Compensating for source and receiver ghost effects in reverse time migration

Transcription

1 Compenating fo ouce and eceive ghot effect in evee time migation Yu Zhang, Gaham Robet and Adel Khalil, CGGVeita Summay o maine eimic data, the ouce and eceive ghot geneated by the fee uface caue angle dependent fequency and amplitude ditotion. o bette intepetation and inveion, thee unwanted effect ae bet coected in a petack depth image. aed on tue amplitude migation theo we popoe to compenate fo the ghot effect in a evee time migation. The numeical example demontate that with the compenation tem, we can geneate a wide bandwidth eflectivity map. In paticula, the low fequency geological vaiation i bette delineated in the image. We alo how that with ome imple modification, the popoed evee time migation can geneate enible velocity petubation fo eimic inveion. Intoduction To intepet ubtle geologic featue, eimic data mut contain both the low and high fequencie equied fo high eolution imaging. High-fidelit low fequency data povide bette penetation to illuminate deep taget, a well a poviding geate tability and moe impotant infomation fo eimic inveion. o uch eaon it i deiable to get a wide bandwidth eimic image. To achieve wide bandwidth petack depth image fom maine eimic data, we have to ovecome the bandwidth limitation impoed by ouce and eceive ghot. Many olution have been popoed ecently. o example, vaiable-depth teame acquiition (Soubaa and Whiting, 011 i emeging to take advantage of the low noie epone of new geneation olid teame and the notch diveity caued by eceive depth vaiation. A a eult, it yield a high quality boadband pectum. The eceive ghot can be emoved in a late poceing tage by ome novel poceing and imaging technique (Soubaa, 010; Soubaa and Lafet, 011. The new method ceate an exceptionally hap and clean wavelet fo intepetation. Howeve, emoving the ouce ghot emain a moe difficult tak if we aume the ouce ae excited at a oughly fixed depth (i.e. lack of notch diveity and with a big hot incement in lateal poition (i.e. evee data aliaing, a what happen motly in maine tow-teame uvey. In thi abtact, we popoe a method to compenate fo ouce and eceive ghot effect in a Revee Time Migation (RTM. y tudying tue amplitude migation theo we demontate that the exitence of ghot ditot both migation pectum and the amplitude veu angle (AVA elation. Hence deghoting i a cucial tep fo AVA analyi. We have developed a theoy to emove the ghot duing RTM to obtain a high fidelit high eolution image. The numeical eult how that both eflectivity and velocity petubation can be well ecoveed with the popoed RTM. Theoy Souce and eceive ghot: Let u aume the ouce depth i z and v i the acoutic wave peed of wate. 0 The ouce ghot geneated by the fee uface eflection i an angle dependent effect, which change both the wavelet amplitude and pectum. To implify ou dicuion, we aume the uface eflectivity i -1. At the ouce location, the ouce ghot acting on the wavefield with the popagation angle take the fom in fequency domain: coz coz i i (, e e co z G i in. (1 In fequency and wavenumbe domain, we have the following elation co 1 k x k. ( y Similal the eceive ghot can be expeed a G coz coz i i (, e e co z i in. (3 v Revee time migation: Tue amplitude RTM ha been developed in Zhang and Sun (009 and Xu et al. (011. To migate a hot ecod Q( x, y ; t, with the hot at ( x, y, z 0 and eceive at ( x, z 0, we have to compute the wavefield oiginating at the ouce location and obeved at the eceive location. ecaue the ouce wavefield expand a time inceae and the ecoded wavefield i computed backwad in time, we denote them by p and p epectively in the following acoutic wave equation: 1 p ( ; ; 0, x t x (4 v t t p ( z 0; t; x ( x x f ( t' dt', and 1 p ( ; ; 0, x t x (5 v t p ( z 0; t; x Q( t, whee v v(x i the velocit f (t i the ouce ignatue, and i the Laplacian opeato. x y z 0

2 Compenating fo ouce/eceive ghot effect in RTM It ha been poven that wave popagation (4 and (5 togethe with the following 3D imaging condition povide AVA fiendly migation amplitude in the ubuface angle domain (Xu et al., 011 v( x R( x; ; ( ' ( ' p pdtdxd ' d', (6 in ' whee and ae the eflection angle and azimuth angle at the imaging location, epectively. Compenating fo the ghot effect in RTM: A defect of the afoementioned tue amplitude RTM theoy i that the ghot effect ae ignoed. Since in RTM, we popagate an atificial ouce wavefield, it i taightfowad to compenate fo the ouce ghot duing the migation. To achieve thi, we need to modify the bounday condition in (4 to the following f ( ( z 0; ; x ( x x, (7 ig (, whee p ˆ ( epeent the ouie tanfom of p (t. A imila idea can be applied to the eceive ide to compenate fo the eceive ghot Q( ( z 0; ; x. (8 G (, Howeve, when eimic data i aliaed, diectly applying compenation fomula (8 may caue intabilit o ome egulaization emedy mut be applied duing the wave popagation. In theo imaging condition (6 povide angle dependent eflectivity (leitein et al., 001. Compenating ghot effect lead to eliable low fequency component in the image. Such infomation can be ued to etimate velocit a demontated in wavefom inveion method (Taantola, To obtain velocity petubation fom an RTM, we jut need to modify bounday condition (8 and imaging condition (6 a follow (Jin et al. 199 Q( ( z 0; ; x, (9 ig (, v( x p ( x; t; x p ( x; t; x dtdx. (10 Numeical expeiment and example The fit example i deigned to pove the eliable amplitude and pectum epone of RTM afte compenating fo the ghot effect. A imila tet wa done in Zhang and Sun (009 without ghot in the eimic data. Hee we aume both ouce and eceive ghot ae ecoded. igue 1 how a D ingle hot ecod ove five hoizontal eflecto at diffeent depth, with the hot in the cente of the ection and the eceive out to an offet of 7500m on eithe ide. The hot and the eceive depth ae 10m and 15m, epectivel and the wate velocity i 1500m/. In the modeling, we aume the eflectivity i unifom at all eflection point ove all eflection angle. Due to the exitence of ghot, both the wavelet amplitude and pectum ae ditoted aco tavel time and lateal ditance, in addition to the effect of geometical peading. If we ue the conventional tue amplitude RTM fomulation (4 and (5, tack all the migated common image hot gathe to geneate ubuface offet gathe (Sava and omel, 003, and then convet them to ubuface angle domain common image gathe (CIG, a hown in igue, we end up with a ditotion in the pectum of the migated image (left and an incoect AVA tend (ight. Afte we have compenated fo the ghot effect on both ouce and eceive ide, the wavelet on the migated angle gathe have wide and moe balanced fequency bandwidth and appea much hape (igue 3, left. Alo, the nomalized peak amplitude along eflecto in the eflection angle domain convege well which indicate the eflectivity i well ecoveed and the AVA elation i moe eliable (igue 3, ight. igue 1: A hot ecod ove five hoizontal eflecto in a medium with v=1500m/. oth ouce and eceive ghot ae ecoded. In the econd example, we apply RTM to the 004 P D model (illette and andbeg-dahl, 005. The ynthetic data wa geneated by high ode finite-diffeence acoutic modeling uing both velocity and denity model, with hot pacing 50m, eceive pacing 5m and 1000m maximum offet. oth ouce and eceive ghot ae ecoded with z z 1. 5m. In igue 4, we compae the conventional tacked RTM image (left, the RTM image with both ouce and eceive ghot compenation (middle, and the impedance model (ight, which i the poduct of the velocity and denity. It i clea that the new RTM image (middle ha much moe balanced enegy ove the migation bandwidth, which bette delineate the alt boundaie, eflectivity polaity and the textue of the geological layeing. Alo, the new image how moe low fequency eneg well coelated to the tend of impedance vaiation (ight. Thi tet how that the compenated low fequencie deived fom deghoting ae quite eliable. Next, we ue ou tue amplitude RTM to compenate fo the ghot and to poduce velocity petubation intead of eflectivit a decibed by the modified bounday

3 Compenating fo ouce/eceive ghot effect in RTM condition (9 and imaging condition (10. Hee we ued the Sigbeea model to geneate the ynthetic data et, with the ouce depth at 5ft. We migate the data uing a contant gadient backgound velocity (igue 5, left. The RTM image with ouce ghot compenation i hown in the middle of igue 5. The ight pictue of igue 5 i the eal velocity petubation, deived by ubtacting the migation velocity fom the exact modeling velocity. With the ghot compenation, the RTM image doe a good job in econtucting the oiginal velocity petubation, a pedicted by the theoy. In igue 6, we chooe one imaging location, and compae the velocity petubation computed fom RTM (left with it eal cuve (ight. The oveall match of the two i quite good, except fo a caling diffeence, which can be calibated by a linea each. igue. Left: A migated angle domain CIG uing conventional tue amplitude RTM. Right: The AVA cuve picked fom the left. igue 3. Left: A migated angle domain CIG fom tue amplitude RTM with ouce and eceive ghot compenation. Right: The AVA cuve picked fom the left. igue 4. Left: The conventional tacked RTM image. Middle: The tacked RTM image with ouce and eceive ghot compenation. Right: The exact impedance model.

4 Compenating fo ouce/eceive ghot effect in RTM igue 5. Left: Migation velocity. Middle: Velocity petubation computed fom tue amplitude RTM. Right: The exact velocity petubation. igue 6. Velocity petubation computed fom tue amplitude RTM (left and the exact velocity petubation (ight. The tace location i indicated by the dahed line hown in igue 5 middle and ight plot. igue 7: Cental Noth Sea data et. Left: Conventional RTM image. Right: Souce and eceive deghoted RTM image. inall igue 7 how a compaion between conventional and deghoted RTM image fo a hallow wate data et fom the Cental Noth Sea. The ouce and eceive depth ae 6m and 8m, epectively. We highlight wavelet at about 4.km depth fom each image a wiggle plot. The idelobe ae ignificantly educed afte deghoting. Alo, the RTM with deghoting ha etained lowe fequencie which ha inceaed the bandwidth giving the image a moe continuou and textued appeaance. Concluion Diectly compenating fo the ouce and eceive ghot effect in a petack depth migation i attactive and can impove ou ability in intepeting geological tuctue and ock popetie. We have hown that thi can be incopoated in an RTM. When eimic data ha noie and i pooly ampled, a imple deghoting on the eceive may not wok well in the full bandwidth, but with ome tabilization tateg it help to compenate fo the angle dependent low fequency lo. ack popagating an invee ouce ghot can effectively emove the ghot on the ouce ide. All togethe, the popoed method impove the imaging powe of RTM. A we how in thi abtact, ou method poduce a hape wavelet and moe balanced amplitude. oth angle dependent eflectivity and velocity petubation can be output fom a tue amplitude RTM fo intepetation and inveion. Acknowledgment We acknowledge P and SMARRT JV fo poviding the 004 P and Sigbeea model. We thank ou colleague in CGGVeita fo thei uppot, epecially Richad Wombell fo hi help of the eal data example.

5 Refeence illette,. J. and S. andbeg-dahl, 005, The 004 P velocity benchmak: 67 th Meeting, Euopean Aociation of Geocientit and Enginee, Expanded Abtact., 035. leitein, N., J. K. Cohen, and J. W. Stockwell, 001, Mathematic of multidimenional eimic inveion: Spinge Publihing Co. Jin, S., R. Madaiaga, J. Viieux and G. Lambaé, 199, Two-dimenional aymptotic iteative elatic inveion: Geophy. J. Int., 108, Sava, P. C. and S. omel, 003, Angle-domain common-image gathe by wavefield continuation method: Geophyic, 68, Soubaa, R., 010, Deghoting by joint deconvolution of a migation and a mio migation: 81 t Annual Intenational Meeting, SEG, Expanded Abtact, Soubaa, R. and Y. Lafet, 011, Vaiable-depth teame acquiition: boadband data fo imaging and inveion: 81 t Annual Intenational Meeting, SEG, Expanded Abtact, Soubaa, R. and P. Whiting, 011, Vaiable Depth Steame The New oadband Acquiition Sytem: 81 t Annual Intenational Meeting, SEG, Expanded Abtact, Taantola, A., 1984, Inveion of eimic eflection data in the acoutic appoximation: Geophyic, 49, Xu, S., Y. Zhang and. Tang, 011, 3D angle gathe fom evee time migation: Geophyic, Vol. 76, No., S77-S9. Zhang, Y. and J. Sun, 009, Pactical iue of evee time migation: tue-amplitude gathe, noie emoval and hamonicouce encoding, it eak, Vol. 6, 19-5.