1 / 35

Theory of Multisource Crosstalk Reduction by Phase-Encoded Statics

Theory of Multisource Crosstalk Reduction by Phase-Encoded Statics. G. Schuster, X. Wang, Y. Huang, C. Boonyasiriwat King Abdullah University Science & Technology. Outline. Seismic Experiment:. L m = d. 1. 1. L m = d. 2. 2. L m = d. N. N.

varden
Download Presentation

Theory of Multisource Crosstalk Reduction by Phase-Encoded Statics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Theory of Multisource Crosstalk Reduction by Phase-Encoded Statics G. Schuster, X. Wang, Y. Huang, C. Boonyasiriwat King Abdullah University Science & Technology

  2. Outline Seismic Experiment: Lm = d 1 1 Lm = d 2 2 Lm = d . . N N . 2. Standard vs Phase Encoded Least Squares Soln. L d 3. Theory Noise Reduction ]m = [N d + N d ] vs [ N L + N L 1 1 m = L d 2 2 2 2 1 1 1 1 2 2 4. Summmary and Road Ahead

  3. Gulf of Mexico Seismic Survey 4 d Predicted data Observed data 1 Goal: Solve overdetermined System of equations for m Time (s) Lm = d 1 1 Problem: Expensive, one migration/shot gather 0 Lm = d 6 X (km) 2 2 Solution:Supergather migration Lm = d . . N N . m

  4. Seismic Inverse Problem 2 Soln: min || Lm-d || migration waveform inversion -1 T T m = [L L] L d T L d Given: d= Lm Find: m(x,y,z)

  5. Computational Challenges -1 T T m = [L L] L d Given: d= Lm Find: d > 10 13 words 7 m > 10 3 20x20x10 km unknown velocity values 4 dx=1 m # time steps ~ 10 4 # shots > 10 Total = 15 10

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

  7. Outline Seismic Experiment: Lm = d 1 1 Lm = d 2 2 Lm = d . . N N . 2. Standard vs Phase Encoded Least Squares Soln. L d 3. Theory Noise Reduction ]m = [N d + N d ] vs [ N L + N L 1 1 m = L d 2 2 2 2 1 1 1 1 2 2 4. Summmary and Road Ahead

  8. Conventional Least Squares Solution: L= & d = L d 1 1 L d Given: Lm=d 2 2 In general, huge dimension matrix Find: m s.t. min||Lm-d|| 2 Solution: m = [L L] L d -1 T T or if L is too big m = m – aL (Lm - d) (k+1) (k) (k) T (k) = m – aL (L m - d ) (k) (k) [ ] T + L (L m - d ) T 1 1 1 2 2 2 Note: subscripts agree Problem: L is too big for IO bound hardware

  9. Conventional Least Squares Solution: L= & d = L d 1 1 L d Given: Lm=d 2 2 In general, huge dimension matrix Find: m s.t. min||Lm-d|| 2 Solution: m = [L L] L d -1 T T m = m – aL (Lm - d) (k+1) (k) (k) T (k) = m – aL (L m - d ) (k) (k) [ ] T + L (L m - d ) T 1 1 1 2 2 2 Problem: Expensive, FD solve/CSG Solution: Blend+encode Data Problem: L is too big for IO bound hardware

  10. Blending+Phase Encoding Blending Blending Phase Phase 1 d d d Lm= Lm= Lm= 1 1 3 2 2 3 Encoded supergather O(1/S) cost! Encoding Matrix d = N d + N d + N d in w domain 1 1 2 3 2 3 Encoded supergather modeler L = NL + N L + NL m [ ]m 1 2 3 1 2 3 e iwt

  11. Blended Phase-Encoded Least Squares Solution L =&d = N d + N d N L + N L 1 2 1 1 1 2 2 2 Given: Lm=d In general, SMALL dimension matrix Find: m s.t. min||Lm-d|| 2 Solution: m = [LL] Ld -1 T T or if L is too big m = m – aL (Lm - d) T (k+1) (k+1) (k) (k) (k) (k) (k) = m – aL (L m - d ) (k) (k) (k) (k) [ (k) (k) ] (k) (k) T + L (L m - d ) T (k) Iterations are proxy For ensemble averaging 1 1 1 2 2 2 + Crosstalk * * (k) + L N N (L m - d ) (k) (k) (k) (k) (k) (k) T L N N (L m - d ) (k) T + (k) (k) (k) (k) 2 1 2 1 1 1 2 2 2 1

  12. Outline Seismic Experiment: Lm = d 1 1 Lm = d 2 2 Lm = d . . N N . 2. Standard vs Phase Encoded Least Squares Soln. L d 3. Theory Noise Reduction ]m = [N d + N d ] vs [ N L + N L 1 1 m = L d 2 2 2 2 1 1 1 1 2 2 4. Summary

  13. Ensemble Average of Crosstalk Term With Random Time Shifts e -iwt 2 + Crosstalk: Noise = e e e iw(t - t ) iwt <Noise>: < > -iwt < > = < > 1 1 2 2 Gaussian PDF 2 e iw(t - t ) -.25 s (t - t ) e = 1 2 1 2 -2 2 Crosstalk term decreases with increasing w and s -s w e ~ dtdt 1 2 * * * L N N (L m - d ) N N T L N N (L m - d ) T 1 1 2 1 2 1 1 1 2 2 2 2 1

  14. Crosstalk Prediction Formula ~ X = O( ) 2 2 e -s w Pt. Scatt. Stand. Mig. Pt. Scatt.. Mig. of Supergathers. Depth s = .01 s X Offset Pt. Scatt.. Mig. of Supergathers. Pt. Scatt.. Mig. of Supergathers. s = .05 s s = .1 s .01 1.0 s L (L m - d ) + L (L m - d ) T T 2 1 1 2 1 2

  15. sgn(t ) Ensemble Average of Crosstalk Term With Random Polarity sgn(t) + Crosstalk: Noise < > = < > sgn(t ) sgn(t ) <Noise>: = 0 1 2 Conclusion: Random polarity better than random time shifts Further Analysis: Variance of the crosstalk noise says that random polarity & random time shifts has ½ less than variance of polarity alone ( ) 2 < > * * * * L N N (L m - d ) N N N N T L N N (L m - d ) T 1 1 1 2 1 2 1 1 1 2 2 2 2 2 1

  16. Dt < +/- < +/-, Dt < +/-, Dt, Dx Key Theory+Num. Results for 320 CSG Supergather (Xin Wang, Yunsong Huang) Time Statics Polarity Polarity+Time Statics Polarity+Time Statics+Location Statics b) Time static σ = 0.1 s c) Noise a) Standard migration (320 CSG) a) Polarity b) Noise 0.4 0.4 0.18 0.4 0.4 0.4 Z (km) Z (km) Z (km) Z (km) Z (km) SNR 1.48 1.48 1.48 1.48 1.48 0 Time static σ (s) X (km) X (km) X (km) X (km) X (km) 6.75 6.75 6.75 6.75 6.75 0.1 0.01 0 0 0 0 0 e) Noise f) SNR d) Source polarity & static Polarity and time static polarity Time static

  17. Key Results Theory of Multisource Imaging of Encoded Supergathers(Xin Wang) Sig/Noise = GI < GIN b) Image of 5 stacks a) Image of 1 stack 0 # geophones/supergather # subsupergatherss Z (km) # iterations 0 0 Z (km) Z (km) 1.5 X (km) X (km) 6.75 6.7 X (km) 0 0 0 6.7 d) SNR vs Iterations c) Image of 50 stacks 1.5 1.5 10 Prediction Bulk shift SNR Observed 1 115 1 Iteration Number

  18. ~ ~ 1 GS G GI [s(t) +n(t) ] S S Standard Migration SNR Zero-mean white noise Assume: d(t) = Standard Migration SNR Neglect geometric spreading . . . . GS . . Cost ~ O(S) # CSGs . . . . . . # geophones/CSG Iterative Multisrc. Mig. SNR Cost ~ O(I) Standard Migration SNR SNR= migrate # iterations . migrate stack migrate iterate . SNR= . . . migrate SNR= . . . . .

  19. Outline Seismic Experiment: Lm = d 1 1 Lm = d 2 2 Lm = d . . N N . 2. Standard vs Phase Encoded Least Squares Soln. L d 3. Theory Noise Reduction ]m = [N d + N d ] vs [ N L + N L 1 1 m = L d 2 2 2 2 1 1 1 1 2 2 4. Summary

  20. 3. Summary ]m = [N d + N d ] N L + N L [ L d 2 2 2 2 1 1 1 1 1 1 m = L d vs O( ) 2 2 Dt < +/- < +/-, Dt < +/-, Dt, Dx GI GS 2 2 e -s w 1. ~ < > Time Statics Polarity Polarity+Time Statics Polarity+Time Statics+Location Statics 2. SNR: VS 4. Passive Seismic Interferometry = Multisrc Imaging L (L m - d ) + L (L m - d ) T T 2 1 1 2 1 2

  21. Summary L d 1 1 m = ]m = [N d + N d ] N L + N L [ L d 2 2 2 2 1 1 1 1 2 2 Stnd. MigMultsrc. LSM IO 1 1/320 1 <1/10 Cost ~ Less 1 1 SNR~ Resolution dx 1 1 Cost vs Quality

  22. The SNR of MLSM image grows as the square root of the number of iterations. 7 GI SNR = SNR 0 300 1 Number of Iterations

  23. Dt < +/- < +/-, Dt < +/-, Dt, Dx Key Theory+Num. Results for 320 CSG Supergather (Xin Wang, Yunsong Huang) Time Statics Polarity Polarity+Time Statics Polarity+Time Statics+Location Statics b) Time static σ = 0.1 s c) Noise a) Standard migration (320 CSG) a) Polarity b) Noise 0.4 0.4 0.18 0.4 0.4 0.4 Z (km) Z (km) Z (km) Z (km) Z (km) SNR 1.48 1.48 1.48 1.48 1.48 0 Time static σ (s) X (km) X (km) X (km) X (km) X (km) 6.75 6.75 6.75 6.75 6.75 0.1 0.01 0 0 0 0 0 e) Noise f) SNR d) Source polarity & static Polarity and time static polarity Time static

  24. Key Results Theory of Multisource Imaging of Encoded Supergathers(Xin Wang) Sig/Noise = GI < GIN b) Image of 5 stacks a) Image of 1 stack 0 # geophones/supergather # subsupergatherss Z (km) # iterations 0 0 Z (km) Z (km) 1.5 X (km) X (km) 6.75 6.7 X (km) 0 0 0 6.7 d) SNR vs Iterations c) Image of 50 stacks 1.5 1.5 10 Prediction SNR Observed 1 115 1 Iteration Number

  25. Key Results Theory of Multisource Imaging of Encoded Supergathers(Boonyasiriwat) Sig/Noise = GI < GIN # geophones/supergather # subsupergatherss # iterations Dynamic Polarity Tomogram (1089 CSGs/supergather) 3.5 km 1/300 1/1000 Dynamic QMC Tomogram (99 CSGs/supergather)

  26. Ld +L d 1 2 2 1 = L d +L d + =[L +L ](d + d ) 1 2 1 2 1 1 2 2 d +d =[L +L ]m 1 2 1 2 mmig=LTd Multisource Migration: Multisource Phase Encoded Imaging { { L d Forward Model: T T T T T T m = m + (k+1) (k) Crosstalk noise Standard migration

  27. Dt < +/- < +/-, Dt < +/-, Dt, Dx Time Statics Polarity Polarity+Time Statics Polarity+Time Statics+Location Statics Dt < +/- < +/-, Dt < +/-, Dt, Dx Relative Merits of 4 Encoding Strategies Time Statics Polarity Polarity+Time Statics Polarity+Time Statics+Location Statics d d d Lm= Lm= Lm= 1 1 3 2 2 3 Supergather #1 Supergather #2 Supergather #3 Supergather #4 supergather

  28. Ld +L d 1 2 2 1 = L d +L d + =[L +L ](d + d ) 1 2 1 2 1 1 2 2 d +d =[L +L ]m 1 2 1 2 mmig=LTd Multisource Migration: Phase Encoded Multisource Migration { { d L Forward Model: mmig T T mmig T T T T + + Crosstalk noise mmig T T T T = L d +L d + Ld +Ld 1 2 2 1 1 1 2 2 mmig = L d +L d 1 1 2 2 Standard migration

  29. Ld +L d 1 2 2 1 = L d +L d + =[L +L ](d + d ) 1 2 1 2 1 1 2 2 d +d =[L +L ]m 1 2 1 2 mmig=LTd Multisource Migration: Phase Encoded MultisrceLeast Squares Migration { { L d Forward Model: mmig T T T T T T m = m + (k+1) (k) Crosstalk noise Standard migration

  30. Outline Seismic Experiment: Lm = d 1 1 Lm = d 2 2 Lm = d . . N N . 2. Standard vs Phase Encoded Least Squares Soln. L d 3. Theory Noise Reduction ]m = [N d + N d ] vs [ N L + N L 1 1 m = L d 2 2 2 2 1 1 1 1 2 2 4. Numerical Tests

  31. RTM & FWI Problem & Possible Soln. Problem: RTM & FWI computationally costly Solution: Multisource LSM & FWI Preconditioning speeds up by factor 2-3 LSM reduces crosstalk

  32. d +d =[L +L ]m 1 2 1 2 mmig=LTd Multisource Migration: Multisource Least Squares Migration { { L d Forward Model: Phase encoding Kirchhoff kernel Standard migration Crosstalk term

  33. Multisource Least Squares Migration Crosstalk term

  34. Conventional Least Squares Solution: L= & d = L d 1 1 L d Given: Lm=d 2 2 In general, huge dimension matrix Find: m s.t. min||Lm-d|| 2 Solution: m = [L L] L d -1 T T or if L is too big m = m – aL (Lm - d) (k+1) (k) (k) T (k) = m – aL (L m - d ) (k) [ ] T + L (L m - d ) T 1 1 1 2 2 2 Note: subscripts agree Problem: L is too big for IO bound hardware

  35. Key Results Theory of Multisource Imaging of Encoded Supergathers(Boonyasiriwat) Sig/Noise = GI < GIN # geophones/supergather # subsupergatherss # iterations Dynamic Polarity Tomogram (1089 CSGs/supergather) 3.5 km 1/300 1/1000 Dynamic QMC Tomogram (99 CSGs/supergather)

More Related