0.2709 0.1152 0.294377054
0.05 2.49228 0.58575 -0.06043 -3.20215 0.31485 7.75532 0.03798 -0.03143 -0.06708 0.06382 0.2728 0.1181 0.297266631
0.10 2.11994 0.75179 -0.07448 -3.10538 0.30253 8.21405 0.02667 -0.00062 -0.04906 0.07910 0.2728 0.1167 0.296713212
0.15 1.64489 0.83683 -0.07544 -2.75848 0.25490 8.31786 0.02578 0.01703 -0.04184 0.07840 0.2788 0.1192 0.303212928
0.20 0.92065 0.96815 -0.07903 -2.49264 0.21790 8.21914 0.06557 0.02105 -0.02098 0.08438 0.2821 0.1081 0.302102665
0.25 0.13978 1.13068 -0.08761 -2.33824 0.20089 7.20688 0.09810 0.03919 -0.04853 0.08577 0.2871 0.0990 0.303689661
0.30 -0.84006 1.37439 -0.10349 -2.19123 0.18139 6.54299 0.12847 0.04340 -0.05554 0.09221 0.2902 0.0976 0.306172827
0.35 -1.32207 1.47055 -0.10873 -2.12993 0.17485 6.24751 0.16213 0.06695 -0.04722 0.09003 0.2983 0.1054 0.316373276
0.40 -1.70320 1.55930 -0.11388 -2.12718 0.17137 6.57173 0.21222 0.09201 -0.05145 0.09903 0.2998 0.1101 0.319377598
0.45 -1.97201 1.61645 -0.11742 -2.16619 0.17700 6.78082 0.24121 0.11675 -0.05202 0.09943 0.3037 0.1123 0.323797746
0.50 -2.76925 1.83268 -0.13202 -2.12969 0.16877 7.17423 0.25944 0.13562 -0.04283 0.08579 0.3078 0.1163 0.329038797
0.55 -3.51672 2.02523 -0.14495 -2.04211 0.15617 6.76170 0.26498 0.14446 -0.04259 0.06945 0.3070 0.1274 0.332384958
0.60 -3.92759 2.08471 -0.14648 -1.88144 0.13621 6.10103 0.27718 0.15156 -0.03853 0.05932 0.3007 0.1430 0.332970704
0.65 -4.49490 2.21154 -0.15522 -1.79031 0.12916 5.19135 0.28574 0.15239 -0.03423 0.05111 0.3004 0.1546 0.337848072
0.70 -4.62925 2.21764 -0.15491 -1.79800 0.13495 4.46323 0.30348 0.15652 -0.04146 0.04661 0.2978 0.1626 0.339298688
0.75 -4.95053 2.29142 -0.15983 -1.81321 0.13920 4.27945 0.31516 0.16333 -0.04050 0.04253 0.2973 0.1602 0.337714865
0.80 -5.32863 2.38389 -0.16571 -1.77273 0.13273 4.37011 0.32153 0.17366 -0.03946 0.03373 0.2927 0.1584 0.332812034
0.85 -5.75799 2.50635 -0.17479 -1.77068 0.13096 4.62192 0.33520 0.18480 -0.03786 0.02867 0.2917 0.1543 0.32999603
0.90 -5.82689 2.50287 -0.17367 -1.76295 0.13059 4.65393 0.34849 0.19061 -0.02884 0.02475 0.2915 0.1521 0.328795772
0.95 -5.90592 2.51405 -0.17417 -1.79854 0.13535 4.84540 0.35919 0.19411 -0.02209 0.02502 0.2912 0.1484 0.326833291
1.00 -6.17066 2.58558 -0.17938 -1.80717 0.13599 4.97596 0.36619 0.19519 -0.02269 0.02121 0.2895 0.1483 0.325273946
1.05 -6.60337 2.69584 -0.18646 -1.73843 0.12485 5.04489 0.37278 0.19461 -0.02613 0.01115 0.2888 0.1465 0.323832812
1.10 -6.90379 2.77044 -0.19171 -1.71109 0.12227 5.00975 0.37756 0.19423 -0.02655 0.00140 0.2896 0.1427 0.322848958
1.15 -6.96180 2.75857 -0.18890 -1.66588 0.11447 5.08902 0.38149 0.19402 -0.02088 0.00148 0.2871 0.1435 0.320965201
1.20 -6.99236 2.73427 -0.18491 -1.59120 0.10265 5.03274 0.38120 0.19309 -0.01623 0.00413 0.2878 0.1439 0.321770182
1.25 -6.74613 2.62375 -0.17392 -1.52886 0.09129 5.08347 0.38782 0.19392 -0.01826 0.00413 0.2863 0.1453 0.321060399
1.30 -6.51719 2.51869 -0.16330 -1.46527 0.08005 5.14423 0.38862 0.19273 -0.01902 -0.00369 0.2869 0.1427 0.320429243
1.35 -6.55821 2.52238 -0.16307 -1.48223 0.08173 5.29006 0.38677 0.19082 -0.01842 -0.00897 0.2885 0.1428 0.321906959
1.40 -6.61945 2.52611 -0.16274 -1.48257 0.08213 5.33490 0.38625 0.19285 -0.01607 -0.00876 0.2875 0.1458 0.322356774
1.45 -6.62737 2.49858 -0.15910 -1.43310 0.07577 5.19412 0.38285 0.19161 -0.01288 -0.00564 0.2857 0.1477 0.321620553
1.50 -6.71787 2.49486 -0.15689 -1.35301 0.06379 5.15750 0.37867 0.18812 -0.01208 -0.00215 0.2839 0.1468 0.319608276
1.55 -6.80776 2.50291 -0.15629 -1.31227 0.05697 5.27441 0.37267 0.18568 -0.00845 -0.00047 0.2845 0.1450 0.319319981
1.60 -6.83632 2.51009 -0.15676 -1.33260 0.05870 5.54539 0.36952 0.18149 -0.00533 -0.00006 0.2844 0.1457 0.319549448
1.65 -6.88684 2.54048 -0.15995 -1.40931 0.06860 5.93828 0.36531 0.17617 -0.00852 -0.00301 0.2841 0.1503 0.321407685
1.70 -6.94600 2.57151 -0.16294 -1.47676 0.07672 6.36599 0.35936 0.17301 -0.01204 -0.00744 0.2840 0.1537 0.32292366
1.75 -7.09166 2.62938 -0.16794 -1.54037 0.08428 6.82292 0.35284 0.16945 -0.01386 -0.01387 0.2840 0.1558 0.323928449
1.80 -7.22818 2.66824 -0.17057 -1.54273 0.08325 7.11603 0.34775 0.16743 -0.01402 -0.01492 0.2834 0.1582 0.324565556
1.85 -7.29772 2.67565 -0.17004 -1.50936 0.07663 7.31928 0.34561 0.16730 -0.01526 -0.01192 0.2828 0.1592 0.32453117
1.90 -7.35522 2.67749 -0.16934 -1.46988 0.07065 7.25988 0.34142 0.16325 -0.01563 -0.00703 0.2826 0.1611 0.325293667
1.95 -7.40716 2.68206 -0.16906 -1.43816 0.06525 7.25344 0.33720 0.16171 -0.01848 -0.00351 0.2832 0.1642 0.327358947
2.00 -7.50404 2.71004 -0.17130 -1.44395 0.06602 7.26059 0.33298 0.15839 -0.02258 -0.00486 0.2835 0.1657 0.328372867
2.05 -7.55598 2.72737 -0.17291 -1.45794 0.06774 7.40320 0.33010 0.15496 -0.02626 -0.00731 0.2836 0.1665 0.328863513
2.10 -7.53463 2.71709 -0.17221 -1.46662 0.06940 7.46168 0.32645 0.15337 -0.02920 -0.00871 0.2832 0.1663 0.328417311
2.15 -7.50811 2.71035 -0.17212 -1.49679 0.07429 7.51273 0.32439 0.15264 -0.03484 -0.01225 0.2830 0.1661 0.328143581
2.20 -8.09168 2.91159 -0.18920 -1.55644 0.08428 7.77062 0.31354 0.14430 -0.03985 -0.01927 0.2830 0.1627 0.326435736
2.25 -8.11057 2.92087 -0.19044 -1.59537 0.09052 7.87702 0.30997 0.14430 -0.04155 -0.02322 0.2830 0.1627 0.326435736
2.30 -8.16272 2.93325 -0.19155 -1.60461 0.09284 7.91753 0.30826 0.14412 -0.04238 -0.02626 0.2829 0.1633 0.326648588
2.35 -7.94704 2.85328 -0.18539 -1.57428 0.09077 7.61956 0.32071 0.14321 -0.04963 -0.02342 0.2815 0.1632 0.325386678
2.40 -7.96679 2.85363 -0.18561 -1.57833 0.09288 7.59643 0.31801 0.14301 -0.04910 -0.02570 0.2826 0.1645 0.326990841
2.45 -7.97878 2.84900 -0.18527 -1.57728 0.09428 7.50338 0.31401 0.14324 -0.04812 -0.02643 0.2825 0.1665 0.327915385
2.50 -7.88403 2.81817 -0.18320 -1.60381 0.09887 7.53947 0.31104 0.14332 -0.04710 -0.02769 0.2818 0.1681 0.328129319
2.55 -7.68101 2.75720 -0.17905 -1.65212 0.10680 7.61893 0.30875 0.14343 -0.04607 -0.02819 0.2818 0.1688 0.328488478
2.60 -7.72574 2.82043 -0.18717 -1.88782 0.14049 8.12248 0.31122 0.14255 -0.05106 -0.02966 0.2838 0.1741 0.332946317
2.65 -7.53288 2.74824 -0.18142 -1.89525 0.14356 7.92236 0.30935 0.14223 -0.05024 -0.02930 0.2845 0.1759 0.334486263
2.70 -7.41587 2.69012 -0.17632 -1.87041 0.14283 7.49999 0.30688 0.14074 -0.04887 -0.02963 0.2854 0.1772 0.335936006
2.75 -7.34541 2.65352 -0.17313 -1.86079 0.14340 7.26668 0.30635 0.14052 -0.04743 -0.02919 0.2862 0.1783 0.337196278
2.80 -7.24561 2.61028 -0.16951 -1.85612 0.14444 7.11861 0.30534 0.13923 -0.04731 -0.02751 0.2867 0.1794 0.338202972
2.85 -7.07107 2.56123 -0.16616 -1.90422 0.15127 7.36277 0.30508 0.13933 -0.04522 -0.02776 0.2869 0.1788 0.338054803
2.90 -6.99332 2.52699 -0.16303 -1.89704 0.15039 7.45038 0.30362 0.13776 -0.04203 -0.02615 0.2874 0.1784 0.338268119
2.95 -6.95669 2.51006 -0.16142 -1.90132 0.15081 7.60234 0.29987 0.13584 -0.03863 -0.02487 0.2872 0.1783 0.338045456
3.00 -6.92924 2.45899 -0.15513 -1.76801 0.13314 7.21950 0.29772 0.13198 -0.03855 -0.02469 0.2876 0.1785 0.338490783
4.00 -6.92924 2.45899 -0.15513 -1.76801 0.13314 7.21950 0.29772 0.13198 -0.03855 -0.02469 0.2876 0.1785 0.338490783
pgv -2.12833 1.21448 -0.08137 -2.46942 0.22349 6.41443 0.20354 0.08484 -0.05856 0.01305 0.2562 0.1083 0.278149834
""")
class SandikkayaDinsever2018(GMPE):
"""
Implements the nonlinear site amplification model of Sandikkaya &
Dinsever (2018)
Sandikkaya, M. A. and Dinsever, L. D. (2018) "A Site Amplification Model
for Crustal Earthquakes", Geosciences, 264(8),
doi:10.3390/geosciences8070264
Note that the nonlinear amplification model has its own standard deviation,
which should be applied with the phi0 model of the original GMPE. This
is not defined for all GMPEs in the literature, nor is the retrieval
of it consistently applied in OpenQuake. Therefore we allow the user
to define manually the input phi0 model, and if this is not possible a
"default" phi0 is taken by reducing the original GMPE's phi by 15 %.
The amplification model is compatible only with GMPEs with separate
inter- and intra-event standard deviation, otherwise an error is raised.
:param gmpe:
Input GMPE for calculation on reference rock and standrd deviation
at the period of interest on surface rock
:param phi_0:
Single-station within-event standard deviation (as a period-dependent
dictionary or None)
:param str region:
Defines the region for the region-adjusted version of the model
"""
experimental = True
#: Supported tectonic region type is undefined
DEFINED_FOR_TECTONIC_REGION_TYPE = "Active Shallow Crust"
#: Supported intensity measure types are not set
DEFINED_FOR_INTENSITY_MEASURE_TYPES = set((PGA, SA))
#: Supported intensity measure component is horizontal
#: :attr:`~openquake.hazardlib.const.IMC.HORIZONTAL`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.HORIZONTAL
#: Supported standard deviation type
DEFINED_FOR_STANDARD_DEVIATION_TYPES = set([const.StdDev.TOTAL])
#: Required site parameters will be set be selected GMPES
REQUIRES_SITES_PARAMETERS = set(('vs30', 'z1pt0'))
#: Required rupture parameter is magnitude, others will be set later
REQUIRES_RUPTURE_PARAMETERS = set(('mag', ))
#: Required distance metrics will be set by the GMPEs
REQUIRES_DISTANCES = set()
#: Defined reference velocity is 800 m/s
DEFINED_FOR_REFERENCE_VELOCITY = 760.0
def __init__(self,
gmpe_name,
reference_velocity=760.,
region=None,
phi_0=None,
**kwargs):
super().__init__()
if isinstance(gmpe_name, str):
self.gmpe = registry[gmpe_name](**kwargs)
else:
# An instantiated class is passed as an argument
self.gmpe = copy.deepcopy(gmpe_name)
# Define the reference velocity - set to 760. by default
self.rock_vs30 = reference_velocity if reference_velocity else\
self.DEFINED_FOR_REFERENCE_VELOCITY
for name in uppernames:
setattr(self, name,
frozenset(getattr(self, name) | getattr(self.gmpe, name)))
stddev_check = (const.StdDev.INTER_EVENT in
self.DEFINED_FOR_STANDARD_DEVIATION_TYPES) and\
(const.StdDev.INTRA_EVENT in
self.DEFINED_FOR_STANDARD_DEVIATION_TYPES)
if not stddev_check:
raise ValueError("Input GMPE %s not defined for inter- and intra-"
"event standard deviation" % str(self.gmpe))
if isinstance(phi_0, dict):
# Input phi_0 model
iphi_0 = {}
for key in phi_0:
iphi_0[from_string(key)] = phi_0[key]
self.phi_0 = CoeffsTable(sa_damping=5, table=iphi_0)
else:
# No input phi_0 model
self.phi_0 = None
# Regionalisation of the linear site term is possible
# check if region is in the set of supported terms and
# raise error otherwise
if region is not None:
if region in REGION_SET:
self.region = "ck{:s}".format(region)
else:
raise ValueError("Region must be one of: %s" %
" ".join(REGION_SET))
else:
self.region = region
def get_mean_and_stddevs(self, sctx, rctx, dctx, imt, stddev_types):
"""
Returns the mean and standard deviations
"""
sctx_r = copy.copy(sctx)
sctx_r.vs30 = self.rock_vs30 * np.ones_like(sctx_r.vs30)
mean, stddevs = self.gmpe.get_mean_and_stddevs(
sctx_r, rctx, dctx, imt,
[const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT])
psarock = np.exp(mean)
C = self.COEFFS_SITE[imt]
if self.region:
ck = self.COEFFS_REG[imt][self.region]
else:
ck = 0.0
ampl = self.get_site_amplification(C, psarock, sctx, ck)
mean += ampl
stddevs = self.get_stddevs(C, stddevs, psarock, sctx.vs30, imt,
stddev_types)
return mean, stddevs
def get_site_amplification(self, C, psarock, sites, ck):
"""
Returns the site amplification model define in equation (9)
"""
vs30_s = np.copy(sites.vs30)
vs30_s[vs30_s > 1000.] = 1000.
fn_lin = (C["b1"] + ck) * np.log(vs30_s / 760.)
fn_z = C["b2"] * np.log(sites.z1pt0)
fn_nl = C["b3"] * np.log((psarock + 0.1 * g) / (0.1 * g)) *\
np.exp(-np.exp(2.0 * np.log(sites.vs30) - 11.))
return fn_lin + fn_z + fn_nl
def get_stddevs(self, C, istddevs, psa_rock, vs30, imt, stddev_types):
"""
Returns the standard deviation adjusted for the site-response model
"""
tau, phi = istddevs
ysig = np.copy(psa_rock)
ysig[ysig > 0.35] = 0.35
ysig[ysig < 0.005] = 0.005
vsig = np.copy(vs30)
vsig[vsig > 600.0] = 600.0
vsig[vsig < 150.] = 150.
sigma_s = C["sigma_s"] * C["c0"] * (C["c1"] * np.log(ysig) +
C["c2"] * np.log(vsig))
if self.phi_0:
phi0 = self.phi_0[imt] + np.zeros(vs30.shape)
else:
# In the case that no input phi0 is defined take 'approximate'
# phi0 as 85 % of phi
phi0 = 0.85 * phi
phi = np.sqrt(phi0**2. + sigma_s**2.)
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.sqrt(tau**2. + phi**2.) + np.zeros(vs30.shape))
elif stddev_type == const.StdDev.INTRA_EVENT:
stddevs.append(phi)
elif stddev_type == const.StdDev.INTER_EVENT:
stddevs.append(tau + np.zeros(vs30.shape))
return stddevs
COEFFS_SITE = CoeffsTable(sa_damping=5,
table="""\
imt b1 b3 b2 sigma_s c0 c2 c1
pga -0.53307 -0.46412 0.02105 0.47096 1.24013 0.09542 -0.05865
0.010 -0.53307 -0.46412 0.02105 0.47096 1.24013 0.09542 -0.05865
0.025 -0.50842 -0.39040 0.02023 0.47508 1.24682 0.09906 -0.05951
0.040 -0.45025 -0.31255 0.01858 0.48906 1.33552 0.12324 -0.06481
0.050 -0.38023 -0.23187 0.02029 0.50412 1.67790 0.18762 -0.08741
0.070 -0.35050 -0.18413 0.02376 0.50892 1.57403 0.12994 -0.07910
0.100 -0.42752 -0.37652 0.03221 0.49777 1.52282 0.12604 -0.07408
0.150 -0.55919 -0.53679 0.03248 0.47977 1.31863 0.11085 -0.05612
0.200 -0.66730 -0.65710 0.02956 0.46896 1.21025 0.10065 -0.04777
0.250 -0.73135 -0.69189 0.02516 0.45698 1.13978 0.07837 -0.03958
0.300 -0.78840 -0.68208 0.03152 0.45065 1.05645 0.04621 -0.03245
0.350 -0.83320 -0.69252 0.03233 0.44141 1.01481 0.05533 -0.02765
0.400 -0.86810 -0.74537 0.03521 0.43589 1.00182 0.05914 -0.02363
0.450 -0.88575 -0.73547 0.03923 0.42954 0.94803 0.06557 -0.01790
0.500 -0.89944 -0.69269 0.04159 0.42699 0.94724 0.06067 -0.01710
0.600 -0.91493 -0.63480 0.04580 0.41593 0.95504 0.07576 -0.01606
0.700 -0.93236 -0.63204 0.04993 0.40303 1.01362 0.08323 -0.01527
0.750 -0.93217 -0.63780 0.04989 0.40219 1.03634 0.08203 -0.01622
0.800 -0.92975 -0.65092 0.05114 0.39766 1.05807 0.08385 -0.01434
0.900 -0.92777 -0.57775 0.05266 0.38861 1.11036 0.09388 -0.01658
1.000 -0.93815 -0.60041 0.05421 0.38150 1.16634 0.09095 -0.01502
1.200 -0.93377 -0.56801 0.05576 0.36982 1.29484 0.08078 -0.01434
1.400 -0.93847 -0.48684 0.05782 0.35868 1.32222 0.08353 -0.00681
1.600 -0.92242 -0.40484 0.05645 0.35713 1.30431 0.07158 -0.00268
1.800 -0.91608 -0.29053 0.05615 0.34643 1.35426 0.07341 0.00000
2.000 -0.90369 -0.18149 0.05307 0.34133 1.38763 0.06790 0.00000
2.500 -0.89442 -0.04175 0.05954 0.33960 1.41986 0.08582 0.00000
3.000 -0.87386 0.00000 0.05596 0.35349 1.37795 0.10208 0.00000
3.500 -0.85510 0.00000 0.05469 0.35286 1.34678 0.07501 0.00000
4.000 -0.84680 0.00000 0.05469 0.36845 1.25830 0.05876 0.00000
""")
COEFFS_REG = CoeffsTable(sa_damping=5,
table="""\
imt ckUSNZ ckJP ckTW ckCH ckWA ckGRTR ckWMT ckNWE
pga -0.0302 0.0117 -0.0233 0.01580 0.10010 -0.0118 0.01720 0.0314
0.010 -0.0302 0.0117 -0.0233 0.01580 0.10010 -0.0118 0.01720 0.0314
0.025 -0.0303 0.0135 -0.0272 0.01500 0.10130 -0.0100 0.01740 0.0264
0.040 -0.0336 0.0298 -0.0394 0.01110 0.10590 -0.0148 0.01010 0.0178
0.050 -0.0400 0.0575 -0.0541 0.00990 0.10710 -0.0240 -0.00930 0.0038
0.070 -0.0346 0.0508 -0.0560 -0.00120 0.11190 -0.0190 -0.01140 -0.0206
0.100 -0.0287 0.0199 -0.0450 0.02200 0.12510 -0.0095 0.00840 -0.0222
0.150 -0.0187 -0.0228 -0.0114 0.01430 0.11050 0.0044 0.02580 -0.0307
0.200 -0.0196 -0.0439 0.0089 0.00560 0.11340 0.0133 0.03500 -0.0254
0.250 -0.0227 -0.0543 0.0222 0.00590 0.10160 0.0162 0.04800 0.0274
0.300 -0.0216 -0.0583 0.0300 -0.00003 0.08600 0.0153 0.05800 0.0407
0.350 -0.0187 -0.0583 0.0301 0.00250 0.08900 0.0135 0.05340 0.0650
0.400 -0.0239 -0.0544 0.0313 0.00800 0.09462 0.0070 0.05177 0.0728
0.450 -0.0254 -0.0502 0.0327 0.01420 0.09990 0.0041 0.05190 0.0798
0.500 -0.0322 -0.0461 0.0360 0.01560 0.10730 -0.0022 0.05530 0.0879
0.600 -0.0388 -0.0389 0.0356 0.01630 0.12090 -0.0125 0.05650 0.0978
0.700 -0.0411 -0.0333 0.0336 0.02200 0.12460 -0.0197 0.04830 0.1104
0.750 -0.0416 -0.0305 0.0339 0.02520 0.12240 -0.0269 0.04850 0.1166
0.800 -0.0436 -0.0289 0.0346 0.02970 0.12440 -0.0321 0.05120 0.1193
0.900 -0.0412 -0.0262 0.0289 0.03250 0.12390 -0.0408 0.05740 0.1303
1.000 -0.0397 -0.0195 0.0146 0.03750 0.12730 -0.0434 0.06730 0.1369
1.200 -0.0395 -0.0071 -0.0025 0.04630 0.13760 -0.0467 0.06680 0.0914
1.400 -0.0365 -0.0036 -0.0115 0.05740 0.13970 -0.0446 0.06400 0.0893
1.600 -0.0361 0.0073 -0.0188 0.06200 0.13190 -0.0473 0.06000 0.0914
1.800 -0.0307 0.0108 -0.0252 0.06090 0.13320 -0.0452 0.05230 0.1062
2.000 -0.0280 0.0129 -0.0328 0.05910 0.14080 -0.0445 0.04100 0.1092
2.500 -0.0336 0.0277 -0.0413 0.05880 0.14710 -0.0316 0.01970 0.0509
3.000 -0.0325 0.0369 -0.0579 0.05660 0.16790 -0.0268 0.01380 0.1050
3.500 -0.0272 0.0461 -0.0630 0.05250 0.14220 -0.0294 0.02160 0.1560
4.000 -0.0203 0.0503 -0.0641 0.05720 0.19450 -0.0242 0.01380 0.2198
""")
class AtkinsonBoore2003SSlab(AtkinsonBoore2003SInter):
"""
Implements GMPE developed by G. M Atkinson and D. Boore and published as
"Empirical Ground-Motion Relations for Subduction-Zone Earthquakes and
Their Application to Cascadia and Other Regions" (Bulletin of the
Seismological Society of America, Volume 93, Number 4, pages 1703-1929,
2003). The class implements the global model but not the corrections for
Japan/Cascadia. SA values at 4 s (not supported by the original equations)
are obtained from mean value at 3 s divided by a factor equal to 0.550
(scaling factor computed in the context of the SHARE project and obtained
as average ratio between median values at 4 and 3 seconds as predicted by
SHARE subduction GMPEs). The class implements the equations for 'Subduction
IntraSlab' (that's why the class name ends with 'SSlab').
"""
#: Supported tectonic region type is subduction interface
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.SUBDUCTION_INTRASLAB
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.
"""
# extracting dictionary of coefficients specific to required
# intensity measure type.
C = self.COEFFS_SSLAB[imt]
# cap magnitude values at 8.0, see page 1709
mag = rup.mag
if mag >= 8.0:
mag = 8.0
# compute PGA on rock (needed for site amplification calculation)
G = 10**(0.301 - 0.01 * mag)
pga_rock = self._compute_mean(
self.COEFFS_SSLAB[PGA()],
G,
mag,
rup.hypo_depth,
dists.rrup,
sites.vs30,
# by passing pga_rock > 500 the soil
# amplification is 0
np.zeros_like(sites.vs30) + 600,
PGA())
pga_rock = 10**(pga_rock)
# compute actual mean and convert from log10 to ln and units from
# cm/s**2 to g
mean = self._compute_mean(C, G, mag, rup.hypo_depth, dists.rrup,
sites.vs30, pga_rock, imt)
mean = np.log((10**mean) * 1e-2 / g)
if isinstance(imt, SA) and imt.period == 4.0:
mean /= 0.550
stddevs = self._get_stddevs(C, stddev_types, sites.vs30.shape[0])
return mean, stddevs
COEFFS_SSLAB = CoeffsTable(sa_damping=5,
table="""\
IMT c1 c2 c3 c4 c5 c6 c7 sigma s1 s2
pga -0.04713 0.69090 0.01130 -0.00202 0.19000 0.24000 0.29000 0.27000 0.23000 0.14000
0.0400 0.50697 0.63273 0.01275 -0.00234 0.15000 0.20000 0.20000 0.25000 0.24000 0.07000
0.1000 0.43928 0.66675 0.01080 -0.00219 0.15000 0.23000 0.20000 0.28000 0.27000 0.07000
0.2000 0.51589 0.69186 0.00572 -0.00192 0.15000 0.27000 0.25000 0.28000 0.26000 0.10000
0.4000 0.00545 0.77270 0.00173 -0.00178 0.13000 0.37000 0.38000 0.28000 0.26000 0.10000
1.0000 -1.02133 0.87890 0.00130 -0.00173 0.10000 0.30000 0.55000 0.29000 0.27000 0.11000
2.0000 -2.39234 0.99640 0.00364 -0.00118 0.10000 0.25000 0.40000 0.30000 0.28000 0.11000
3.0000 -3.70012 1.11690 0.00615 -0.00045 0.10000 0.25000 0.36000 0.30000 0.29000 0.08000
4.0000 -3.70012 1.11690 0.00615 -0.00045 0.10000 0.25000 0.36000 0.30000 0.29000 0.08000
""")
class BooreEtAl1993GSCBest(GMPE):
"""
Implement equation used by the Geological Survey of Canada (GSC) for
the 2010 Western Canada National Seismic Hazard Model. The class implements
the model of David M. Boore, William B. Joyner, and Thomas E. Fumal
("Estimation of Response Spectra and Peak Accelerations from Western North
American Earthquakes: An Interim Report", 1993, U.S. Geological Survey,
Open File Report 93-509).
Equation coefficients provided by GSC for the random horizontal component
and corresponding to the 'Best' case (that is mean unaffected)
"""
#: Supported tectonic region type is active shallow crust, given
#: that the equations have been derived for Western North America
DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.ACTIVE_SHALLOW_CRUST
#: Supported intensity measure types are spectral acceleration,
#: and peak ground acceleration
DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA}
#: Supported intensity measure component is random horizontal
#: :attr:`~openquake.hazardlib.const.IMC.RANDOM_HORIZONTAL`,
DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.RANDOM_HORIZONTAL
#: Supported standard deviation type is total
DEFINED_FOR_STANDARD_DEVIATION_TYPES = {const.StdDev.TOTAL}
#: site params are not required
REQUIRES_SITES_PARAMETERS = set()
#: Required rupture parameter is magnitude
REQUIRES_RUPTURE_PARAMETERS = {'mag'}
#: Required distance measure is Rjb distance
#: see paragraph 'Predictor Variables', page 6.
REQUIRES_DISTANCES = {'rjb'}
def compute(self, ctx, imts, mean, sig, tau, phi):
"""
See :meth:`superclass method
<.base.GroundShakingIntensityModel.compute>`
for spec of input and result values.
"""
for m, imt in enumerate(imts):
C = self.COEFFS[imt]
mag = ctx.mag - 6
d = np.sqrt(ctx.rjb**2 + C['c7']**2)
mean[m] += C['c1'] + C['c2'] * mag + C['c3'] * mag**2 + C['c6']
idx = d <= 100.
mean[m, idx] += C['c5'] * np.log10(d[idx])
idx = d > 100.
mean[m,
idx] += (C['c5'] * np.log10(100.) - np.log10(d[idx] / 100.) +
C['c4'] * (d[idx] - 100.))
# convert from log10 to ln and from cm/s**2 to g
mean[m] = np.log((10.0**(mean[m] - 2.0)) / g)
sig[m] = C['sigma']
#: coefficient table provided by GSC
COEFFS = CoeffsTable(sa_damping=5,
table="""\
IMT c1 c2 c3 c4 c5 c6 c7 sigma
pga 2.887 0.229 0.0 -0.00326 -0.778 0.162 5.57 0.529
0.1 3.451 0.327 -0.098 -0.00395 -0.934 0.046 6.27 0.479
0.2 3.464 0.309 -0.090 -0.00259 -0.924 0.190 7.02 0.495
0.3 3.295 0.334 -0.070 -0.00202 -0.893 0.239 5.94 0.520
0.5 2.980 0.384 -0.039 -0.00148 -0.846 0.279 4.13 0.562
1.0 2.522 0.450 -0.014 -0.00097 -0.798 0.314 2.90 0.622
2.0 2.234 0.471 -0.037 -0.00064 -0.812 0.360 5.85 0.675
""")
