Bounding of near-fault ground motion based on radiated seismic energy with a consideration of fault frictional mechanisms

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1 Erthq Sc (00)3: D: 0.007/ Bundng f ner-fult grund mtn bed n rdted emc energy wth cndertn f fult frctnl mechnm Bpng Sh Byn Lu nd Lngyun Meng Erth Scence Cllege f the Grdute Schl, Chnee Acdemy f Scence, Bejng 00049, Chn Abtrct The energy rdted emc wve trngly depend n the fult rupture prce cted wth rupture peed nd dynmc frctnl mechnm nvlved n the fult lp mtn. Fllwng McGrr nd Fletcher pprch, we derved phyc-bed reltnhp f the weghted verge fult lp velcty v pprent tre, rupture peed nd ttc tre drp bed n dynmc crculr fult mdel. The reultnt functn cn be pprxmtely ued t bund ner-fult grund mtn nd emc energy cted wth ner-fult cemc defrmtn. Fult frctnl verht nd underht mechnm gverned by mple lp-wekenng cnttutve reltn re ncluded n ur cndertn by ung dynmc rupture mdel nmed M- nd D-mdel nd prped by Mdrg (976) nd Btwrght. We ppled the bve functn t the 008 gret Wenchun erthquke nd the 999 Jj (Ch-Ch) erthquke t nfer the ner-fult grund mtn clled lp weghted verge prtcle velcty nd btned tht uch mdel-dependent predctn f weghted verge grund velcte cntent t the reult derved frm the ner-fult trng mtn bervtn. Mrever, we cmpred ur reult wth the reult by McGrr nd Fletcher pprch, nd we fund tht the vlue f the weghted verge prtcle velcte we btned fr thee tw erthquke re generlly mller nd cler t the vlue by drect ntegrtn f trng mtn recrdng f the ner-fult prtcle velcty wvefrm dt. In ther wrd, f th reult cme t be true, t wuld be trghtfrwrd wy ued t cntrn the ner-fult grund mtn r t etmte urce prmeter uch rupture peed, ttc nd dynmc tre drp. Key wrd: tre drp; rdted energy; pprent tre; crculr-fult-mdel; rupture peed CLC number: P35.9 Dcument cde: A Intrductn A we knw, the rdted emc energy E nd the emc mment M re tw f the mt fundmentl erthquke urce prmeter ued t nfer fult rupture prperte. In prctce, the emc mment cmmnly ued t meure the ze f erthquke nd btned frm ympttclly lw frequence f grund dplcement. E repreent the hgh frequency pectrl nfrmtn but the crner frequency. Frm prctcl pnt f vew, E nd energy mgntude M e re gd meure f the ptentl f erthquke t prduce dmge grund mtn. The rt f thee tw prmeter multpled by μ, the mdulu f fult rgdty, yeld the pprent tre τ (Wy nd Brune, 968): eceved 5 My 009; ccepted n reved frm My 009; publhed 0 Augut 00. Crrepndng uthr. e-ml: bh@guc.c.cn The Semlgcl Scety f Chn nd Sprnger-Verlg Berln Hedelberg 00 τ =μe /M, τ the tre tht cue emc energy rdtn nd crrepnd t rdted emc energy E per unt re per unt lp. Chy et l (006) fund ytemtc vrtn n pprent tre functn f fcl mechnm nd the dtrbutn f pprent tree trngly relted t tectnc crcumtnce. Mrever, Chy nd Btwrght (009) l ndcted tht the dfferentl energy rdtn frm tw erthquke (Kyuhu nd Tttr) n Jpn wth dentcl mment mgntude. The pprent tre fr Kyuhu erthquke /4 mller thn the pprent tre fr the Tttr erthquke. A pnted ut by Chy nd Btwrght (009), th reult h mplctn fr the emc engneerng cmmunty becue t ugget tht emc mment lne nuffcent t quntfy emc hzrd ptentl. In ther pect, Brune nd Thtcher (00) rgued tht, fr the 999 Jj (Ch-Ch) M W 7.6 thrutng erthquke, the pprent tre derved frm ner-fult trng mtn dt much lrger thn

2 358 Erthq Sc (00)3: tht btned frm teleemc dt, nd th ncntence culd be explned by fult gemetry effect n whch the grund mtn n the ftwll were much le thn the n the hngng wll, reultng n much le energy rdtng dwnwrd cmpred wth the energy trpped n the hngng wll (Brune nd Thtcher, 00). McGrr nd Fletcher (00) ntrduced technque fr etmtng pprent tre nd rdted emc energy. They fund tht the rt f fr-feld t ner-fult energe typclly le thn /3, cncludng tht mt f the energy remn ner the fult nd cted wth permnent fult defrmtn. Wth cmbntn f the prtn f the trn energy chnge tht nt dpted n the frctnl prce nd dynmc crculr fult mdel derved by Mdrg (976) whch clled M-mdel lter n n th pper, McGrr nd Fletcher derved the rt f fr-feld E t ner-fult energy E nf : τ =, () E τ + Δ τ / nf where the ttc tre drp. In fct, the bve equtn l mple tht the ner-fult pprent tre n culd be expreed by τ = τ +0.5Δ τ, nd fr the M-mdel (Btwrght, 980), the rt f ttc t dynmc tre drp h: v C 7π β = ρ d 4 v β >, () where d the dynmc tre drp [r effectve tre drp, (Brune, 970)]. β nd v re the her-wve nd rupture peed, repectvely. C(v /β) the Ktrv functn (Dhlen, 974), wth vlue f 0.59 t v /β = 0.6, 0.7 t v /β =0.75, nd 0.8 t v /β = 0.9, repectvely. The cle fctr ρ =.5 nd.0 crrepnd t the M- nd D-mdel, repectvely (Mdrg, 976, Btwrght, 980). In fct, the nequlty f / d > l mple tht dynmc frctnl verht (Svge nd Wd, 97) ccur durng n erthquke fult mtn. In generl, mn-zung (993) prped prmeter, dented by ε= /(τ +0.5 ), t clfy the frctnl mdel: ε greter thn fr frctnl verht mechnm nd ε le fr frctnl underht mechnm (Knmr, 006) r prtl tre drp mdel (Brune, 970). Therefre, the reult f n ε = /( τ ) < bed n the McGrr nd Fletcher pprch gven by equtn () lwy ndcte dynmc frctnl underht f we tke equtn () (ner-fult effect) nt th cndertn. Obvuly, the frctnl mechnm nferred frm the ner-fult lutn ncntent wth fr-feld lutn gven by equtn () whch w derved frm the M-mdel. On the ther hnd, the mxmum verht ccur when ε= n whch τ =0 nd / d = f the frcture energy umed t be zer. ecent tudy frm dynmc mdelng bed n the lp-wekenng mdel gve tht the frcture energy, rdted emc energy nd relxng wrk dne due t the dynmc frctnl verht re 60%, 3% nd 7% f the energy cted wth the ttc tre drp (Fvreu nd Archulet, 003), repectvely. Such relxng wrk l mple tht the prtn f the trn energy chnge n the fult culd be further prttned nt tw prt: ne drectly cted wth ner-fult c-emc defrmtn ccmpned by hgh frequency rdtn, nd the ther the wrk dne by the tre relxtn n the fult fter the rret f the lp dcued by Fvreu nd Archelut (003). In th tudy, fllwng the pprch ntrduced by McGrr nd Fletcher (00, 00), we wll re-derve the mthemtcl expren reltng t the emc energy n the ner-fult bed n the lp-wekenng mdel fr crculr fult mdel. We wll l hw tht the derved new functn r mdfctn f McGrr nd Fletcher equtn hve unfrm expren n whch the frctnl verht, underht nd ttl tre drp mdel re nvlved n the cndertn wthut ny further umptn. Wth cmbntn f fr-feld rdted energy E nd emc mment btned frm teleemc nvern, we prpe ueful wy ued t bund ner-fult prtcle mtn defned by lp-weghted verge lp rte. Fnlly, tw et f rel trng mtn dt f velcty wvefrm frm the 999 M W 7.6 Jj erthquke nd the 008 M W 7.9 Wenchun erthquke re ued t nfer the ner-fult grund mtn cted wth the rupture prperte. Bref mdel. Energy prttn In generl, the energy rdted thrugh urfce S 0 cmpletely enclng fnte fult cn be expreed (ver nd Knmr, 005):

3 Erthq Sc (00)3: = ( ) d effd σ j+σj njδu S γ S t 0 dt σ d ( ) d, t0 () t jnjδ u& S+ σj σj nu j S S (3) where ds the urfce element, n pen urfce repreentng the fult plne, nd σ j, Δu, n j, t 0 nd t re the tre, dlctn n, unt nrml t, the tme when lp begn t pnt x n, nd n rbtrry tme fter lp mtn h ceed, repectvely, nd (t) the ruptured fult urfce t tme t, nd γ eff the effectve frcture energy. The upercrpt nd refer t befre nd fter the lp ccurred. The frt term n equtn (3) the eltc energy n the fult, whch de nt depend n the ntntneu tre σ j, but nly n the ntl nd fnl tre vlue; the lt term vnhe f S 0 tken fr enugh frm the fult, becue 0 u nd ( σj σ j ) decree /r nd /r 3, repectvely. The fnl expren fr E n the fr-feld gven by 0 = ( ) Δ d effd σj σj nj u S S γ t dt σ n Δu& d S, t (4) 0 () t j j An lterntve expren f equtn (4) cn be btned fter ntegrtng lt term by prt: E σ σ n u S γ S 0 = ( ) Δ d effd + j j j t dt σ& jnjδud S. (5) t0 () t In equtn (5), the frt term crrepnd t the trn energy chnge befre nd fter the erthquke fultng, the ecnd nd thrd term gve the energy brbed n the fult plne, whch cntn the ntntneu her trctn τ =σ j n j. The ntl nd fnl her k k trctn re τ = σ n (k=0, ). ver nd Knmr j j (005) pnted ut tht the term γ eff n the bve equtn cntned ll the tre nd velcty ngulrte relted t rupture prpgtn, nd the ntegrl ver (t) hd n ngulrte. Therefre, we cn exchnge the rder f ntegrtn, nd the lt term n equtn (5) gve tht t tm & σ & 0 () j j σ t t () t 0 j j tm Δu τδu Δud t = ( τ τ)dδ u. 0 0 dt n ΔudS = ds n Δudt = The equtn (5) cn be wrtten E u S S 0 = ( τ τ)δ d γeffd + ο Δu ( τ 0 τ)dδud S. (6) Frm equtn (6), Ccc et l (006) ndcted tht f the fnl tre τ equl t the redul tre τ f nd the dynmc tre τ d cntnt nd equl t the mnmum tre, the lt term (Ktrv term) crrepnd t the frcture energy. In generl ce, the fnl tre de nt crrepnd t the dynmc tre vlue, the fult rupture prcee undertke the frctnl underht n whch τ >τ f r frctnl verht n whch τ <τ. Svge nd Wd (97) explted the f bve reltn n the frm f τ = μe /M < / ( =τ 0 τ the ttc tre drp, τ f the frctnl tre, μ the her rgdty, nd M the clr emc mment) whch knwn Svge nd Wd nequlty mplyng frctnl verht mechnm. Fgure hw tw type f dynmc frctnl mdel wth mple lp wekenng frctnl mtn f fultng n whch the frctnl tre vre functn f lp y y τ ( τ τf) Δu, Δu Dc τ =, (7) τf Δu Dc where D c the crtcl lp wekenng dtnce, τ y the yeld tre relted t the fult trength, nd τ = τ crrepnd t ttl tre drp mdel. Mrever, fr the lp wekenng mdel hwn n Fgure, the frcture energy n equtn (6) ncluded n the Ktrv term, tht the effectve urfce energy de nt le wthn the tre veru lp curve, nd t huld be neglected n ny ther fult zne mdel. Fr fult zne mdel wth the lp mtn beyng the lp-wekenng crtern nd the frctnl verht nd underht re nvlved durng the dynmc rupture, the equtn (6) cn be further mplfed Δu 0 = ( τ τ)δu ds ds τ dδ, u (8) therwe, Δu 0 = ( τ τ)δu ds + d S ( τf τ )dδ f. u E 0 (9) If τ = τ f = cnnt umed durng fult rupturng. The lt term n equtn (9) crrepnd t frcture energy dpted durng crck extendng. 0 f

4 360 Erthq Sc (00)3: Fgure A mple frctnl verht n the lp-wekenng mdel (), w e the eltttc wrk prvded by the eltc crut defrmtn, w f the frcture wrk pent t the rupture frnt nd w r the relxtn wrk fter the rret f the lp. A mple frctnl verht n the lp-wekenng mdel (b), the frcture wrk pent t the rupture frnt, nd w f w r the rdtn frctn wrk pent t the rret (brupt tre drp mdel). The rdted emc energy denty gven by e=w q e wf wr fr frctnl verht nd e=w q e w f +wr fr frctnl verht.. Crculr fult rupture mdel Fr elf-mlr crculr crck mdel wth n gven verge lp dplcement S, the energy dpted frcture wrk E f nd G=E f + π (τ f τ )S = 0.5 π ( τ )S the ttl energy dptn n frctn nd frcture mnu τ π S f frctnl verht ccur. In generl, fr crculr fult mdel, the dynmc rupture behvr relted t the lp dplcement nd lp velcty functn n the fult re hwn n Fgure nd b (Btwrght, 980) n whch nd b crrepnd t the M- nd D-mdel, repectvely. Fr cmprn purpe, Fgure c l gve lp dplcement nd lp velcty functn reultnt frm the Brune mdel. Brune mdel the d hc mdel whch h been cmmnly ued n the bervtn emlgy t nfer the erthquke urce prmeter uch fult ze nd ttc tre drp. In cntrt, M- nd D-mdel re the dynmc mdel whch ue n ctul dynmc frcture multn t cte the dmeter (fult ze) wth the rdted gnl nd crner frequency. Bth M- nd D-mdel decrbe the urce grw frm pnt n the fult wth unfrm rupture velcty. Fr D-mdel, the rupture frnt begn t decelerte when the entre rupture hel, lwng cntnuuly. In cntrt, fr M-mdel, the rupture h brupt tppng t fxed rupture permeter. The mtn t n nterr pnt cntnue n the rupture phe untl the P-wve phe generted by the tppng f rupture frnt t the nterr pnt t certn tme. Frm Fgure, the verge lp dplcement nd velcty fr M-mdel lrger thn the frm D-mdel nd Brune mdel. Actully, n the M- nd D-mdel, the fnl lp dtrbutn lng the fult re

5 Erthq Sc (00)3: ρδu& Δ u = v ( r/ ), d vd Δ u& = v μ μc( ) β β (0) where ρ =.5 nd.0 crrepnd t the M- nd D-mdel, repectvely. In equtn (0), d the dynmc tre drp (r the effectve tre, Brune, 970) whch determned by dfference between the ntl tre nd the dynmc frctnl tre. Bed n the lutn f dynmc mdelng fr crculr fult, Mdrg (976) ued equtn (9) t derve fr-feld emc energy rdtn fr plne crculr fult mdel wth the rdu. In equtn (9), f we defne =τ 0 τ, the ttc tre drp nd d =τ 0 τ f, the dynmc tre drp, fr plne crculr fult mdel, we hve Fgure () Slp dplcement, Δu, nd lp velcty, Δ u&, fr the M-mdel wth v =0.9β, t fve dfferent rd. The mtn t ech rdu elf-mlr untl the rrvl tme f the P-wve tp phe frm the permeter f the fult; (b) Slp dplcement, Δu, nd lp velcty, Δ u&, fr the D-mdel wth v =0.9β, t fve dfferent rd. The mtn t ech rdu elf-mlr untl τ =0.8α/v when the fult begn t decelerte; (c) Brune ner-fult lp pule mdel n whch Δ u& = d β/μ exp( πf c t) nd crner frequency f c =0.37β/α. τ τ 0 π = Δ dd u r θ 0 0 π Δu r θ τf τ u Ef dd ( )dδ. () Fr M- nd D-mdel (Mdrg, 976, Btwrght, 980), the rdted energy cn be wrtten pprxmtely d 3 π v = ρ g( ), () μ 3 d β nd the exct lutn v C( ) d 3 π β v = ρ g( ) μ 3 v (3) d β β where ρ =.5 whch btned frm dynmc lutn fr crculr mdel (Mdrg, 976). v the rupture velcty. g(v /β) repreent the reltve munt f vlble energy cnumed frcture energy whch gven by E f =(π d /3μ) 3 g(v /β). In M-mdel, g(v /β) vre mntnclly frm 0.7 t v =0.6β t 0. t 0.9β (Mdrg, 976). In fct, g(v /β) cmplcte functn f v /β nd v /α (β nd α re the S- nd P-wve velcte, repectvely, nd t vlue l trngly depend n the A 0, the cntnt lp velcty t the center

6 36 Erthq Sc (00)3: f the fult, whch re drectly relted t the C(v /β, v /α), the Ktrv functn (Ktrv, 964, Dhlen, 974) by C(v /β, v /α)= A 0 α/β. A pnted ut by Dhlen (974), the functn f A 0 h cmplcte ntegrl expren nd dffcult t evlute n cle frm. Fr the pecl ce f Pn ld, α =3β, the numercl lutn f C(v /β) w gven by Dhlen (974). In the lmt v <<β, C(v /β) (4/7π) (v /β). Obvuly, th lmt the pplctn f equtn (3) ued n the quntttve etmtng f rdtn energy nd urce prmeter evlutn when the rupture velcty vre durng the rupture prpgtn. Fr crculr rupture mdel, we cn btn the reltn f M =6/(7 α 3 ), where nd M cn be determned frm emc pectrum. Therefre, the pprent tre fr the M- nd D-mdel 7π d τ = 48 Δ τ v C β v ρ β g Δ. Δ v τd β Tble Surce prmeter v v /β frm equtn (4) V r /β C(v /β) g(v /β) τ α / (ρ =) τ α / (ρ =.5) τ (4) It bvu tht, wth gven, the pprent tre frm the D-mdel much lrger thn the pprent tre f the M-mdel, nd D-mdel exhbt frctnl underht becue f / d < reultnt frm equtn (). 3 Ner-fult wrk When crck wth rdu nerted nt hmgeneu medum under unfrm her tre, the trn energy releed. After ubtrctng the energy dpted n frctn, the trn energy chnge gven by Δ W=π Δ τ D/, whch vlble fr mechncl wrk fr crck extenn. Durng fult lp mtn, dynmc frctnl verht r underht cn ccur. Indeed, the M- nd D-mdel exhbt frctnl verht nd underht, repectvely. Fr frctnl verht mechnm, τ, the fnl tre lrger thn τ f, the frctnl tre, nd Wr=( τf τ) Dπ =π D(d ) the wrk dne by the tre relxtn n the fult fter the rret f the lp dcued by Fvreu nd Archelut (003). Therefre, the wrk dne durng the cemc defrmtn huld be πd d W =Δ W Wr= Δ τ = M μ Δ d Δ τ. τ Thu, the ner-fult energy cn be clculted by 7π M d Enf = + W = ρ 48 μ d v C β v d g Δ + Δ. v τ τ β μ β M (5) (6) The rt f fr-feld energy t ner-fult energy E ( ) = = =. Enf C d τ+ τ+ f v τ τ (7) C = d / 0. In fct, equtn (6) nd (7) l tfed fr the D-mdel ce. A C > mple prtl tre drp mechnm r frctnl underht where C < ndcte tht frctnl verht h ccurred. Orwn hypthe met when C =. In the verht ce, the mnmum bund f C =0 prvde wy t check fr ncntence n urce prmeter. If v /β=0.9, then C(v /β=0.9)=0.8. In th ce, we hve = d =. fr the M-mdel nd = d =0.8 fr the D-mdel. Therefre, n thee three ce, the rt f E t E nf re τ τ+0.3 E τ = τ τ+0.5 verht ( ) == underht. Enf τ +0.7 f v ttltre drp (8) Bed n the M-mdel, McGrr nd Fletcher (00) frt gve the mlr reult t equtn (8) wthut cndertn f frctnl verht nd underht nherted n the M- r D-mdel. It need t pnt ut tht,

7 Erthq Sc (00)3: n fct, M-mdel telf frctnl verht mdel becue d / lwy le thn. Thu, the equtn we hve derved generlzed frm nvlved dfferent frctnl mechnm nd h cler phycl menng tht, when E r τ equl t 0, E nf l equl t 0, becue, n uch ce, / d = crrepnd t C =0. 3. Ner-fult lp mtn Bed n the tme htry f lp cr fult, the ner-feld emc energy E nf cn l be clculted ung (Anhehpr nd Brune, 994) D& ()d t t d Aρβ D< D& > Enf = d Aρβ =, (9) where the ntegrtn re ver fult re A nd tme t, ρ denty, D(t) the tme-dependent lp r pprxmtely the ner-fult grund velcty. The lp wegh ted verge lp velcty cn be defned dd Dt & () d t Dt & ()dd dt D& ()d t t <D>= & = = D D D where D the fnl lp (verge). Frm equtn (6) nd (7), we hve d τ +( ) < D& >= β (0) μ Fr ttl tre drp mdel, d / =, < D& >=( τ+δ τ) βμ /, therwe, equtn (0) cn be wrtten v 48 Δ < D& β τ β >= τ + 7π v ρ μ C β () In fct, equtn (0) nd () cn be ued t cntrn the lp velcty n the fult r ner-feld grund mtn uch weghted verge prtcle velcty pprxmtely f we knw fr-feld rdted energy, emc mment nd rupture peed. In the ther hnd, f we hve ner-feld trng grund mtn recrdng nd knw the ttc tre drp, the verge rupture peed l cn be etmted frm equtn (). Wht we need t knw n thee clcultn the dynmc frctnl mechnm durng the erthquke fultng. Becue prmeter ρ re mdel-dependent cntnt, the frctnl verht r underht mechnm cn drectly decrbed by the M- nd D-mdel, repectvely. Accrdngly, wth the defntn gven by Svge nd Wd (97), the prmeter, dented by ε= /(τ ) (mn-zung, 993) culd be ued t clfy the frctnl mdel f the pprent tre τ nd ttc tre drp knwn. ε greter thn fr frctnl verht mechnm nd ε le fr frctnl underht mechnm (Knmr, 006) r prtl tre drp mdel (Brune, 970). Fr mt lrge hllw erthquke, t generlly etblhed tht the rupture peed but 75% t 85% f β (Knmr nd Hetn, 000). Knmr nd Hetn (000) l ndcted tht renble rnge f but 3 MP t 0 MP, nd d vre frm 3 MP t MP crrepndngly. Abercrmbe nd ce (005) uggeted tht the rt f /τ f but 0 huld be renble fr lrge erthquke f the fr-feld rdted energy meurement re crrect. If th cnclun rght, then ε.67 mple tht the lrge erthquke undertke trng frctnl verht mechnm. If n verge τ but 0.7 MP (Perez-Cmp et l, 003), the rt f /τ =0 mple n verge tre drp fr lrge erthquke f 7 MP, nd f the rt 3, then t wuld mply n verge tre drp f. MP. Bed n the M-mdel, the rt f /τ but 0 l mple n verge rupture peed but 75% f her wve peed. Therefre, the weghted verge prtcle velcty frm equtn () but 56 cm/ f μ= MP ued fr the rgdty f the crut nd her wve peed β=3 km/ ued n ur clcultn. The Brune mdel f u& = Δσβ/ μ predct the pek grund velcty (PGV) but 70 cm/, nd the PGV predcted by McGrr nd Fletcher (00) pprch but 84 cm/. Actully, the Brune mdel n ntntneu mdel wthut ny cndertn f fnte rupture peed durng erthquke fultng. In the ther hnd, McGrr nd Fletcher pprch pecfc ce, crrepndng t / d = n equtn (0). Althugh they hve ued the M-mdel lutn n ther dervtn f ner-fult emc energy equtn, the reultnt functn gven by equtn () gnre the pprent dfferentl extng n the clcultn f ner-fult wrk wth r wthut cnderng f dfferent frctnl mechnm. It bvu tht bth Brune mdel nd McGrr nd Fletcher pprch uully veretmte the ner-fult grund mtn r the lp rte n the fult.

8 364 Erthq Sc (00)3: Applctn Ce : My, 008 M W 7.9 gret Wenchun erthquke The 008 Wenchun, Schun, Chn, erthquke (M W 7.9) chrcterzed by dp-lp revere fultng, ruptured but 300 km lng nrthet-trkng, wet-dppng Lngmenhn thrut fult belt lcted n the mrgn f the etern Tbetn plteu. Bed n the erthquke ctlg frm GCMT, USGS/NEIC, nd Chnee Erthquke Netwrk Center (CENC), ncludng USGS energy nd brdbnd lutn, the prmry urce prmeter gven tht, fr Wenchun event, the emc mment M = N m nd the fr-feld rdted energy E = N m, nd the crrepndng pprent tre, τ, but 0.55 MP f μ= MP ued n ur clcultn. The ttc tre drp derved frm n-tu brehle trn meter dt recrded t the Centrl Lngmenhn fult zne but.6 MP whch cntent wth the reult f.58 MP etmted by =C D/W fr lng dp-lp erthquke, where D~.3m (Wng et l, 008) the verge lp nd W~ km the verge wdth, nd C the gemetrcl fctr gven by C =4(λ+μ)/[π(λ+μ))] r C =8(λ+μ)/[π(λ+μ)] dependng n whether the lp brek the free urfce r nt. Mrever, ccrdng t the Svge nd Wd (97) nequlty, τ << l ndcte tht, fr the 008 Wenchun erthquke, the dynmc frctnl mtn n the fult underwent n verht prce. Strng mtn recrd frm the mn hck hw tht The Ntnl Strng Mtn Obervtn Netwrk Sytem (NSMONS) reprted tht mre thn 460 trng mtn ttn were trggered nd the lrget pek grund ccelertn w recrded t Wlng ttn n Wenchun cunty whch lcted n the hngng wll nd but 4 km cle t mn fult. The PGA recrded n the EW, NS, nd UD drectn re cm/, 65.9 cm/ nd 948. cm/, repectvely. The trng grund mtn recrd btned t Qngpng ttn n Mnzhu cty rnk the ecnd lrget ne n PGA. It PGA recrded n the EW, NS nd UD drectn re 84. cm/, 80.7 cm/ nd 6.9 cm/, repectvely. The ttn lctn ner the mddle f rupturng fult whch ndcted n Fgure 3, nd the neret dtnce t the mn fult but 5 km. Inde Fgure 3, the wvefrm f grund velcty tme htre recrded t Qngpng ttn nd multed by cmpte urce mdel fr Qngpng ttn re l t r r dplyed. Wth the ntegrtn f V V d t dvded by 0 D, the verge lp dplcement, Fgure 4 hw the cumultve vlue f weghted verge prtcle velcte n tme dmn t Qngpng ttn. Fr cmprn purpe, the multed reult re l hwn n th fgure. It cler tht the reultnt <D> & I but 7 cm/ fr rel recrdng nd but 30 cm/ fr trng mtn multn. Bed n the urce prmeter Fgure 3 The ptl dtrbutn f the mn fult lng the Lngmenhn fult zne fr the 008 M W 7.9 gret Wenchun erthquke. The neret ttn lcted n Qngpng wth hrtet dtnce t the mn fult f but 5 km. The trng recrdng nd multed wvefrm l re dplyed nde th fgure.

9 Erthq Sc (00)3: Fgure 4 Cumultve qured velcty fr Qngpng recrdng nd numercl multn. Tble Slp weghted verge velcte derved frm equtn () fr dfferent vlue f v /β v /β < D & > /cm D hwn n Fgure 3, we l derved the weghted verge prtcle velcty f <D> & frm equtn () wth v /β rngng frm 0.6 t 0.9 (Tble ). Obvuly, thee reult lted n Tble re much mlr t tht btned by ntegrtn f qured velcty tme htre f Qngpng recrdng, but much mller thn 37 cm/ btned by McGrr nd Fletcher pprch gven by < D& >=( τ+0.5δ τ) In ther wrd, f we hvener-fult trng mtn recrdng nd knw fr-feld rdted emc energy, equtn (0) nd () cn l be ued t etmte the dynmc tre drp nd ttc tre drp bed n the M-mdel, D-mdel r Brune mdel. The nly thng we need t tke cre tht, when we ue Brune mdel fr etmtng, the reultnt tre drp nly /5 tme f M-mdel r the ze f lclzed ubevent but.7 tme f M-mdel. Ce : September, 999 M W 7.6 Jj erthquke The 999 Jj erthquke (M W 7.6) ruptured the grund urfce lng the Chelunpu fult n centrl Twn f Chn. The erthquke trggered lmt ll trng mtn ttn perted by the Centrl Wether Bureu rund the epcentrl re. eult frm ner-fult grund mtn bervtn well frm fr-feld emgrm reveled tht the fult f the Jj erthquke cn be dvded nt tw egment tht brek the urfce nd the chrcter f grund mtn exhbt mjr chnge between the uthern nd nrthern egment f the fult n whch there re tw gnfcnt mment relee durng the fultng. Bth egment f the fult exhbt thrut type f mtn, the verge dlctn n uthern prt but m, n cntrt, the verge dlctn n nrthern prt reche but 6 m (Xu et l, 00) r 8 m (Hung et l, 00). In th tudy, we ue trng mtn recrdng frm three neret ttn t the mn fult t nfer the weghted verge prtcle velcte cle t the fult nd mke cmprn wth the reult derved frm equtn (). The trng recrdng we hve ued re TCU05, TCU0 nd TCU076. The lctn f ttn re hwn n Fgure 5. TCU076 n the ftwll nd ner the uthern egment wth hrtet dtnce t the mn fult but 3. km. TCU05 nd TCU0 re ner the nrthern egment nd fr frm the epcenter. The hrtet dtnce t the mn fult fr TCU05 nd TCU0 re.8 km nd. km, repectvely. The ttn f TCU05 lcted n the hngng wll nd the ttn f TCU0 nd TCU076 re n the ftwll. Frm the U.S. Gelgcl Survey erthquke ctlg, M = N m, nd the vlue f E etmted frm the methd develped by Chy nd Btwrght (995). 0 6 N m. Th led t E /M = r the pprent tre τ but.5 MP. Fgure 5b hw the tme htre f velcte recrded t ttn f TCU05, TCU0 nd TCU076. Fgure 6 hw the cumultve vlue f weghted verge prtcle velcte f < D & > I n tme dmn t TCU05, TCU0 nd TCU076. The urce prmeter ued n < D & > D etmtng frm equtn () re gven n Tble 3, nd the fnl reult f < D & > D whch btned bth frm equtn () nd the ntegrtn f qured prtcle velcty tme htre re l ummrzed n Tble 3. The ubcrpt f I nd D ndcte, < D & >, the weghted verge velcte re btned bth frm drect ntegrtn f qured prtcle velcty recrdng nd dervng by equtn (), repectvely. Tble 3 Surce prmeter nd derved verge prtcle velcty < D & > D /cm Sttn /MP < D & > I /cm v /β=0.9 v /β=0.75 v /β=0.6 TCU TCU TCU Dcun nd cnclun The reult f th tudy hw tht there re tll certn uncertnte n ur undertndng f erthquke

10 366 Erthq Sc (00)3: () Fgure 5 The mn fult nd lctn f trng mtn fr the 999 M W 7.6 Jj erthquke (); Three cmpnent f the prtcle velcty tme htre t three ttn (b).

11 Erthq Sc (00)3: Fgure 6 Cumultve qured velcty fr TCU05, TCU0 nd TCU076 recrdng. fultng prce. The reult d enble u t plce me cntrnt n the ner-fult grund mtn predctn,but the ccurcy f meurement f rdted emc energy, rupture peed nd tre drp tll ur future cncern. The mechnm f the dynmc frctnl verht r underht durng the erthquke fultng re l rguble, nd new hgh qulty dt re gthered nd mprvement re mde n current evlutn technque, t wll be pble t better quntfy prmeter uch the rt f / d, whch wll prvde better decrptn f the urce prce. Brune mdel nd M-mdel (Mdrg, 976) re n cnmmn uge fr determnng erthquke urce prmter frm the pectr meurement f Ω nd crner frequency f c. Fr v =0.9β, the M-mdel dentcl t Brune mdel wth τ =0.3. The prncpl dfference between thee tw mdel n ther uge tht the rupture rdu derved frm the S-wve pectr ung Brune mdel.77 tme tht btned ung M-mdel. Therefre, the tre drp btned ung M-mdel 5.5 tme the frm the Brune mdel. Bth the Brune nd M-mdel re n current ue fr nterpretng emc wth n cnenu t whch gve the mt ccurte reult. Fr dpng fult, ymmetrc ner-fult grund mtn cued by the ymmetrc gemetry f thrut fult nt ncluded n th tudy. Dynmc multn f thrut fultng (Ogleby et l, 998, Sh et l, 998) ndcte the mtn f the hngng wll lrger thn tht f the ftwll. The rt f the ner-fult pek grund velcte between the hngng wll nd ftwll but 3 4 fr 30 dppng thrut fult. Fr exmple, f we tke nt ccunt uch gemetrc effect relted t the lrger mplfctn f grund mtn n the hngng wll decrbed by wvefrm t ttn TCU05 recrdng, the reultnt tre drp but.0 MP by ung equtn (), whch mlr t.9 MP etmted frm the wvefrm t ttn TCU0 (Hwng et l, 00), nd the ncntnce f tre drp rngng frm.9 MP frm TCU0 t 0. MP frm TCU05 fr the me egment f the mn fult cn be remved. Fllwng McGrr nd Fletcher (00) pprch wth cmbntn f fr-feld rdted emc energy, emc mment nd ner-fult defrmtn wrk, n th tudy we derved the reltnhp f fult lp velcty v pprent tre, rupture peed nd ttc tre drp. Cmprng wth prevu dervtn gven by McGrr nd Fletcher, the current reult nclude the cndertn f the dynmc frctnl verht nd underht mechnm decrbed by M- nd D-mdel (Btwrght, 980, Mdrg, 976). We ppled th technque t the 008 gret Wenchun erthquke nd the 999 Jj (Ch-Ch) erthquke, nd btned the weghted verge prtcle velcte fr ech event. Mrever, we cmpred the mdel-dependent predctn f < D & > t the reult btned by drect ntegrtn f qured prtcle velcty wvefrm berved t ner-fult trng mtn ttn, nd we fund tht the vlue we btned fr < D & > re n the me rnge f numercl ntegrtn f rel emc dt. If th reult cme t be true, t wuld be trghtfrwrd wy f btnng the urce prmeter, uch ttc nd dynmc tre drp, rupture peed r verge lp n the fult, f we hve the ner-fult trng mtn dt nd mke the meurement f the emc mment nd fr-feld emc energy crrectly. Acknwledgment Th wrk w upprted by the Knwledge Innvtn Prgrm f Chnee Acdemy f Scence (KZCX-YW-Q08-) nd One-Hundred-Indvdul Prgrm f Chnee Acdemy f Scence. eference Abercrmbe E nd ce J (005). Cn bervtn f erthquke clng cntrn lp wekenng? Gephy J Int 6(): Anhehpr A nd Brune J N (994). Frctnl het genertn nd emc rdtn n fm rubber mdel f erthquke. Pure Appl Gephy 4(3-4): Btwrght J L (980). Spectrl thery fr crculr emc urce: Smple etmte f urce dmenn, dynmc tre drp, nd rdted emc energy. Bull Sem Sc Amer 70(): 7. Brune J N (`970). Tectnc tre nd the pectr f emc her wve frm erthquke. J Gephy e 75(6):

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