True Amplitude Reverse Time Migration: from Reflectivity to Velocity and Impedance Perturbations

Transcription

1 Tue Amplitude Revee Time Migation: fom Reflectivity to Velocity and Impedance Petubation Yu Zhang, Lian Duan* and Gaham Robet, CGGVeita, Cawle UK SUMMARY Conventional petack depth imaging method aim at poducing a tuctual image, which delineate the inteface of the geological vaiation o the eflectivity of the eath. With the help of boadband acquiition and poceing technique, the bandwidth gap between depth imaging and eimic inveion i educing. Hee, we popoe a theoy to how how impedance and velocity petubation can be etimated fom the angle domain common image gathe poduced by a tue amplitude evee time migation. The nea angle tacked image povide the impedance petubation etimate, while the fa angle image can be ued to etimate the velocity petubation. Togethe with the ghot compenation technique, the method decibed hee can be a ueful tool of eimic inveion fo maine exploation. oth ynthetic and eal data example have demontated that the method i eliable and povide additional infomation fo intepeting geological tuctue and ock popetie. 75 th EAGE Confeence & Exhibition incopoating SPE EUROPEC 13 London, UK, 1-13 June 13

2 Intoduction Revee Time Migation (RTM ha become a high end technique to image and intepet ubtle and complex geologic featue, not only becaue it coectly handle complex velocitie and popagate wave without angle limitation, but alo it take advantage of a complete et of acoutic wave (eflection, tanmiion, diffaction, pimatic wave, etc. to image ubuface tuctue with eaonably good amplitude (Zhang and Sun, 9; Xu et al., 11. Indeed, RTM i conventionally ued a a tool fo imaging the eflectivity o the inteface of the ubuface geology. Recentl the concept of ghot compenation popoed by Zhang et al. (1 bing the poibility of etimating the velocity petubation of the geology uing RTM fo eimic inveion. The method extend the low fequency bandwidth of the image by emoving the ouce and eceive ghot duing the conventional RTM. The velocity petubation can thu be obtained a it i the integation of the tacked eflectivity image. Hee, we futhe extend thi theo wheeby we deive a theoy fo pedicting the impedance and velocity petubation uing the Angle Domain Common Image Gathe (ADCIG fom an RTM and demontate ou theoy though both ynthetic and eal data example. Theoy o a zeo-phaed and deignatued hot ecod Q( x, y ; x, y; t with the hot at ( x, y, z and eceive at ( x, y, z, the RTM baed on the theoy of tue amplitude migation can be ummaied a the fowad popagation of the ouce wavefield p : 1 p ( x; t ( x x f ( t, v t (1 and the backwad popagation of the eceive wavefield p : 1 p ( ;, x t v t ( p z ; t Q( x, y; x, y, whee v v z denote the velocit f (t denote the ouce wavelet with a flat pectum, and denote the Laplacian opeato. To obtain a common-hot image with coect migation amplitude, we need to apply the deconvolution imaging condition (Zhang et al., 5. Howeve, in pactice, the co-coelation imaging condition: R( x p ( x; t p ( x; t dt (3 i often pefeable fo eaon of tability. Although thi doe not appea to be conitent with tueamplitude migation, Zhang et al. (7 poved that the imaging condition 3 i a pope choice to obtain tue amplitude ADCIG fom a wave equation baed migation. o thi to occu, the fowad popagation 1 need to be modified accodingly (Zhang and Sun, 9: 1 p ( ;, x t v t (4 t p z ; t ( x x f ( t' dt'. Thi equation i diffeent fom the conventional wave equation 1 fo the fowad wavefield, becaue the ouce i teated a a bounday condition intead of a ight-hand-ide focing tem in the popagation. uthemoe, to geneate the angle-dependent eflectivit the following 3D imaging condition povide AVA (amplitude veu angle fiendly migation amplitude in the ubuface angle domain (Xu et al., 11: v( x R( x; ; ( ' ( ' p p dtdxd ' d', (5 in ' whee and ae the eflection angle and azimuth angle at the imaging location, epectively. o maine acquiition, both the ouce ghot G and eceive ghot G effect mut be taken into conideation and can be eaily compenated duing the wave popagation of the RTM. Zhang et al. (1 modified the bounday condition in and 4 a follow: 75 th EAGE Confeence & Exhibition incopoating SPE EUROPEC 13 London, UK, 1-13 June 13

3 f ( pˆ z ; ; x ( x x, and Q( x, y; ; x, y pˆ z ; ; x, (6 ig (, G (, whee and denote the popagation angle at the uface fo the ouce and eceive, epectivel and p ˆ ( denote the ouie tanfom of p (t ; and demontated that compenating ghot effect lead to eliable ecovey of low fequency component in the image. Hee, we take one tep futhe and ue RTM to etimate velocity o impedance petubation. Conideing the acoutic equation with both velocity v(x and denity (x vaiation a follow: 1 1 p( x; x ( x x ( t. v t (7 o given initial velocity v ( x and denity ( x model, the petubed wavefield p( x; x p p atifie the following equation: 1 1 v p( x; x ( ; ;, p x t x 3 v t v t (8 whee v v v and denote the velocity and denity petubation, epectively. Uing the imila method developed in Jin et al. (199 and ogu and Lambae (1997, we obtain the aybaed elation between the petubed geological model and wavefield: v v x co co i co 3 co ' A A e Q ( ' dx dx dd ', (9 v in ' v x v x whee A ( A i the amplitude of the Geen' function fom the ouce (eceive to the image point, ( i the taveltime between the ouce (eceive and the image point. In the context of RTM, equation 9 can be ephaed by modifying the imaging condition 6 a follow v ( v vx pˆ ( ˆ p ( in co co ' ( ' dx dx dd '. (1 v v in ' i Equation 1 tell u that if we output ubuface angle gathe with a pope imaging condition, the nea angle image pedict the impedance petubation ( v /( v, while the fa angle image can be ued to etimate the velocity petubation v / v. Theefoe, we can epaate the effect of velocity and denity on the tacked image by outputting ADCIG. Numeical and eal data example The fit example i deigned to pove the eliability of impedance and velocity petubation etimation uing RTM afte ghot compenation. Hee, we contuct a hoizontally invaiant geological model to 4km in depth. igue 1 left peent the hot ecod with the hot in the cente of the ection and the eceive pead to both ide with maximum offet of 1km. oth the ouce and eceive ghot ae ecoded. Setting the backgound velocity and denity to m/ and kg/m 3, epectivel we ue the ghot compenated RTM fomulation, 4 and 6 to popagate the wavefield, apply imaging condition 1 to geneate the ubuface offet gathe (Sava and omel, 3, and then convet them to ADCIG, a hown in igue 1 ight. aed on ou theo the tace diectly etimate the impedance petubation while velocity petubation can be calculated uing any nonzeo degee tace. Howeve, a fa angle tace will bette eae the numeical eo than a nea angle tace, when epaating the velocity petubation fom the impedance petubation uing equation 1. We thu elect the and 66 tace fo the pupoe of etimating the impedance and velocity petubation. Afte imple ecaling, one could ee fom igue that the etimated petubation (ed match with the exact petubation (blue eaonably well. The mimatch of the velocity petubation at depth moe than 3km i due to the lack of lage efection angle ove the limited offet ange and the tetch of an event on the fa angle CIG. In the econd example, we apply RTM to the P4 D model (illette and andbeg-dahl, 5. The ynthetic data i geneated by high ode finite-diffeence acoutic modeling uing both velocity and denity model, with hot pacing 5m, eceive pacing 5m and 8km maximum offet. oth ouce and eceive ghot ae ecoded at 1.5m depth. In igue 3, we compae the impedance 75 th EAGE Confeence & Exhibition incopoating SPE EUROPEC 13 London, UK, 1-13 June 13

4 petubation output fom a ghot-compenated RTM (top ight with the exact impedance petubation (top left, which i the poduct of the model velocity and denity petubation. o detailed invetigation, we peent the etimated and exact impedance at a given location, indicated by the blue dahed line in the top image. The etimated impedance petubation epoduce almot the exact olution, except at the haply changing impedance boundaie, fo example, at the wate bottom o at the top of alt bounday. Thi i due to the lage model petubation which doen t fully atify the lineaization aumption in deiving equation 8 and the lack of vey low fequencie in eimic data. Thi eult demontate the applicability of ou theoy to geological model with complex tuctue. igue 1: A hot ecod (left and a migated ADCIG (ight uing the tue amplitude RTM. The CIG figue demontate the elected and 66 tace (dahed blue line. igue The impedance (top and velocity (bottom petubation fo the ynthetic expeiment, which peent the exact petubation (blue and computed petubation fom the tue amplitude RTM (ed. igue 3 The exact (top left and etimated (top ight impedance petubation fo the numeical expeiment uing P4 model. The detailed plot (bottom of the exact (blue and etimated (ed impedance petubation at the given location (vetical dahed blue line. In igue 4 we peent ghot-compenated RTM image, a tacked eflectivity image (left and an impedance petubation ection (middle, fo a hallow wate dataet fom the Cental Noth Sea. The ouce and eceive depth ae 6m and 7m, epectively. The low fequency component ae compenated in both image, which give the ection a moe continuou and textued appeaance chaacteitic of boadband data. In paticula, we compae the etimated impedance petubation 75 th EAGE Confeence & Exhibition incopoating SPE EUROPEC 13 London, UK, 1-13 June 13

5 fom RTM againt the filteed well-log data (ight at a given location (the ed vetical line in the middle image. It can be een that the etimated impedance povide a good appoximation to the meaued data. The ghot-compenated RTM i not only a technique to achieve an image with boad bandwidth, but alo a ueful tool to etimate the impedance o velocity of the eal-wold ubuface geology. igue 4. Ghot-compenated RTM image fom a Cental Noth Sea dataet: the tacked eflectivity image (left and the impedance petubation ection (middle. The compaion between the meaued impedance uing filteed well-log (black and the etimated impedance fom RTM (ed at the given location (the vetical ed line in the middle image i hown on the ight. Concluion We have developed a theoy of tue amplitude RTM to delineate the impedance and velocity petubation of ubuface tuctue. The nea angle tacked image povide the impedance petubation etimate, while fa angle image can be ued to etimate the velocity petubation. Togethe with the ghot compenation technique, the method decibed hee can be a ueful tool of eimic inveion fo maine exploation and ued to bidge the gap between full wavefom inveion (Taantola, 1984 and evee time migation. oth ynthetic and eal data example have hown the method i eliable and povide additional geological infomation fo intepetation and inveion. Acknowledgement We acknowledge P fo poviding the 4 P model. We thank Richad Wombell fo hi help on the eal data example and Gille Lambae fo helpful dicuion. Refeence illette,. J. and S. andbeg-dahl, 5, The 4 P velocity benchmak: 67 th Meeting, Euopean Aociation of Geocientit and Enginee, Expanded Abtact., 35. ogu, E. and G. Lambae, 1997, Paameteization tudy fo acoutic and elatic ay+on inveion, J. Seimic Exploation, 6, Jin, S., R. Madaiaga, J. Viieux and G. Lambaé, 199, Two-dimenional aymptotic iteative elatic inveion: Geophy. J. Int., 18, Sava, P. C. and S. omel, 3, Angle-domain common-image gathe by wavefield continuation method: Geophyic, 68, Taantola, A., 1984, Inveion of eimic eflection data in the acoutic appoximation: Geophyic, 49, Xu, S., Y. Zhang and. Tang, 11, 3D angle gathe fom evee time migation: Geophyic, Vol. 76, No., S77-S9. Zhang, Y., Zhang, G. and leitein, N., 5, Theoy of tue amplitude one-way wave equation and tue amplitude common-hot migation: Geophyic, 7, E1-1. Zhang, Y., Xu, S., leitein, N. and Zhang, G., 7, Tue amplitude angle domain common image gathe fom one-way wave equation migation: Geophyic, 7, S Zhang, Y. and Sun, J., 9, Pactical iue of evee time migation: tue-amplitude gathe, noie emoval and hamonic-ouce encoding, it eak, Vol. 6, Zhang, Y., Robet, G. and Khalil, G., 1, Compenating fo ouce and eceive ghot effect in evee time migation: 8 nd Annual Intenational Meeting, SEG, Expanded Abtact, SPMI th EAGE Confeence & Exhibition incopoating SPE EUROPEC 13 London, UK, 1-13 June 13