Benefits & Limitations of Least Squares Migration W.Dai,D.Zhang,X.Wang,GTSKAUST RTM Least Squares RTM GOM RTM GOM LSRTM

Can We Improve Quality Seismic Can We Improve Quality SeismicImaging? Better Velocity Updates: FWI & MVA Better Quality Images: LSM & Multiples

Outline 1.Theory: Multisource LSM 2.Examples: Synthetic & Field Data 3.Summary

Standard Migration vs Multisource Migration Benefit: Reduced computation and memory Liability: Crosstalk noise … Given: d 1 and d 2 Find: m Soln: m=L 1 d 1 + L 2 d 2 TT Given: d 1 + d 2 Find: m = L 1 d 1 + L 2 d 2 TT + L 1 d 2 + L 2 d 1 TT Soln: m = (L 1 + L 2 )(d 1 +d 2 ) T Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)

K=1 K=10 Multisource LSM & FWI Inverse problem: || d – L m || 2 ~~ 1 2 J = arg min m  misfit m (k+1) = m (k) +  L  ~T~T Iterative update: + L 1 d 2 + L 2 d 1 TT L 1 d 1 + L 2 d 2 TT

Brief Early History Multisource Phase Encoded Imaging Romero, Ghiglia, Ober, & Morton, Geophysics, (2000) Krebs, Anderson, Hinkley, Neelamani, Lee, Baumstein, Lacasse, SEG Zhan+GTS, (2009) Virieux and Operto, EAGE, (2009) Dai, and GTS, SEG, (2009) Migration Waveform Inversion and Least Squares Migration Biondi, SEG, (2009)

Outline 1.Theory: Multisource LSM 2.Examples: 2D Marmousi Data 3.Summary

X (km) 0 Z (km) 1.48 a) Original b) Standard Migration Migration Images Migration Images (input SNR = 10dB) X (km) c) Standard Migration with 1/8 subsampled shots 0 Z (km) X (km) d) 304 shots/gather 26 iterations 304 shots in total an example shot and its aperture (Huang and Schuster, 2011, Multisource Least-squares Migration of Marine Streamer with Frequency-division Encoding ) Shots per supergather gain Computational gain Conventional migration: SNR=30dB

Shots per supergather gain Computational gain Conventional migration: Sensitivity to input noise level SNR=10dB SNR=30dB SNR=20dB

Outline 1.Theory: Multisource LSM 2.Examples: 3D SEG Salt 3.Summary

a swath swaths, 50% overlap 16 cables 100 m 6 6 km m sources 20 m 4096 sources in total SEG/EAGE Model+Marine Data (Yunsong Huang) 13.4 km 3.7 km

Numerical Results (Yunsong Huang) 6.7 km True reflectivities 3.7 km Conventional migration 13.4 km shots/super-gather, 16 iterations 8 x gain in computational efficiency 3.7 km

Outline 1.Theory: Multisource LSM 2.Examples: 2D GOM Data LSRTM 3.Summary

Plane-wave LSRTM of 2D GOM Data 0X (km) 16 0 Z (km) km/s Model size: 16 x 2.5 km.Source freq: 25 hz Shots: 515Cable: 6km Receivers: 480

0X (km) 16 0 Z (km) 2.5 Conventional GOM RTM (cost: 1) (Wei Dai) Z (km) 2.5 Plane-wave RTM (cost: 0.2) Plane-wave LSRTM (cost: 12) Encoded Plane-wave LSRTM (cost: 0.4) 0

0X (km) 16 0 Z (km) 2.5 Z (km) 2.5 Plane-wave RTM (cost: 0.2) Plane-wave LSRTM (cost: 12) Encoded Plane-wave LSRTM (cost: 0.4) 0 RTM LSM Conventional GOM RTM (cost: 1) (Wei Dai)

Outline 1.Theory: Multisource LSM 2.Examples: 2D GOM Data LSRTM 3.Summary 1.Theory: Multisource LSM 2.Examples: 2D GOM Data KLSM 3.Summary

1.5 Z (km) X (km) Z (km) 0.9 Multisource Least-squares Migration Image (>10X) Kirchhoff Migration Image (1X) K M KLS M (X. Wang)

Alias and Gap Data GOM data, aliased source and gap between 9.5 km and 10 km Model Size: 3407 X 401 Interval: 6.25 m # of shots: 248, ds = 75 m # of receiver: 480, dg = 12.5 m Streamer length: 6 km Record length: s, dt=2ms # 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 wave is generated from stacking near offset ocean bottom reflections.

Plane-wave LSRTM of 2D GOM Data 0X (km) 16 0 Z (km) km/s Model size: 16 x 2.5 km.Source freq: 25 hz Shots: 515Cable: 6km Receivers: 480 Mute 0.5 km data

KM VS LSM VS MSLSM KM image

KM VS LSM VS MSLSM LSM Image after 30 Iterations

KM VS LSM VS MSLSM MSLSM Image after 30 Iterations

Outline 1.Theory: Multisource LSM 2.Examples: 2D Salt Body with Multiples 3.Summary

X (km) 16 Z (km) RTM SEG Salt Data (Dongliang Zhang) Z (km) LSRTM with Born Multiples st -order Multiples

X (km) 16 Z (km) RTM SEG Salt Data (Dongliang Zhang) Z (km) LSRTM with Born Multiples LSRTM RTM

X (km) 30 Z (km) GOM Salt Data (Dongliang Zhang) Z (km) RTM with Multiples

X (km) 30 Z (km) Starting Velocity Model Z (km) FWI (Abdullah AlTheyab)

What have we Empirically Learned about Quality? 1.LSM no better than RTM if inaccurate v(x,y,z) 3. Speckle noise in LSM 4. Multiples can be significantly enhanced if separated properly from primaries properly from primaries 5. FWI works for easy GOM data, not for hard salt 6. FWI & LSM quality degrades below 2 km? 7. Why? Unaccounted Physics? 1). Attenuation, 2). V(x,y,z), 3). ??? 2). V(x,y,z), 3). ??? 2. Cost MLSM ~ RTM; MLSM better resolution

0 Z (km) X (km) True Reflectivity Acoustic LSRTM 0 X (km) 2 Viscoelastic LSRTM Z (km) X (km) 2 Q Model Q=20 Q=20000

IO 1 ~1/36 Cost Resolution dx 1 ~double Migration SNR Stnd. Mig Multsrc. LSM Stnd. Mig Multsrc. LSM ~1 1 ~ 0.1 Cost vs Quality: Can I<<S? Yes. What have we empirically learned about MLSM? 1