PROBABILITY-CONSISTENT SCENARIO EARTHQUAKE AND ITS APPLICATION IN ESTIMATION OF GROUND MOTIONS

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1 PROBABILITY-COSISTET SCEARIO EARTHQUAKE AD ITS APPLICATIO I ESTIATIO OF GROUD OTIOS Q-feng LUO SUARY Th paper preent a new defnton of probablty-content cenaro earthquae PCSE and an evaluaton method of t magntude, epcentral dtance and orentaton. A an example of applcaton, correpondng to 3% probablty of exceedance, the magntude of PCSE near Shangha area 6.9, t epcentral dtance about 48 m and the orentaton of the epcenter 7.4 E. Oberved record of the Lulong earthquae L 5.3 n 98 are choen a emprcal Green functon to yntheze ground moton of PCSE n the ame area. The pea value of ynthetc acceleragram are about 3 Gal, whch content wth the reult analyzed by probablty emc hazard analy method. The conventonal probablty emc hazard analy method [Cornell, 968] ueful to etmaton of ground moton ntenty for emc degn, but there no emc bacground, uch a magntude, epcenter and orentaton, for the ntenty. Another method, whch alo often ued for emc degn, that the ground moton are mulated for a gven cenaro earthquae and a epcentral dtance, but th method determntc method and the etmated moton are alo determntc rather than probabltc. Some reearcher uggeted a concept of probablty-content cenaro earthquae that ha the advantage of both method. For the etmated ground moton by applyng th concept, there exceeded probablty, and there are ome phycally meanng magntude and focal dtance too. [Ihawa et al, 988a, b and Campo-cota et al, 99]. Unfortunately, accordng to the extng defnton of cenaro earthquae, the exceedng probablty of a ground moton caued by a cenaro earthquae not trctly content wth hazard level deduced from the probablty emc hazard analy method. The purpoe of th paper to preent a new defnton of Probablty-Content Scenaro Earthquae PCSE and an evaluaton method of t magntude, focal dtance and orentaton. A an example, the methodology appled n Shangha area, where there are analy reult wth the conventonal probablty emc analy method. At lat, Oberved record of the Lulong earthquae L 5.3 n 98 are choen a emprcal Green functon to yntheze ground moton of PCSE n the ame area Defnton of PCSE and t evaluaton ITRODUCTIO.. Defnton of PCSE Ung Ihawa and Kameda approach [Ihawa and Kameda, 988 a, b], expected value of magntude and focal dtance of hazard-content earthquae can be defned a Inttute of Structure Eng and Dater Protecton, Tong Unverty, Shangha, Chna. Emal: luo@mal.tong.edu.cn

2 R m P m, r m, r Y y p r P m, r Y Y y p y p here, P the condton probablty of magntude m and focal dtance r. The condton the ground moton ntenty Y y p, p probablty exceedance obtaned from hazard analy and mean th potental emc ource area. Accordng to th defnton, ground moton ntenty Y caued n cenaro earthquae agntude, focal dtance R. wll be larger than y p, but the emc degn level n code hould be y p. It mean that the exceeded probablty of ntenty Y maller than p and atfe equaton p,, u where p the magntude of potental earthquae n th emc zone, whch can caue ground moton ntenty y p on te, u the maxmum magntude of potental earthquae n th zone. In th paper the probablty-content magntude p and probablty-content focal dtance R p are defned a condtonal mean value correpondng to a gven ground moton ntenty y p, conderng p, R p and y p are retraned by attenuaton relatonhp y f, R, then the defnton can be expreed a followng: R p p f m P m, r p, y p Y y p 3 or R p p f R r P m, r p, y p Y y p. 4 here, P m, r Y y p the condton probablty of magntude m and focal dtance r, the condton the ground moton ntenty Y y p. If the mnmum magntude and u the maxmum magntude of potental earthquae n potental emc ource area, the PCSE p, whch caue ground moton ntenty y p on te, atfe p,. 5 u Compare equaton and 5, t obvou that there dfference between the two nd of probablty-content cenaro earthquae defned by equaton and equaton 3 or 4, repectvely. The exceeded probablte of the cenaro earthquae defned by ung former method are maller than p. It mple that the cenaro earthquae defned by equaton not a probablty-content cenaro earthquae PCSE Luo, Evaluaton method of PCSE n model I potental emc zone In model I potental emc zone n whch the emc fault very clear, t treated a lne emc zone [Kureghan and Ang, 977]. A hown n Fg., AB a lne potental emc zone, whoe length L. The

3 mnmum magntude n th emc zone, the maxmum magntude u. Aumng that r the mnmum focal dtance from te S to fault AB and r the maxmum focal dtance, focal dtance R p of PCSE atfe R p r,. 6 r In order to calculate focal dtance R p, the mnmum focal dtance R mn p and maxmum focal dtance R max p of PCSE hould be calculated. Conderng ground moton y p can be caued by mall earthquae n near feld and by large earthquae n far feld, t eay to obtan R mn p and R max p wth try-error method and ground moton attenuaton relatonhp. R p between r and r, generally, R mn p equal to r. Becaue earthquae Fgure. ode I emc ource zone can occurred everywhere n emc zone AB, the dtrbuton of PCSE epcentre aumed a unform dtrbuton, n lne emc zone th nd of unform dtrbuton can be replaced by unform dtrbuton of focal dtance r p, whch can be expreed a f r p, 7 Rmax p Rmn p and the R p of PCSE can be calculated from R p Rmax p + Rmn p. 8 By ntroducng y p and R mn p, p can be deduced from equaton 4. The o pont n Fg. the emc centre of PCSE... Applcaton of PCSE n model II area In model II potental emc zone, the emc fault not clear, but t fault drecton and dtrbuton area are nown [Kureghan and Ang, 977]. A hown n Fg., ABCD a quare potental emc zone, wthout queton the maxmum dtance r and mnmum dtance r from te to emc zone ABCD can be obtaned ealy. Alo aumng that the mnmum magntude n th emc zone, the maxmum magntude u. A ame a above, Fgure. odel II emc ource zone R mn p and R max p can be deduced by try-error method. Correpondng to R mn p and R max p, φ mn p and φ max p can be obtaned. A mentoned above, earthquae may occurred everywhere n zone ABCD, the dtrbuton of PCSE epcentre can be aumed a unform dtrbuton, n quare emc zone th nd of unform dtrbuton can be replaced by unform dtrbuton of focal dtance r p and unform dtrbuton of orentaton φ p. R p of PCSE can be calculated from 3

4 R p Rmax p + Rmn p, 9 and φ p of PCSE can be got from φ p φ max p + φ mn p. Then p can be deduced from equaton 4. Becaue R p and φ p are both nown, the epcentre of PCSE decded. o pont n Fg. the emc centre of PCSE.. Applcaton of PCSE n Shangha regon There are eventeen potental emc zone n Shangha area and Tong Unverty performed the probablty hazard analy n th area. Accordng to ther analy, the potental ource area A one of the mot mportant area that have large contrbuton to the probablty exceedance value p. Fg.3 how the potental emc ource zone A and the te S, whch one te n Shangha cty centre, Correpondng to probablty exceedance 63.%, % and 3%, the pea acceleraton on te S are 4Gal, 84 Gal and 3Gal, repectvely Zhang et al, 99. Fgure 3. Potental ource area A and te S The attenuaton equaton of pea acceleraton Hu, 988 log a log R + 3 choen to calculate PCSE. A the calculaton method of PCSE n odel II emc ource area, three PCSE were calculated from equaton 3 and, whoe magntude 6.3%, % and 3% are 6.5, 6.7 and 6.9, whoe focal dtance R 6.3%, R % and R3% are 97m, 57m and 48m and whoe orentaton φ 6.3%, φ % and φ3% are 7.7 E, 8.75 E, 7.79 E. The three PCSE are labeled wth o., o. and o.3 n Fg.3.. STROG OTIO SIULATIO OF PCSE The mot mportant applcaton of PCSE to apply t to etmatng ground moton for emc degn. In th paper, a an example of applcaton of PCSE, an mproved emprcal Green functon method Luo, 99 ued to yntheze ground moton on te S, the center of Shangha cty ee Fgure 3, for one PCSE p Emprcal Green functon method Snce the appearance of emprcal Green functon method Harzell, 978, n whch the mall earthquae record treated a Green functon to yntheze large earthquae record, many reearcher have appled th method and have made t more practcal Irura, 983, Dan et al, 989, Luo et al, 99, 994. Th method cont of three man tep: The frt tep to decde the ub-fault number of a large earthquae fault. The econd to modfy mall earthquae record nto that radated from ub-fault event of large earthquae. The lat to add mall event record together. 4

5 In th paper the record of Lulong earthquae L 5.3, whch occurred n orth Chna on 9, Aug, 98, are choen a Green functon to yntheze the ground moton caued by large PCSE 6.9, becaue Lulong earthquae rupture drecton 56 E that almot a ame a the drecton of fault n potental ource zone A ee Fg. 3. In orth Chna and Eat Chna, many earthquae are tre event ESRI, 994, o that the mall and large event are aumed a tre event here. And the L, W and D, ub-event number along large fault length, wdth and dlocaton, can be calculated from Luo, 99 L W D E L L S D D S E L W 3 S, here the ubcrpt mean the value of mall earthquae event, rato of the fault length to wdth, D average dlocaton. emc moment gven by µ DLW. For rectangle tre fault event, t can be expreed a Kanamor and Anderon, 975 π σlw here, 3 σ tre drop. Equaton deduced from equaton 3 and µ DLW. 4 In th method the we apply the approxmate ource pectrum for the far-feld hear wave dplacement propoed by Brune 97 to modfy the oberved mall event moton nto a moton radated from an element fault of the large PCSE. The modfcaton formula decrbed by Dan, et al 989, Luo and Dan, 994, Luo and Hu, 997 A pq r ω r pq abd ω c ω d / c 4 + ω ab c + ω π Q ω r pq r / 4πβ A ω. 5 Here, the ubcrpt, pq, and pq ndcate the value for the mall event, the p, q ub-fault of the large fault and the p, q, element of the large event, repectvely. r the hypocentral dtance, µ the rgdty, β the hear-wave velocty, an magnary unt and Q the qualty factor. a, b, c and d are rato of the fault length L, the wdth W, the average dlocaton D and the tre drop σ of the large event to thoe of the mall event, repectvely. ω c the corner frequency gven by ω c β πλ σ /, and λ LW / π the ze of the ource. The geometrc attenuaton and ntrnc attenuaton of the propagaton wave are condered n term of r / rpq and Q, repectvely. An etmated acceleraton a t of a large earthquae can then be wrtten by a t a t t, 6 L W D p q pq pq here a pq t the Fourer nvere tranform of A pq ω, t pq the travellng tme lag for the rupture proce, the wave propagaton and the re tme for dlocaton. 5

6 . Source parameter Two record recorded on TS-/Beadan taton are choen a emprcal Green functon, becaue the focal dtance from TS- taton to Lulong earthquae epcenter about 4 m, that mlar to the focal dtance from te S to PCSE n Fg.3. The te ol tff, belong to B cla ol from Prvate letter from Prof. K. Peng, 998. It ource parameter are choen from Luo, et.al 99 and hown n Table. By ung the ource parameter n Table and Brune pectrum model mentoned above Brune, 97, the theoretcal Fourer pectra of mall event can be calculated. The comparon of the theoretcal pectra and Fourer pectra of the oberved record n Fg.4 mple that the choen ource parameter of the mall event are acceptable. Acceleraton tme htory of mall event hown n Fg. 5. Fgure 4 Comparon of theoretcal pectra and oberved Fourer pectra Reference to equaton 7 that for magntude between 5.5 to 8.5 n the Eat Chna propoed by R. Dong ESRC, log L 7 and other materal, the fault length L of the PCSE 6.9 choen a 45 m. It aumed that the fault wdth W of large event the half of the fault length and the value of tre drop σ equal to mall event. Other neceary parameter can be calculated from equaton, 3, and 4. All the parameter of mall and large event are lted n Table. Table Source parameter of mall and large event agntude L m L Wm Δσ 5 Pa Depthm D m.8.4 L - W - D - β 3. Rupture velocty V R m/.5 Qualty Q 5.3 Synthetc accelerogram The hear wave velocty β and the fault rupture velocty V R adopted here are 3. m/ and.5 m/ repectvely. The re tme τ of dlocaton calculated from τ µ D / β σ Geller, 976. Blateral rupture pattern condered, pea value of yntheed acceleraton of PCSE n S and EW drecton are 7 Gal and 38 Gal, repectvely. Subequently, the acceleraton repone pectra of yntheed reult are calculated. Fg. 5 how the oberved mall event record and yntheed acceleraton. Fg. 6 how the yntheed acceleraton repone pectra of PCSE.. 6

7 AmpltudeGal - S Amax8. AmpltudeGal - EW Amax8. AmpltudeGal Tmeecond - S Amax Tmeecond AmpltudeGal Tmeecond - EW Amax Tmeecond Fg.5. Oberved mall event record UP and Synthezed acceleraton of PCSE 3. COCLUSIO A defnton of Probablty-Content Scenaro Earthquae PCSE and t evaluaton method were propoed n th paper. Th defnton dfferent from the former cenaro earthquae defnton, whch not content wth exceeded probablty p calculated from conventonal probablty hazard analy method. Becaue not only the exceeded probablty of the ground moton ntenty caued by PCSE content wth p, but alo t magntude, focal dtance and orentaton can be nown, th defnton very ueful for earthquae dater mtgaton. The PCSE defnton wa appled n Shangha regon. The reult how that, correpondng to 3% probablty of exceedance, the magntude of PCSE near Shangha area 6.9, t focal dtance about 48 m and the orentaton of the epcenter 7.4 E. The applcaton prove that the uggeted evaluaton method of PCSE applcable. The oberved record of Lulong earthquae L 5.3 n 98 are choen a emprcal Green functon to yntheze ground moton for PCSE. The pea value of ynthetc acceleragram are about 4 Gal, whch are almot equal to the reult calculated by the probablty hazard analy. The reult how that PCSE ueful n etmaton of ground moton for emc degn. The ynthezed reult alo mply that the mproved emprcal Green functon method valuable for trong moton mulaton. AmpltudeGal 3 h.5 S EW Th reearch upported by the atonal atural Scence Foundaton Of Chna Proect o REFERECES - - Perodecond Fgure 6 Repone pectra Brune, J., 97, Tectonc tre and the pectra of emc hear wave from earthquae, Journal of Geophyc Reearch, 75, 6, pp Campo-cota, A., C. S. Olvera and.l. Soua, 99, Semc Hazard-content tude for Portugal, Proceedng/ th WCEE, adrd, Span,, pp Cornell, C.A. 968, Engneerng emc r analy, Bulletn of the Semologcal Socety of Amerca, 58, 5, pp Dan, K., T. Watanabe and T. Tanaa, 989, A em-emprcal method to yntheze earthquae ground moton baed on approxmate far-feld hear-wave dplacement, Journal of Structural and Contructon Engneerng Tranacton of AIJ, 396, pp7-36. ESRCEngneerng Semology Reearch Centre, 994, Tranng Boo on Regulaton of Semc Securty Evaluaton n Chna, Hangzhou. 7

8 Geller, R. J., 976, Scalng relaton for earthquae ource parameter and magntude, Bulletn of the Semologcal Socety of Amerca, 66, 5, pp5-53. Hazell, S.H., 978, Earthquae afterhoc a Green functon, Geophy. Re. Lett. 5, pp-4. Hu, Y. 988, Earthquae Engneerng n Chnee, Semology Pre, Beng. Irura, K., 983, Sem-emprcal etmaton of trong ground moton durng large earthquae, Bull. of Dater Preventon Re. Int., Kyoto Unv., 33, 98, pp63-4. Ihawa Y. and H. Kameda, 988a, Hazard-content magntude and dtance for extended emc r analy, Proceedng/9 th WCEE, Toyo-Kyoto, Japan, II, P.89. Ihawa Y. and H. Kameda, 988b, Probablty baed determnaton of pecfc cenaro earthquae, Proceedng/9 th WCEE, Toyo-Kyoto, Japan, II, pp3-. Kanamor, H. and D. L. Anderon, 975, Theoretcal ba of ome emprcal relaton n emology, Bulletn of the Semologcal Socety of Amerca, 65, 4, pp Kureghan, A.D. and A.H-S. Ang, 977, A fault-rupture model for emc r analy, Bulletn of the Semologcal Socety of Amerca, 67, 4, pp Luo, Q. And Y. Hu, 99, An mproved emprcal Green functon method and ynthe of near-feld accelerogram n Lulong Earthquae n Chnee wth Englh abtract, Earthquae Engneerng and Engneerng Vbraton,, 3, pp.-3. Luo, Q. And Y. Hu, 997, Synthe of acceleraton of the 976 Tanghan Earthquae 7.6 n near-and far-feld by ung em-emprcal method n Englh, Acta Semologca Snca, 9, 3, pp Luo, Q., Y. Hu and K. Dan, 994, Smulaton of acceleraton n epcentral regon for 93 Kanto, Japan, earthquae 7.9 n Chnee wth Englh abtract, Earthquae Engneerng and Engneerng Vbraton, 4, 4, pp Luo, Q. and K. Dan, 994, Stattcal-emprcal Green functon method for etmatng near-feld earthquae ground moton n Chnee wth Englh abtract, Journal of atural Dater, 3, 3, pp.-. Luo, Q., 996, Probablty-content cenaro earthquae and t determnaton n Chnee wth Englh abtract, Earthquae Engneerng and Engneerng Vbraton, 6, 3, pp.-9. Zhang, Z. et al, 99, Semc mcrozonaton of Shangha area, Reearch report of Tong Unverty, Sponored by Scence and Technology of Shangha uncpalty, Shangha. 8