Multisource Least-squares Migration of Marine Data Xin Wang & Gerard Schuster Nov 7, 2012

Outline Motivation Gain high quality image by least-squares migration Improve the efficiency by multisource technique Theory Multisource Kirchhoff migration Multisource least-squares migration Numerical Tests Synthetic data test Marine data test Conclusion

Motivation of LSM KM ImageLeast-squares Migration Image 3.4 Z (km) 0 0 X (km) 14 Advantages of LSM compared to KM: Decrease artifacts, balance amplitudes, increase resolution, natural anti- alias and anti-gap filter (Nemeth,1999). Drawbacks of LSM High computational, IO and memory cost.

Motivation of MLSM Problems of LSM High computational, IO and memory cost. Solution: Multisource phase-encoding technique. Multisource KM Image Multisource LSM Image Multisource -> Crosstalk MLSM To:  Increase efficiency  Remove artifacts  Suppress crosstalk

Outline Motivation Gain high quality image by least-squares migration Improve the efficiency by multisource technique Theory Multisource Kirchhoff migration Multisource least-squares migration Numerical Tests Synthetic data test Marine data test Conclusion

Generate Supergather Data Time (s) 0 Depth (km) CSG 1 CSG 2 Encoding shift 1 s d1d1 shift － 0.5 s P1P1 P2P2 Time (s) 0 Supergather d + =

Decoding Time (s) 0 Supergather Time (s) 0 Depth (km) CSG 1 CSG 2 Decoding shift -1 s dd P1TP1T P2TP2T shift 0.5 s ->+

Multisource Migration Time (s) 0 Depth (km) CSG 1 CSG 2 migration artifacts crosstalk noise L1TP1Td1L1TP1Td1 L2TP2Td2L2TP2Td2 L1TP1Td2L1TP1Td2 L2TP2Td1L2TP2Td1

Multisource Least-squares Migration L = N 1 L 1 + N 2 L 2 & d = N 1 d 1 + N 2 d 2 Find: m s.t. min || Lm – d || 2 Given: Lm = d Solution: m = [ L T L ] -1 L T d Solution: m = [ L T L ] -1 L T d m (k+1) = m (k) – a L T ( Lm – d ) or if L is too big = m (k) – a ( L 1 T ( L 1 m – d 1 ) + L 2 T ( L 2 m – d 2 ) = m (k) – a ( L 1 T ( L 1 m – d 1 ) + L 2 T ( L 2 m – d 2 ) + L 2 T N 2 T N 1 (L 1 m – d 1 ) + L 1 T N 1 T N 2 ( L 2 m – d 2 ) ) Crosstalk

Workflow Modeling supergather d = L m (k) calculate data residual d - d obs calculate gradient L T (d – d obs ) calculate analytical step length calculate numerical step length Update reflectivity m (k+1) and refresh d obs LSM MLSM Save IO and memory cost d obs More IO save Applicable to GPU

Outline Motivation Gain high quality image by least-squares migration Improve the efficiency by multisource technique Theory Multisource Kirchhoff migration Multisource least-squares migration Numerical Tests Synthetic data test Marine data test Conclusion

Numerical Results Marmousi2 # of shots: 192, ds = 60 m # of receiver: 120, dg = 20 m Streamer length: 2.4 km # of supergather: 16 # of shots in supergather: Z (km) 0 Velocity Model 0 X （ km) km/s Synthetic data are generated with FD solution to acoustic wave-equation.

KM vs LSM KM Image LSM Image, 15 Iterations 3.4 Z (km) 0 0 X （ km) Z (km) 0 0 X （ km) 14

KM vs LSM (zoom view) Zoom view of red box 6 X (km) 7 Velocity Model 6 X (km) 7 KM Image 1.2 Z (km) 0.6 Reflectivity Model LSM Image, 15 Iterations KM LSM True

KM vs LSM (zoom view) Zoom view of blue box 5.2 X (km) 7.2 Velocity Model 5.2 X (km) 7.2 KM Image 2.6 Z (km) 2.2 Reflectivity Model LSM Image, 15 Iterations

MLSM (static and hybrid encoding) 3.4 Z (km) 0 MLSM Image, Static Encoding, 15 Iterations 0 X (km) 14 MLSM Image, Hybrid Encoding, 15 Iterations Static encoding: Same N for all iterations. Hybrid encoding: Change N for every 5 iterations. 3.4 Z (km) 0 0 X (km) 14

MLSM Image, Dynamic Encoding, 15 Iterations LSM Image, 15 Iterations MLSM (dynamic encoding) vs LSM Dynamic encoding: Change N for every iteration. 3.4 Z (km) 0 0 X (km) Z (km) 0 0 X (km) 14

MSLSM (dynamic encoding) vs LSM Zoom view of red box 6 X (km) Z (km) 0.6 LSM Image, 15 Iters MLSM Image, Static, 15 Iters MLSM Image, Hybrid, 15 Iters MLSM Image, Dynamic, 15 Iters

MLSM (dynamic encoding) vs LSM Zoom view of blue box 5.2 X (km) Z (km) 2.2 LSM Image, 15 Iters MLSM Image, Static, 15 Iters MSLSM Image, Hybrid, 15 Iters MLSM Image, Dynamic, 15 Iters

Comparison of CPU and IO Cost Image quality CPU costIO cost KM ★★ 11 LSM ★★★★★ 30 MLSM (dynamic) ★★★★ MLSM (hybrid) ★★★ MLSM (static) ★★ Assumption: conventional data cannot be stored in memory, but supergather data are small enough to be kept in the memory. MLSM (dynamic) ★★★★

Marine Data # of shots: 496, ds = 37.5 m # of receiver: 480, dg = 12.5 m Streamer length: 6 km # of shots in supergather: Z (km) 0 Velocity Model 0 X （ km) km/s Velocity model is from FWI. (Boonyasiriwat et al., 2010) A Hz bandpass filter is applied. # of supergather: 32 Source wavelet is generated from stacking near offset ocean bottom reflections.

Marine Data Test 1.88 Z (km) 0.6 KM Image 5 X （ km) 13.8

Marine Data Test RTM Image 1.88 Z (km) X （ km) 13.8

Marine Data Test LSM image, 30 iterations 1.88 Z (km) X （ km) 13.8

Marine Data Test MLSM image, dynamic encoding, 50 iterations 1.88 Z (km) X （ km) 13.8

KM vs RTM vs LSM vs MSLSM Zoom view of red box 10.5 X (km) Z (km) 0.9 KM Image RTM Image LSM Image, 20 Iters MLSM Image, Dynamic, 20 Iters

KM vs RTM vs LSM vs MLSM 10.5 X (km) Z (km) 0.9 KM Image

10.5 X (km) Z (km) 0.9 KM vs RTM vs LSM vs MLSM RTM Image

10.5 X (km) Z (km) 0.9 KM vs RTM vs LSM vs MLSM MLSM Image, Dynamic, 20 Iterations

Outline Motivation Gain high quality image by least-squares migration Improve the efficiency by multisource technique Theory Multisource Kirchhoff migration Multisource least-squares migration Numerical Tests Synthetic data test Marine data test Conclusion

MLSM can improve image quality over conventional Migration. MLSM can improve the efficiency, and save IO cost.  Dynamic MLSM reduces IO cost to 1/30.  Wave equation based migration method can save the computational cost. KM ImageMLSM Image

Acknowledgement We thank for the 2011 CSIM sponsors for their financial support.