Anisotropy Estimation and Image Remapping Using Model Based Moveout

Transcription

1 Aniotropy Etiation and Iae Reappin Uin Model Baed Moveout Z. Liu* (PGS), N.D. Whitore (PGS) & C. Zhou (PGS) SUMMARY Typically odel paraeter etiation i achieved throuh ultiple iteration of linearized tooraphy and depth iration. In thi paper we dicu a ethod to reduce the iration effort by applyin local approiation to the iain and odellin operator uin a odel baed oveout, which i a appin between iaed pecular reflection in initial and updated odel. Thi allow for very efficient iain and odel tetin, o that ultiple iteration of iain and linearized tooraphy or eneralized iterative inverion can be applied. The odel baed oveout and tooraphy i deontrated for aniotropic inverion in the cae of known uburface control, where the vertical velocity i known and the tak i to etiate the aniotropic Thoen paraeter for VTI edia. The ethod require an iterative joint inverion of thee paraeter by projectin reidual depth error onto odel update.

2 Introduction Iain in aniotropic edia brin not only the challene of ore advanced iain alorith, but alo the burden of etiatin the odel paraeter required for the iain proce. Typically odel paraeter etiation i achieved throuh ultiple iteration of linearized tooraphy and depth iration. In thi paper we dicu a ethod to reduce the reiration effort by applyin local approiation to the iain and odellin operator uin a odel baed oveout, which i a appin between iaed pecular reflection in initial and updated odel. Thi allow for very efficient iain and odel tetin, o that ultiple iteration of iain and linearized tooraphy or eneralized iterative inverion can be applied. The odel baed oveout ue travel tie and ray paraeter inforation for reappin and can be ued a an event deiration-reiration and can alo do pecular re-appin of the iae. Unfortunately, it i typically not poible to reolve all of the odel paraeter (velocity, aniotropy) uin urface data alone. We require a priori inforation to reduce the null pace of the inverion. Thi prior inforation can be in the for of educated uein or interpretation or inforation coin fro uburface control uch a well lo, check hot urvey, and vertical or offet VSP. In thi paper we how an eaple coparin a odel baed oveout of the iae in a tartin and updated odel to actual Kirchhoff depth iration of the updated odel. We alo dicu aniotropic inverion in the cae of known uburface control, where the vertical velocity i known and the tak i to etiate the aniotropic Thoen paraeter for VTI edia. The ethod require an iterative joint inverion of thee paraeter by projectin reidual depth error onto odel update. Becaue the odel baed oveout i relatively fat relative to reiration, a lare nuber of odel can be teted and thu tooraphic update can be achieved efficiently at control location (e.. well location). Updated odel away fro control location can then be approiated by interpolation or etrapolation, followed by a full 3D tooraphic inverion. Method Model Baed Moveout Miration operator ap urface tie data onto uburface iae and can produce offet (or anle) dependent ather by decopoition of the data into eparate input or output ubet. For eaple, in Kirchhoff iration, the output iae i coputed by a urface interal of the input data of the for: 2 (, ) d ξa(, ξ ) U (,, t (, ) t (, )) (1) t where t (, ) and t (, ) are the travel tie fro the ource to iae point and the iae point to the receiver for a odel. Thi interal define an aplitude and phae appin fro the urface data due to ource and receiver location and to all pecular reflection point. S At a pecific pecular point y two ray path connect thi point with the urface location. After the iration of the data with a new velocity odel, then thi pecular reflection point y would ove to a new point y 1 with new ray path connectin urface location a hown in Fiure 1. If the uburface dip and openin anle i known (a in anle ather) or are coputed (a in offet ather), then an approiation to the reiration of the data can be achieved by the followin procein: 1. Kineatic deiration (reappin): for odel and iae point y, copute travel tie and eerent ray paraeter { t (, y), p( } and { t (, p( } and etract data ( y, ), 2. Kineatic reiration (reappin): for odel +1 fro urface point and copute new pecular point at y 1 reap the data ( y, ) to ( y 1, 1)

3 We define the appin M : ( y, ) ( y 1, 1) a odel baed oveout (MMO). Ideally, we would want to ap all uburface point for odel, to new uburface point for odel +1. However, in practice to perfor tooraphic inverion it i ufficient to only ap elected uburface poition (aain note Fiure 1.) In oe cae, (e.. all uburface dip) the MMO i iply ipleented a a ray-traced baed revere and forward oveout procedure, where offet (or anle ather) are apped fro depth ather to tie ather for odel and then reapped to depth ather for odel +1. The baic workflow i hown in ee Fiure 2. Fiure 1 The left how the pecular point fro a iration for a iven odel. The riht how the repoitionin of the pecular point in a new odel copared with the old odel. Thi repoitionin can be achieved by reiration of the data or by approiated by local deiration reiration. Fiure 2 Model baed oveout data appin of ather: Depth ather fro the firt iration are apped fro (offet,depth) to (offet,tie) uin a local pecular deiration of odel, then apped fro (offet,tie) to (offet,depth) uin a local pecular re-iration uin odel +1. Eaple 1 Coparion of Model Baed Moveout and New Miration of Data A coparion between reiration of data and odel baed a local MMO i hown in Fiure 3. The top et of ather (Fiure 3a) i a et of Kirchhoff baed coon offet ather for an initial odel for data in 1 k water depth. The odel wa then updated and then teted by uin MMO to the data reappin the iaed data fro the old odel to the new odel a hown in Fiure 3b. The data wa alo fully irated with the Kirchhoff depth iration for the new odel o that it could be directly copared to the MMO ather, a hown in Fiure 3c. A can be een the MMO and Kirchhoff econd iration are the ae, which i key for uin the MMO a an approiation to iration uin a new odel.

4 3(a) Kirchhoff Offet Gather - tartin odel 3(b) MMO Offet Gather - updated odel 3(c) Kirchhoff Offet Gather - updated odel Fiure 3 Coparion of odel baed oveout to a full depth iration (3a) how an initial Kirchhoff depth iration.; (3b) i the odel baed oveout (MMO) for an updated odel; (3c) i the Kirchhoff iration of the ae updated odel. Note the MMO and the full reiration ather are very iilar and thu MMO approiate a new iration with uch le coputational effort. Eaple 2 Tooraphic updatin for VTI aniotropic etiation near a well. Whether ipleented lobally in 3D via a ray-traced iration or locally via a locally ray-traced iain procedure, MMO provide a very efficient ean of tetin, and conequently, updatin velocity odelwithout the cot of a full reiration. It hould alo be noted that the MMO proce can ued in local odel updatin by applyin the deiration-reiration below datu above which the velocity odel ha been deterined. One application of MMO i to etiate aniotropy paraeter in a vicinity of a well. To deontrate thi we apply thi to a ynthetic dataet (upplied by BP) where we aue a known vertical velocity and etiate the Thoen paraeter and uin joint tooraphic inverion (Zhu, et al. 2011). The proce involve the followin tep: 1. A full pretack depth iration to iae the data with a tartin odel (in thi cae the tartin odel wa aniotropic with. 005 and. 01below the water botto) 2. Pick reidual depth error, copute ray and travel tie, ap the reidual depth error onto travel tie error and olve a linearized joint tooraphy yte to iultaneouly update and to obtain an updated odel. 3. Ue MMO to reap all of the picked event fro the old odel to the new odel, ivin new reidual for the new odel. (Note that no repickin of the data reidual i neceary.) Uin thee newly apped reidual, repeat the joint tooraphy proce and create new update for and. 4. Repeat tep 3 until the reidual error have been reduced to a iniu (or an acceptable level). 5. Apply the full data MMO or a full reiration and then return to tep 2 if neceary.

5 The odel data fro BP wa a full TTI 2D data, where we elected a location that wa in the VTI portion of the odel. To iulate an idealized well ituation, the vertical velocity wa aued to be known. The data wa irated with a Kirchhoff depth iration uin an initial odel with. 05 and. 01 below the water botto. The ather were autoatically picked and a et of tooraphy iteration were perfored. Both the depth ather and the reidual error pick were autoatically reapped uin the MMO for each iteration (no re-pickin wa required). The depth error pick were ued a input to each joint tooraphy iteration. The tartin offet ather and the three iteration of the MMO are hown in the left hand part of Fiure 4. The aniotropy paraeter for the true odel (red) and the third iteration etiate (blue) are hown in the center. The third iteration MMO ather and the true Kirchhoff depth iration ather are diplayed on the riht hand ide. After three iteration the reularized tooraphy produce a ood etiate of the aniotropy paraeter to a depth of 8 k. The accuracy of the pickin and the availability of reaonably lon offet (10 k) aited in obtainin accurate and etiate. (4a) (4b) (4c) (4d) (4e) (4f) (4) (4h) 0 k 2 k 10k Fiure 4 Aniotropic paraeter etiation with vertical velocitie iven fro well control. Gather and event pick for a tartin odel are in (4a). Shown in (4b) (4d) are odel baed oveout (MMO) ather and reapped reidual error pick for three joint tooraphy odel update. The final etiate (blue) and true (red) value of delta and epilon are hown in (4e) and (4f ) repectively. The final MMO ather and Kirchhoff iration for the true odel are hown in (4) and (4h) repectively. Concluion A odel baed oveout (MMO) procedure i defined a reappin of the pecular reflection of iaed data to new poition in a new odel a an approiation to a full iration of the data. In oe cae, the full data a well a event pick can be reapped, allowin for an autoated reiain and tooraphic updatin proce, which doe not require full reiration at each iteration, nor doe it require new reidual to be picked for each iteration. Only ray tracin, equation etup and inverion are required per iteration. A ueful application of thi technoloy i in the etiation of aniotropy in the vicinity of well control. The reappin of the reidual in the MMO i locally equivalent to ap deiration-reiration for ue in 3D tooraphy. Acknowleeent We thank PGS for ivin periion to ive thi preentation and BP for the ynthetic odel data. Reference Zhou, C., Jiao, J., Lin, S., Sherwood, J. and Brandber-Dahl, S. [2011] Multiparaeter joint tooraphy for TTI odel buildin. Geophyic, 76(5), WB183-WB k 4 k 5 k 6 k 7 k 8 k