Precursory Acceleration of Seismicity: From the Theoretical Elegance to the Practical Difficulties

Transcription

1 Preursory Aeleraion of Seismiiy: From he heoreial Elegane o he Praial Diffiulies Andreas zanis Deparmen of Geophysis and Geohermy, Universiy of Ahens Filippos Vallianaos Deparmen of Naural Resoures Engineering, ehnologial Eduaional Insiue of Cree, Chania Branh.

2 BACKGROUND I has been redibly argued ha he earhquake generaion proess is a riial phenomenon ulminaing wih a large even ha orresponds o some riial poin. In his view, a grea earhquake represens he end of a yle on is assoiaed faul nework and he beginning of a new one. he dynami organizaion of he faul nework evolves as he yle progresses and a grea earhquake beomes more probable, hereby rendering possible he prediion of he yle s s end by monioring he approah of he faul nework oward a riial sae. his proess may be desribed by a power-law ime-o o-failure saling of he umulaive Benioff srain: d d ε = k m α ε = K + A is he ime when he riial sae is aained, A <0, m<1 and K = =. Observaional evidene has orroboraed he power-law saling in many ases and has empirially deermined ha m 0.. Ben-Zion and yakhovsky 00 heoreially predi give m=1/. Rundle e al. 000 show ha he power-law aivaion assoiaed wih he exiaion in proximiy of a spinodal insabiliy is essenially idenial o he power- law aeleraion of Benioff srain wih m=0.5.

3 PHYSICA MODES More reenly, he CP earhquake onep has gained suppor from he developmen of regional seismiiy models wih realisi faul geomery ha show aeleraing seismiiy before large evens. Essenially, hese models involve sress ransfer o he faul nework during he yle suh, ha he region of aeleraing seismiiy will sale wih he size of he ulminaing even, as for insane in Bowman and King 001. I is hus possible o undersand he observed haraerisis of o disribued aeleraing seismiiy in erms of a simple proess of inreasing eoni sress in a region already subjeed o sress ss inhomogeneiies a all sale lenghs. hen, he region of aeleraing seismi release is assoiaed wih w he region defined by he sress field required o rupure a faul wih a speified orienaion and rake; i is hus possible o inorporae rae eoni informaion ino he analysis

4 A NEW HEOREICA APPROACH Consider a rusal volume V, enlosed by a surfae S V, ino whih energy is ransferred and sored as elasi deformaion or dissipaed by seismi and aseismi release. Beause seismi release ours only a fauls, seismi dissipaion involves only an effeive sub-volume V eff V de e E S be he surfae densiy of he energy flowing ino V : ES = dsv ou flowing due o seismi release. e E V be he volume densiy of energy ou flowing due o e R be he volume densiy of he energy no relaed o seismi release. Conservaion of energy demands E S S V = E V V eff + R V e be he haraerisi size of V: SV and V. Assume a fraal / hierarhial faul sysem wih <D <, so ha V eff D. Finally, assume ha he seismi release raes sale wih E V : dε d d d α 1,, ε 1 D = γ0[ EV ] = γ ES R D α

5 A NEW HEOREICA APPROACH A NEW HEOREICA APPROACH oninued oninued Beause E S = 0, Ο = S S S S S E E E E E where is a haraerisi ime haraerisi ime for seing ou he preparaion of he global even As, V shrinks shrinks oward he EQ fous oward he EQ fous. Assuming analyiiy Assuming analyiiy of a, Ο + + = Noe ha due o sress loalizaion sress loalizaion as, 0 and = - =. Keeping only he firs order firs order approximaions above: α + + = γ ε D D D D S D D S R E E d d Observe ha for Observe ha for D 0 lim = D

6 A NEW HEOREICA APPROACH oninued On inegraing he firs erm only, ε = ε = eing : K = ε =, A = γ γ α E0 α D α D 1 ES α D [ ] and m = α -D +1, α 1 D 1 α + 1 α D αD ε = K + A If α > 0 and < D + 1/α, hen m < 1 : he elebraed ime-o o-failure equaion If α < 0 he srain rae dereases wih ime deeleraion deeleraion For m 0.5 riial sae and D..4 runaway frauring, α he power-law saling proess depends on: he saling beween deformaion rae and seismi energy release i.e. maerial properies he geomery fraal disribuion and dimension of he faul sysem m

7 YES, BU IS HERE A CAVEA??? From a heoreial poin of view, maers appear o be quie illuminaed: I should be possible o predi he earhquake yle s s end by monioring he approah of he faul nework oward a riial sae. However, would his always be feasible or an realiy be more ompliaed han our expeaion? We will aemp an answer, 1. Firs by presening an example ou of a few,. hen by appealing o he heory.

8 SUDY AREA AND SOURCE OF DAA he Souhwes segmen of he Helleni Ar is he mos aive plae margin of he Medierranean area, wih orrespondingly high seismiiy and relaively frequen ourrenes of large earhquakes. Seismiiy daa aken from he aalogue of he Geodynami Insiue, Naional Observaory of Ahens, hp:// I has been shown ha M W M NOA + 0.5,, for.6 M 6.5 e.g. Papazahos e al, 00 he he magniude of ompleeness is M =.6

9 DAA ANAYSIS ε = = he Benioff srain, defined as wih E i being he energy of he i h even, N he oal number of evens a ime and log 10 E i = M W e.g. Papazahos and Papazahos,, 000. he power-law model is fied wih a non-linear non-linear Nelder-Mead opimisaion proedure, operaing on he norm. he suiabiliy of he power-law behaviour is esed using he CURVAURE C = Power law fi RMS inear fi RMS whih should be signifianly less han 1 if power-law affords a beer approximaion. he analysis enails he following proedure: Power-law model if fied o earhquake daa wihin onenri irular r areas. Radius a whih C is minimum and orresponding model parameers are deemed opimal N he proedure is repeaed on a regular grid and maps of he urvaure, he riial exponen, he riial ime and he predied magniude are ompiled i 1 Ei

10 SW HEENIC ARC OBSERVAIONS ON 1/01/00 Aeleraion Deeleraion he urvaure shows areas of sronger / weaker power-law behaviour Power-law behaviour will noneheless be observed boh when seismiiy is aeleraing m<1 or deeleraing m>1. he answer is given by he disribuion of he riial exponen, whih shows a well sruured buerfly paern wih nearly sharp boundaries beween n exponens greaer or smaller han uniy.

11 CHARACERISICS OF HE POWER-AW BEHAVIOUR x 108 Earhquakes wihin he 1kPa onour; M W > C=0.8; N=166; n=0.6; M=7.4; = Benioff srain ime years Benioff srain 0 x C=0.6; N=145; n= ime years Power-law models are ompued wih earhquakes wihin he areas of sress inrease / derease. Examples for earhquakes wihin he +1kPa onour aeleraion and he -1kPa onour deeleraion are shown. he riial exponen in he aeleraing branh is ¼, onsisen wih he view of power-law aeleraion as a Self-Organising Spinodal SOS a CP sysem undergoing a repeiive series of firs order phase ransiions - Rundle e al., 000.

12 SW HEENIC ARC UPDAED 1/0/00 Norhing km Curvaure a 0/0 Benioff srain.5 x 108 Earhquakes wihin he + 1kPa onour, M > 4.5 W C=0.5; N=174; n=0.7; M=7.4; = Updaed, 1/0/ Easing km C ime years One year laer, he overall paern of aeleraion / deeleraion remains unhanged, bu he seismi release raes appear o have slowed down and an updaed model indiaes a riial ime deferred o he updaed riial exponen is sill onsisen wih he SOS onep 0.7. here s s no signifian hange as o he size of he predied even.

13 SW HEENIC ARC UPDAED 1/0/004 Curvaure a 1/0/ x 108 Earhquakes wihin he 1kPa onour; M W >4.5 C=0.5; n=0.1; M=7.8; =006.9 Updaed 1/0/004 Norhing km Beniof srain Easing km ime years One year laer, he overall paern of aeleraion / deeleraion is sill he same bu he and an updaed model indiaes a riial ime deferred o he slowed down seismi release raes appear o have reenly piked up again. he riial exponen is has inreased m=0.1 bu is sill onsisen wih he CP onep. he predied size of he even appears o have inreased.

14 IS HERE SOMEHING MISSING? he observaions were onsisen wih almos all of he prediions of he CP / sress ransfer model and every ime, i appeared as if a bona-fide prediion had been made. Re-evaluaion evaluaion of seismiiy hanges shows ha he aivaed area may aually be relaxing, or he rusal maerial has siffened and does no release as muh seismi energy; he ime of failure has been deferred o approximaely Empirially speaking: ime-o o-failure modelling of aeleraed seismiiy is a relaively new field of sudy wih few ases-hisories whene o draw experiene, mos of whih, omprise rerospeive analyses of pas earhquakes. Sill, very lile is known as o he developmen of real-ime siuaions and heir probabiliy of suess or failure.

15 WE HINK YES! Faul sysems are no isolaed - deformaion depends on he ime-varying rae of energy ransfer from wihou. We have shown ha he ime-o o-failure power law depends on ime-varying faors: Faul sysem geomery and Maerial Properies. he variaion of hese parameers may drive he sysem bak and forh, beween a subriial self-organising mode wih redued seismi release raes and a full-sale self-organising mode wih aeleraed release raes. he variaion is unonrollable and unprediable, as also are he faors peraining o he nuleaion proess, whih have heir own ime dependene. herefore, even if a full-sale self-organising proess operaes in some area, i is no a all neessary ha a large earhquake will our as soon on as he sysem goes riial. he riial poin model merely predis ha pas he riial ime an earhquake is possible, no erain. In spie of he heoreial elegane i enjoys, he real-ime prediive apaiy of he CP / sress ransfer earhquake onep is sill o be riially esed. Suh esing would be imporan in assessing he feasibiliy of using he model o evaluae shor and inermediae erm seismi hazard.