P284 A Full-wave Equation Based Seismic Illumination Analysis Method

Transcription

1 P284 A Full-wave Equation Baed Seimic Illumination Analyi Method X.-B. Xie* (Univeity of Califonia) & H. Yang (Univeity of Califonia) SUMMARY We popoe a full-wave equation baed method fo eimic illumination analyi. The full-wave finitediffeence method i ued to calculate the wave fom the ouce and eceive to the ubuface taget. A time domain local lowne analyi technique i ued to decompoe the wavefield into angle domain beam. Baed on the angle domain infomation, we fomulate the illumination matix fom which diffeent illumination meauement can be deived. Unlike the one-way wave equation baed method, the cuent appoach doe not have the angle limitation and the eflection/tanmiion enegy can be accuately calculated. The new illumination method can handle tuning wave which ae cucial fo imaging teep tuctue. Thu, thi method i paticulaly ueful fo poviding illumination analyi in evee-time migation. A goup of numeical example ae calculated to demontate the time-domain wavefield decompoition and the ceation of diffeent illumination meauement. The illumination in the 2D BP model i invetigated. Ou pecial attention i focued on the illumination of vetical and ovehung tuctue.

2 Intoduction The illumination of a ubuface taget i affected by many facto, e.g., the limited acquiition apetue, the complex ovebuden tuctue and the eflecto dipping angle. The eimic illumination analyi anwe the quetion that, given a velocity model and the acquiition geomety, how a taget can be imaged. The illumination calculation baed on ay tacing technique (Schneide and Winbow, 1999; Muedte and Ratcliff, 2001; Geliu, et al., 2002) ha no angle limitation but the high-fequency aymptotic appoximation in ay theoy may eveely limit it accuacy in complex egion. The one-way wave equation baed method (Xie and Wu 2002; Xie et al. 2003, 2005b, 2006; Wu and Chen 2002, 2006; Wu et al. 2003; Jin et al. 2003, 2006) i efficient and conitent with mot one-way wave equation baed migation method. Howeve, thi method doe not handle the wide-angle wave accuately. In paticula, it lack of the ability handling tuning wave. In ecent yea, the evee time migation gain attention quickly becaue it doe not have the angle limitation and can popely image the teeply dipping tuctue with tuning wave. In thi tudy, we peent a new illumination analyi appoach which i baed on the full-wave popagato. The new method doe not have angle limitation uually encounteed by a one-way appoach. In addition, it accuately olve the enegy tanmiion in a complex velocity model. Thi method i paticulaly ueful in poviding illumination analyi fo evee time migation. Methodology A taget uually can only be illuminated by wave coming/leaving at pecific diection. Figue 1 i a ketch howing a taget illuminated by a pai of ouce-eceive beam which fom a baic obevation to the taget. Collecting ouce-eceive pai fom all poible diection can compoe the illumination meauement at the taget location. In one-way wave equation baed illumination analyi, the ouce and eceive ide wave ae calculated uing one-way Figue 1. Catoon illutating the geomety of the illumination analyi. popagato. To ovecome the angle limitation of the one-way appoach, hee we ue the fullwave finite-diffeence (FD) method to popagate the ouce and eceive wave. Since the FD method i a time domain appoach, we ue a time-domain local lowne analyi technique (Xie and Lay 1994; Xie et al. 2005a) to decompoe the wavefield into local angle domain and ue them to ceate the illumination meauement. Simila to the deivation in fequency domain (Xie et al. 2003, 2006), we can fomulate the local illumination matix fom time domain calculation. Fo a ouce-eceive pai, the local illumination matix at the taget location can be expeed a (, 2 θ, θg ;, g) = ( 2 ) ( θ, ; ) ( θg, ; g) A v I I, (1) whee i the taget location, and g ae ouce and eceive location, θ and θ g ae incidence and catteing angle of ouce and eceive beam, v i the local velocity, ( θ, ; ) (, ;, ) 2 θ 2 = t, ( θg, ; g) = ( θg, ; g, ) ( g, ; g, t) I G t dt I G t dt, and G( θ, ;, t) and G θ ae angle-domain Geen function which can be calculated uing a local lowne analyi method (Xie et al. 2005a) C eˆ g, ( ) G θ,,, t = W G ;, t, (2) whee G(, g,, t) ( ) ( ) g, g, g, v i the ouce o eceive ide Geen function fom the FD calculation, e ˆ and eˆ g ae unit vecto towad the diection θ and θ g, i the location whee the wavefield v

3 i ampled fo calculation, W ( ) i a pace window centeed at, and C i a nomalization facto. The illumination matix fom the entie acquiition ytem can be obtained by umming up contibution fom individual ouce-eceive pai baed on the acquiition geomety, A, θ, θ = A, θ, θ ;,. (3) ( g) ( g g) Fom the illumination matix, diffeent illumination meauement can be deived (Xie et al. 2005b, 2006) and we will give them in the next ection. Numeical Example We ue numeical example to demontate the calculation of diffeent illumination meauement. Time domain local lowne analyi. Figue 2 how a imple alt dome model ovelapped with the wavefield naphot fom the FD calculation. The velocity model i compoed of a depth-dependent backgound and a alt dome with teep flank. The popagation diection of diffeent wave ae calculated uing equation (2) and hown in 2D lowne map ineted in the figue. Figue 2. Wave popagation diection calculated Local illumination matix. uing equation (2). The angle of thee enegy peak The illumination matix A(, θ, θg ) i in the pola coodinate give popagation diection and the adiue of the cicle give thei local defined in the acquiition lowne. θ, θ. Uing coodinate tanfom θ = ( θ + θ ) 2 and θ ( θ θ ) 2 (,, ) A θ θ d d g g g coodinate ( g ) =, we can obtain the illumination matix in taget coodinate ytem, whee θ d and θ ae dipping and eflection angle, epectively (efe to Figue 1). Figue 3 i a ketch illutating the tuctue of a 2D illumination matix. The hoizontal and vetical coodinate ae incidence and catteing angle while the two diagonal ae dipping and eflection angle, epectively. Note that the aea coveed by a full-wave appoach (lage quae) i much lage than that coveed by a oneway popagato (mall quae). The full-wave method can cove tuctue with dipping angle lage than 90 degee (e.g., ovehung tuctue). The acquiition dip epone. The acquiition dip epone (ADR) can be obtained by ubtituting the dipping angle θ d with the taget dipping angle and integate the illumination matix with epect to eflection angle θ (Xie, et Figue 3. Sketch howing the al., 2006) tuctue of an illumination matix. D(, θn) = A(, θd, θ) δ ( θd θn) dθddθ (4) whee D(, θ n ) i the ADR at taget location and fo tuctue with a dipping angle θ n. Figue 4 how the ADR map in diffeent velocity model and fo ouce-eceive pai with diffeent acquiition geometie. The location of ouce and eceive and the ketch of ay path ae illutated to demontate how thee facto affecting the illumination. Figue 4a how the -45 degee ADR fom a uface acquiition ytem in a contant velocity model.

4 Thi configuation cannot popely image a teep tuctue. Figue 4b how the -120 degee ADR fo a uface acquiition in a v(z) velocity model. Becaue tuning wave ae geneated in thi cae, a uface acquiition ytem can image teep o even ovehung tuctue. Figue 4c how the -90 degee ADR fo VSP acquiition geomety in a contant velocity model. A VSP acquiition can image a vetical taget in a contant velocity model. Illutated in Figue 5a-c ae illumination matixe coeponding to 3 taget location hown in Figue 4a-c. The illumination matix i Figue 4. The [ (, )] 12 D θ n fo diffeent configuation. calculated uing equation (3). In Figue 5a, the enegy i located at dipping angle -45 degee. In Figue 5b, the dipping angle i located at about -120 degee. Shown in Figue 5c i the illumination matix fo VSP geomety. The enegy i located at dipping angle -90 degee but the eflection angle i lightly away fom 0 degee due to the lage eflection angle involved (efe to Figue 4c). Illumination analyi fo the BP model. Shown in Figue 6a i pat of the BP velocity model which i compoed of a complex backgound and alt bodie with ovehang. The ouce cove the uface of the model. Figue 6b-d ae ADR fo 0, -90 and -135 degee, epectively. The 0 degee ADR in Figue 6b i geneally tong thoughout the model and i conitent with the migation eult whee the hoizontal tuctue ae well imaged. The -90 degee ADR in Figue 6c i Figue 5. Illumination matix fo diffeent acquiition geometie and velocity model. eponible fo illuminating the vetical wall of the alt dome. The -135 degee ADR hown in Figue 6d i geneated by tuning wave imila to that illutated in Figue 4b. It contibute to the illumination of the ovehung pat of the alt flank. Imaging thi ovehung tuctue i a majo challenge fo one-way wave equation baed method, while the evee time migation can image thi tuctue atifactoily. The illumination method baed on the full-wave popagato i conitent with the evee time migation and can povide coeponding illumination analyi. Concluion We popoe a new eimic illumination analyi method baed on the full-wave FD calculation. Unlike the one-way wave equation baed method, thi new appoach doe not have angle limitation. Thi method can povide illumination analyi fo evee time migation which emphaize the contibution of wide-angle tuning wave. A goup of numeical example ae calculated to how the wavefield decompoition and the ceation of

5 Figue 6. Illumination in the 2D BP model. diffeent illumination meauement. We calculate ADR in the 2D BP model and invetigate thei elation with the vetical and ovehung alt flank. The eult peented in thi pape ae fo 2D model but thee i no majo obtacle to expand thee eult to 3D cae. Refeence Geliu, L.J., Lecomte, I., and Tabti, H., 2002, Analyi of the eolution function in eimic petack depth imaging: Geophyical Popecting, 50, Jin, S., and Walaven, D., 2003, Wave equation GSP petack depth migation and illumination: The Leading Edge, 22, Jin, S., Luo, M., Xu, S., and Walaven, D., 2006, Illumination amplitude coection with beamlet migation, The Leading Edge, 25, Muedte, D., and Ratcliff, D., 2001, Undetanding ubalt illumination though ay-tace modeling, Pat 1: Simple 2-D alt model: The Leading Edge, 20, Schneide, W.A., and Winbow, G.A., 1999, Efficient and accuate modeling of 3-D eimic illumination: 69th Annual Intenational Meeting, SEG, Expanded Abtact, Wu, R.S., and Chen, L., 2002, Mapping diectional illumination and acquiition-apetue efficacy by beamlet popagato: 72nd Annual Intenational Meeting, SEG, Expanded Abtact, Wu, R.S., and Chen, L., 2006, Diectional illumination analyi uing beamlet decompoition and popagation, Geophyic, 71, S147-S159. Wu, R.S., Chen, L., and Xie, X.B., 2003, Diectional illumination and acquiition dipepone, 65th Confeence and Technical Exhibition, EAGE, Expanded abtact, P147. Xie, X. B., Ge Z., and Lay, T., 2005a, Invetigating exploion ouce enegy patitioning and Lg-wave excitation uing a finite-diffeence plu lowne analyi method, Bull. Seim. Soc. Am. 95, Xie, X.B., Jin, S., and Wu, R.S., 2003, Thee-dimenional illumination analyi uing waveequation baed popagato: 73d Annual Intenational Meeting, SEG, Expanded Abtact, Xie, X.B., Jin, S.W., and Wu, R.S., 2006, Wave equation baed eimic illumination analyi, Geophyic, 71, S Xie, X. B. and Lay, T., 1994, The excitation of Lg wave by exploion: A finite-diffeence invetigation, Bull. Seim. Soc. Am. 84, Xie, X.B., and Wu, R.S., 2002, Extacting angle domain infomation fom migated wavefield: 72nd Annual Intenational Meeting, SEG, Expanded Abtact, Xie, X.B., Wu, R.S., Fehle, M., and Huang, L., 2005b, Seimic eolution and illumination: A wave-equation-baed analyi, 75th Annual Intenational Meeting, SEG, Expanded Abtact,