Prestack signal enhancement by non-hyperbolic MultiFocusing

Transcription

1 Petack ignal enhancement by non-hypebolic MultiFocuing Evgeny Landa*, OPEA, Pau, Fance Alex Bekovitch, Geomage, Modi in, Iael and Kotya Deev, Geomage, Modi in, Iael Abtact MultiFocuing technology can damatically impove the quality of eimic imaging epecially in cae of low fold data, poo ignal- to- noie atio and pae 3D acquiition. At the ame time, local paamete of the obeved wavefield in petack eimic ecod ae of geat inteet fo many eimic application uch a ignal enhancement, velocity model building etc. We popoe to employ the MultiFocuing idea to achieve thi goal. A local common offet MultiFocuing appoximation fo taveltime tacking uface deciption i ued. It allow accuately appoximate taveltime of eimic event in the vicinity of abitay offet. We peent a ignal enhancement cheme and demontate it efficiency. Intoduction Time imaging uually contitute a key fit tep in the eimic imaging wokflow. Fo thee eaon, impoving the quality of time imaging i a focu of intenive eeach. MultiFocuing (MF i a method with the potential to geatly impove the quality of time imaging. In contat to the pocedue of CMP-baed method, in the MF appoach popoed by Bekovitch et al. (994 and decibed in Bekovitch et al. (8 and Landa et al.,, each zeo-offet tace i contucted by tacking tace that need not belong to the ame CMP gathe but, athe, whoe ouce and eceive ae within the limit of a cetain apetue in the vicinity of the cental (imaging point. The ize of uch an apetue i detemined by the ize of the fit Fenel zone. The numbe of tace falling in thi zone can ignificantly exceed the numbe of tace belonging to one CMP gathe. Thi allow a conideable inceae in the ignal-to-noie atio fo the taget eflection. Since the tace being tacked no longe belong to the ame CMP gathe, thi pocedue equie a moe geneal moveout coection than the one ued in conventional CMP tacking. Fo a given ouce-eceive pai, the MultiFocuing moveout equation i baed on the pheical appoximation of the eflection event wavefont nea the obevation uface. The moveout coection expeed by the zeo-offet MultiFocuing (ZOMF fomula i, in D cae, a thee-paamete uface which accuately appoximate the actual taveltime in the vicinity of the imaging point. The thee paamete ae: the emegence angle of the nomal ay β and the adii of cuvatue ce and cee of the two fundamental wavefont, namely, nomal incident point and nomal wave epectively. One of the main limitation of the ZOMF method i a quai-hypebolic appoximation fo tavel-time uface. The opeato in thi cae i contucted aound a zeo-offet ay and, in pinciple, i valid fo hot offet. The idea of uing accuate taveltime appoximation fo petack ignal enhancement i not new. Both MultiFocuing and common eflection uface tack (CS can be ued fo thi pupoe (Baykulov and Gajewki, 9, Buzlukov et al.,. But the global, quai-hypebolic zeo-offet opeato ued in thee method limit the efficiency of thi application fo cae of complex geology and/o tong lateal velocity GeoConvention 3: Integation

2 vaiation. In thee cae, the taveltime of eimic event become non-hypebolic and MF/CS zeooffet opeato appoximation tat to be inaccuate. Simila effect can be caued by aniotopy o lage offet. The popoed COMF pocedue i fee of thi limitation due to a local chaacte of the new common-offet coection and epaate poceing fo each deied offet. In thi pape, we intoduce a genealization of the ZOMF coection fo the abitay offet cae. We efe to thi new time coection a common-offet MultiFocuing (COMF. Thee ae a numbe of poible application of the COMF uch a non-hypebolic time imaging, petack ignal enhancement, AA, velocity model building etc. We illutate petack ignal enhancement in cae of non-hypebolic aival taveltime fo eflected event. Common-offet MultiFocuing coection One of the main limitation of the ZOMF method i a hypebolic appoximation fo actual tavel-time uface. To inceae the accuacy of the MF appoximation and to take into account nonhypebolicity of the taveltime uface, we intoduce a local MF time coection fo an abitay non-zeo-offet tace. Figue illutate chematically the new method. A ay which we call cental tat at the uface S point, and the emegent angle to the vetical. Thi ay hit the eflecto at the point, O, and etun back to the uface point and the emegence angle. Thi pai of ay belong to a X CMP point located at and half offet h. A paaxial ay tat fom an abitay ouce S located at ditance X X fom the middle point, S O coe the cental ay at point F and aive Figue. Schematic epeentation of the commonoffet multifocuing. afte at eceive located at ditance X eflecting at point P. Wavefont paamete, namely, cuvatue and emegence angle fo diffeent wave popagating along the ay, can be computed uing dynamic ay-theoy fundamental olution (Čevený et al.,. emitting fom the point F upwad to the uface, and Let u conide two fictitiou wavefont: emitting fom the point F downwad, eflected at the eflecto and emeging at the point. Thee two fictitiou wavefont ae chaacteized by two adii of cuvatue and. The common-offet Multifocuing (COMF etablihe connection between two fictitiou wave and and dynamic paamete of the common offet ay S O, namely, adii of cuvatue of the common hot, common eceive and geometical peading function L. The tavel time coection t in thi cae can be witten a: t ( in X ( X whee i a nea uface velocity, and ( in X ( X. GeoConvention 3: Integation

3 ,, L, L L L and focuing paamete can be deived olving the following ytem of equation ( in X Y ( ( Y co co ( in X Y ( ( Y co co whee Y i the o-called aymmetical coefficient. The tavel time coection fo abitay uface CMP poition and offet h (Figue i a function of obevation geomety, nea uface velocity and 5 unknown paamete:,,,,, L. COMF taveltime fomula povide an adequate epeentation of aival time fo a ay pai with abitay ouce-eceive configuation. The COMF coection fomula i emakably accuate even fo tongly cuved eflecto. The moveout coection i an appopiate bai fo the common-offet tacking pocedue, a it can align eimic event in a vicinity of an abitay cental ay. Implementation of the COMF method i technically challenging becaue it equie defining five moveout paamete in D fo each time ample of the common-offet image. Etimation of optimal paamete conit of calculating a coelation meaue (e.g., emblance a a function of unknown paamete, and chooing an appopiate coelation maximum. The paamete ae etimated fo each imaging point, fo each offet and fo each time ample. It i impotant to note that the decibed pocedue i applied locally within a mall vicinity of each eimic tace and doe not equie global full offet appoximation. In thi way, we avoid hypebolic o quai-hypebolic appoximation fo taveltime cuve/uface a it i uually equied in many conventional time imaging pocedue uch a CMP, PSTM, ZOMF, etc. Output of the COMF i patially tacked common-offet ection and optimal wavefont paamete (emegency angle and cuvatue. Enhanced eimic gathe The ignal enhancement pocedue conit of two tep: paamete etimation fo each defined tace on each common offet ection, and then, accoding to the etimated paamete, the patial tack calculate a tacking time uface aound a pecified uface location and pefom ummation of data along that uface. The eult of the ummation i aigned to the ame uface location, offet, and time coodinate. epeating thi pocedue fo all deied point geneate a new gathe that i called the COMF enhanced gathe. Figue a. Synthetic Mamoui-type model. GeoConvention 3: Integation 3

4 Figue b illutate a ynthetic CMP gathe computed fo a Mamoui-type model hown in Figue a. Seimic event at about ec ae chaacteized by tong non-hypebolic aival due to a tong velocity anomaly in the model. Figue 3a how the ame CMP gathe afte applying zeo-offet MF ignal enhancement when the enhancing opeato wa etimated uing zeo-offet MF appoach. A it wa expected, a non-hypebolic pat of the event wa deteioated by non coheent ummation along hypebolic opeato defined by ZOMF. Figue 3b how the gathe afte applying COMF ignal enhancement. A patial tacking opeato wa developed though etimation of five paamete fo each CMP poition, each offet value and each time ample. Apetue fo etimation wa 5m in CMP diection and 5m in offet diection. The eulting gathe how pefect econtuction of the nonhypebolic pat of the gathe. Figue b. Oiginal CMP gathe. Stongly nonhypebolic in the deep pat Figue 3a. The ame CMP gathe a hown in Fig. b afte ZOMF ignal enhancement. Event in the deep pat ae deteioated. Figue 3b. The ame CMP gathe a hown in Fig. b afte COMF ignal enhancement. Deep event ae pefectly econtucted. To illutate coectne and efficiency of ou pocedue we pefomed petack depth migation uing oiginal data with andom noie added and both et of the enhanced gathe fo the tue velocity model. Figue 4a how the PSDM eult uing the oiginal gathe. Figue 4b i a depth ection obtained fom gathe enhanced by the zeo-offet MF opeato and Figue 4c illutate the PSDM ection uing the COMF opeato. A it wa expected, diffeence between the two image appea at place whee the aival taveltime on the oiginal gathe ae tongly non-hypebolic. Concluion Common-offet MultiFocuing povide an efficient way fo model independent petack ignal enhancement which can impove imaging in cae of low ignal to noie atio and non-hypebolic movout. The method i baed on a local MultiFocuing appoximation fo locally coheent eimic event and allow, fo each tace and each time ample, an accuate etimation of the wavefont paamete (cuvatue, geometical peading and emegence angle in hot and eceive domain. We have peented and illutated petack ignal enhancement GeoConvention 3: Integation 4

5 . Figue 4a. PSDM image obtained fom the oiginal gathe with andom noie. Figue 4b. PSDM image obtained fom the ZOMF enhanced gathe. Place of non-hypebolic taveltime uface ae deteioated. Figue 4c. PSDM image obtained fom the COMF enhanced gathe. The image i vey cloe to the coect one hown in figue 4a. efeence Baykulov, M. and Gajewki, D. [9] Petack eimic data enhancement with patial common-eflection-uface (CS tack, Geophyic, 74, Bekovitch, A., Gelchinky, B., and Keyda, S. [994] Baic Fomula fo MultiFocuing Stack. 56th EAGE Confeence and Exhibition. Expanded Abtact. Bekovitch, A., Belfe, I., and Landa, E. [8] Multifocuing a a method of impoving ubuface imaging, The Leading Edge,, Buzlukov,, Baina,, and Landa. [] Petack Data Enhancement Uing Local Taveltime Appoximation. 7nd EAGE Confeence and Exhibition, Extended abtact Čevený,. [] Seimic ay theoy. Cambidge Univeity Pe. Landa E., Keyda, S., and Moe, T.J. [] MultiFocuing eviited - inhomogeneou media and cuved inteface. Geophyical Popecting, 58, GeoConvention 3: Integation 5