Angle domain illumination analysis along a target horizon Jian Mao, Sang Suh and Bin Wang, TGS

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1 Downloaded /9/3 to Reditibution ubject to SEG licene o copyiht; ee Tem of Ue at Anle domain illumination analyi alon a taet hoizon Jian Mao, San Suh and Bin Wan, TGS Summay We develop an efficient cheme of illumination analyi alon a taet hoizon. With thi cheme, we can calculate the Diectional Illumination (DI) fom the ouce and the Acquiition Dip Repone (ADR) alon a taet hoizon in vey hot tunaound time. Theefoe, it can be a ueful tool to tudy the influence of the model (e.. alt body) and the acquiition ytem (e.. hot ditibution and apetue ize). The eult can be a uide fo acquiition dein and model buildin. With the illumination map alon the taet hoizon, it alo i helpful fo the intepetation in aea whee the imae amplitude ae not eliable. Hee, we ue the wave-equation baed miation and local plane wave decompoition method to et the fequency domain illumination in the local anle domain. We pe-calculated and aved the anle domain Geen function alon the taet hoizon. Thee Geen function ae euable o that we can ave a lot of computational and I/O cot. We ue the 3D SEG/EAGE alt model and a eal model example to demontate the validity of ou method. Intoduction Seimic illumination analyi i a ueful tool that ive potential detectin powe of a pecific acquiition ytem fo a iven ubuface tuctue. Fo example, if thee a hue alt body in the uvey aea, which i vey common in Gulf of Mexico, we uually have illumination iue in the ubalt aea. The illumination analyi can ive u an etimation of the eney ditibution in thoe aea, which can help u impove ou acquiition dein and et bette undetandin of the miation imae. Both ay tacin (Bea et al., ) and wave-equation baed illumination analyi method (Rickett, 3; Jin and Xu, ) have been developed in ecent yea. Ray-baed method ae efficient, but will have lae eo when the model i complex. Theefoe we pefe wave-equation baed method. Becaue the ubuface tuctue uually have cetain dippin anle and the total illumination cannot ive u any anle infomation, a lot of effot ha been made towad anle domain illumination (Wu and Chen, ; Xie et al., ; Cao and Wu, 9). Anle decompoition i vey expenive, epecially in the 3D cae. To make the calculation moe efficient, we made ome implementation fo hih pefomance illumination analyi in the 3D cae (Mao and Wu, 7; Mao et al., ). The ouce ide illumination (DI) i elatively eay to calculate. Howeve, the illumination of a ouce coupled with eceive i moe impotant and i a moe accuate etimation of the ubuface illumination fo a iven acquiition ytem. We call thi kind of illumination Acquiition Dip Repone (ADR). A imila appoach uin ay-tacin ha been epoted by Lecomte (), and i widely ued thouh NORSAR oftwae. Howeve, if the taet hoizon i in a complex aea uch a ubalt, a waveequation popaato i moe accuate. In ode to calculate ADR, we need to calculate the Geen function fo evey eceive, which i vey expenive fo a lae model and lae data et. In a eal cae, we uually focu on a hoizon which could be a eevoi eal. A a eult, we popoed to calculate the illumination alon a taet hoizon, which i affodable and efficient. In thi pape, we develop an efficient cheme of illumination analyi alon a taet hoizon. Hee, we ue the wave-equation baed miation and local plane wave decompoition method to et the fequency domain illumination in the local anle domain. Since we pecalculated and aved the anle domain Geen function on the taet hoizon, we only need to fom the illumination by the ummation of the Geen function combination fo the iven acquiition ytem. Thi cheme povide a ueful tool fo acquiition dein and analyzin the imae amplitude. We calculated eveal numeical example includin the DI and ADR map fo the 3D SEG/EAGE alt model and a eal model on ome iven taet hoizon. Illumination analyi in the local anle domain Fo a iven acquiition eomety, we ue a wave-equation baed popaato to et the fequency-pace domain Geen function fom the ouce to the ubuface point (x,z). The pace domain Geen function can be decompoed at the imae eion to a ummation of local wavenumbe component. That i Gx, z,, Gx, z, θ,,, () θ whee G, z,, function and G, z,,, x i the fequency-pace Geen x θ i it local-anle component at θ. In the 3D cae, θ i a two dimenional vecto,,, which ae dip anle and azimuthal anle, epectively. Similaly, the fequency-pace Geen function fom the ubuface point (x,z) to eceive can be decompoed Gx, z,, Gx, z, θ,,, () θ whee G, z,, function and G, z,,, x i the fequency-pace Geen x θ i it local-anle 3 SEG DOI SEG Houton 3 Annual Meetin Pae 9

2 Anle domain illumination analyi alon a taet hoizon Downloaded /9/3 to Reditibution ubject to SEG licene o copyiht; ee Tem of Ue at component at θ. We ue the ecipocity pinciple in the calculation of the eceive Geen function, which mean we calculate the Geen function fom the eceive to the ubuface point and ue it fo ou illumination analyi. In ode to evaluate the local anle domain illuminationn eney ditibution fo a iven acquiition ytem in a velocity model, we um up the contibution fom all the ouce at the imae point, fo each local anle. That i D ax, z, θ, G x, z, θ,,, (3) whee D a Then we can et the total illumination by the ummation of all the anle D tot tal x, z, G x, z, θ,,. () In ode to evaluate the apetue and popaation effect of the iven acquiition eomety on eney ditibution fo a pecific pai of incident/eceivin anle, we ue unit impule a the ouce at both ouce and eceive point fo the entie acquiition confiuation and aume a unit cattein coefficient at each pace point. Fo a iven taett hoizon, we know the poition of the hoizon in the model. Then we can calculate the nomal anle at evey point on the hoizon. In thi cae, we have a et of local incident anle, θ. The coepondin eceivin anle, θ, can anle at point (x,z) on the taet hoizon. Then we can et a numbe of ADR on the hoizon, which ae defined a A x, z, θ, θ, G x, z, θ,, Gx, z, θ,,. () x, z, θ, i the diectional illumination map. θ be calculated by θ θ θ, whee θ i the nomal n We can futhe um up all the eflected eney to et the total ADR a follow A d x, z, Ex, z, θ, θ,. () θ, θ The value of the ADR map meaue the dip-anle epone of the acquiition ytem, includin the ouce and eceive apetue, and popaation effect. Efficient cheme of illumination analyi alon the taet hoizon In ode to make the calculation fat, we developed a new cheme fo thi taet oiented illumination analyi. Uually, the apetue fo adjacent hot will have a bi ovelap aea. If we calculate the Geen function on each eceive location fo each hot, thee will be epeated calculation. So ou chemee i to calculate all the Geen function on the taet hoizon in the acquiition aea and ave them. Then we loop ove the hot and ead in the n Geen function ued in the apetue and fom the illumination. When we finih one hot, we keep the Geen function which ae located in the apetue of next hot, and ead in the Geen function which ae not ued in lat hot. Thi will ave a lot of I/O time. We ummaized the cheme in Fiue, which how how we do thee fat illumination cheme on the taet hoizon. Fiue : Flowchat of the illumination cheme Numeical example Fiue : Velocity lice fom the 3D SEG model To demontate the application of the illumination analyi, we fit calculated eveal numeical example uin the 3D SEG/EAGE alt velocity model. Thi example imulate the illumination condition of the -hot data et. The id ize fo the model i 7, 7 and cell alon the x, y and z axe, epectively, with m fo both the hoizontal and depth h inteval. Fiue i a velocity lice fom the model. The oane line indicate the picked hoizon in the ubalt aea. Next, we calculated the DI and ADR map on the taet hoizon. We calculated anle domain DI and ADR map with a et of incident anle. In Fiue 3, we onlyy elected theee anle component to 3 SEG DOI SEG Houton 3 Annual Meetin Pae 9

3 Anle domain illumination analyi alon a taet hoizon Downloaded /9/3 to Reditibution ubject to SEG licene o copyiht; ee Tem of Ue at plot. DI map only how how much eney can be popaated to the taet hoizon. ADR map can etimatee how much eney can be eceived by the iven acquiition ytem. A a eult, ADR will be moe conitent with the imae amplitude. Afte a ummation, we can et the total ADR a hown in Fiue. Fiue 3: Anle domain DI map (left hand ide) and the coepondin ADR map (iht hand ide) fo the taet hoizon. The incident anle fo thee DI and ADR map ae (, ), (, ) and (, ) fom top to the bottom. CDP( (km) CDP( (km) x Fiue : A field data et (uppe: velocity model, lowe: miation imae) Fiue : Total ADR map on the taet hoizon Fiue : Subalt taet hoizon in the field data model Then we wok on a field data example model. Fiue how the velocity cube and RTM imae, whichh ha a couple of alt bodie in it. We can ee the imae amplitude i nott balanced in thee ub-alt aea due to the illumination poblem, in uch aea illumination analyi will be helpful fo futue acquiition dein. Fiue how the depth location of a ivenn taet hoizon. We eneated two diffeent acquiition ytem fo tetin (the apetue ize fo thee two ytem ae the ame but the hot ae located on diffeent ide of the apetue). Fiue 7 and ae the DI and ADR map fo Acquiition on the taet hoizon. Fiue 9 i the totall ADR. Fiue and ae anle domain ADR and total ADR map on the taet hoizon fo Acquiition. Fom thee eult, we can ee that the illuminated aea ae diffeent fo diffeent acquiition ytem. A a eult, we can ue the illumination eult a a uide when we dein cetain acquiition eometie to illuminate cetain taet aea. Afte we do the miation, 3 SEG DOI SEG Houton 3 Annual Meetin Pae 93

4 Anle domain illumination analyi alon a taet hoizon Downloaded /9/3 to Reditibution ubject to SEG licene o copyiht; ee Tem of Ue at we can alo ue thee map to compenate fo the imae amplitude alon the taet hoizon. Fiue 7: DI map fo the taet hoizon. The incident anle fo thee thee DI map ae (, ), (, ) and (, ). Fiue : ADR map on the taet hoizon. The incident anle fo thee thee DI map ae (, ), (, ) and (, ). Fiue 9: Total ADR on the taet hoizon.. x x x x 7 Fiue : ADR map on the taet hoizon. The incident anle fo thee thee DI map ae (, ), (, ) and (, ). Concluion Fiue : Total ADR on the taet hoizon We developed an efficient method of anle domain illumination analyi alon a taet hoizon. The DI and ADR map on the taet hoizon can be vey ueful fo acquiition dein and fo the intepete when the imae amplitude i uneliable on the hoizon. Numeical example of the 3D SEG/EAGE alt model and a field data model illutated the validity and efficiency of the new cheme. Fo futhe wok, we may develop an amplitude compenation method to eneate AVO fiendly anle athe. Acknowledement x We thank TGS fo the pemiion to publih thi wok. We alo thank Zhimin Li, Jean Ji, Ioan Vlad, Yan He, and Xian Xiao fo helpful dicuion, and Lauie Geie and Chuck Maon fo eviewin thi pape. x x x 7 3 SEG DOI SEG Houton 3 Annual Meetin Pae 9

5 Downloaded /9/3 to Reditibution ubject to SEG licene o copyiht; ee Tem of Ue at EDITED REFERENCES Note: Thi efeence lit i a copy-edited veion of the efeence lit ubmitted by the autho. Refeence lit fo the 3 SEG Technical Poam Expanded Abtact have been copy edited o that efeence povided with the online metadata fo each pape will achieve a hih deee of linkin to cited ouce that appea on the Web. REFERENCES Bea, G., C.-P. Lu, R. Lu, D. Willen, and I. Waton,, The contuction of ubuface illumination and amplitude map via ay tacin: The Leadin Ede, 9, 7 7, Cao, J., and R.-S. Wu, 9, Full-wave diectional illumination analyi in the fequency domain: Geophyic, 7, no., S S93, Jin, S., and S. Xu,, Viibility analyi fo taet-oiented evee time miation and optimizin acquiition paamete: The Leadin Ede, 9, , Lecomte, I.,, Illumination, eolution, and incidence-anle in PSDM: A tutoial: 7th Annual Intenational Meetin, SEG, Expanded Abtact,. Mao, J., and R.-S. Wu, 7, Illumination analyi uin local exponential beamlet: 77th Annual Intenational Meetin, SEG, Expanded Abtact, Mao, J., R.-S. Wu, and J.-H. Gao,, Diectional illumination analyi uin the local exponential fame: Geophyic, 7, no., S3 S7, Rickett, J. E., 3, Illumination-baed nomalization fo wave-equation depth miation: Geophyic,, , Wu, R.-S., and L. Chen,, Diectional illumination analyi uin beamlet decompoition and popaation: Geophyic, 7, no., S7 S9, Xie, X.-B., S. Jin, and R.-S. Wu,, Wave-equation-baed eimic illumination analyi: Geophyic, 7, no., S9 S77, 3 SEG DOI SEG Houton 3 Annual Meetin Pae 9