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Applications of Interferometry

Applications of Interferometry. VSP. VSP. SSP. A. B. A. B. A. B. x. x. x. VSP Multiple Interferometry. 3x3 Classification Matrix. SSP. VSP. SWP. SSP. SSP. SSP. SSP. VSP. SSP. SWP. VSP. VSP. SSP. VSP. VSP. VSP. SWP. SSP. SWP. SWP. SWP. VSP. SWP. SWP. Outline.

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Applications of Interferometry

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  1. Applications of Interferometry

  2. VSP VSP SSP A B A B A B x x x VSP Multiple Interferometry

  3. 3x3 Classification Matrix SSP VSP SWP SSP SSP SSP SSP VSP SSP SWP VSP VSP SSP VSP VSP VSP SWP SSP SWP SWP SWP VSP SWP SWP

  4. Outline • Background for Non-geo types • What is Seismic Interferometry? • Reciprocity Equation Correlation Type • Classification Matrix • Applications: VSP-SWP • Conclusions

  5. Theory VSP -> SSP

  6. n r = 2i Im[G(A|B)] 2 d x k Source line * * G(B|x) G(A|x) (4) = G(A|B) - G(B|A) Reciprocity Correlation Equation Given: VSP data G(A|x) Find: SSP data G(A|B) B A x

  7. o o S o S well S Reciprocity Correlation Equation Given: VSP data G(A|x) Find: SSP data G(A|B) A B x

  8. n { } * * * S + S + S - G(A|x) = G(A|B) - G(B|A) G(B|x) G(A|x) G(B|x) x o k o o o o G(A|x)* G(B|x) = Im[G(A|B)] well 2 d x S o S well S Reciprocity Correlation Equation Given: VSP data G(A|x) Find: SSP data G(A|B) A B x

  9. x k G(A|x)* G(B|x) = Im[G(A|B)] G(A|x) G(B|x)* G(B|A) A B A B A B x x x Reciprocity Correlation Equation VSP => SSP Given: VSP data G(A|x) Find: SSP data G(A|B)

  10. Examples 1. 2D Synthetic VSP Data 2. 2D Field VSP Data 3. 3D VSP Data

  11. Velocity Model Well X (m) 925 0 0 V (m/s) 4000 Depth (m) 1900 1300 Shots: 92; Receivers: 91 (50m -950 m)

  12. CSG 51 Ghost Component 0 S A Time (s) Well G X 3 50 950m 50 950m

  13. VSP VSP SSP 1. FK Filter up and downgoing waves x x k G(A|x)* G(B|x) G(A|x)* = Im[G(A|B)] G(B|x) 2. Correlation: f(A,B,x) = f(A,B,x) 3. Summation: k = Im[G(A|B)] M(x) = Mig(G(A|B)) 4. Migration: A B A B A B x x x Implementation

  14. CSG 51 Primary Component 0 Time (s) S A Well G X 3 50 950m 50 950m

  15. 8 Receivers Lesson: Super-illumination Primary 1st-order multiple 0 Depth (m) 1300 X (m) 0 0 X (m) 925 925

  16. Examples 1. 2D Synthetic VSP Data 2. 2D Field VSP Data:Friendswood Data 3. 3D VSP Data

  17. Friendswood RVSP Experiment Well X (m) 300 0 0 V (m/s) 4000 Depth (m) 1900 310 Shots: 98; Receivers: 24

  18. Depth (ft) 30 900 0 Raw Data(CRG15) Time (s) 0.3

  19. Depth (ft) 30 900 0 Ghosts Time (s) 0.3

  20. X (ft) X (ft) 0 400 0 400 200 Standard mig Xcorr. mig Depth (ft) 1300

  21. Examples 1. 2D Synthetic VSP Data 2. 2D Field VSP Data: GOM Data 3. 3D VSP Data: GOM BP Data

  22. 3D SEG Salt Model Test (He, 2006)

  23. VSP Multiples Migration Stack of 6 receiver gathers ( Courtesy of P/GSI: ~¼ million traces, ~3 GB memory, ~4 hours on a PC ) (He, 2006)

  24. VSP->SSP Summary G(A|x)* G(B|x) = G(A|B) x B A B B A A x x x ! k Key Point #1: Common Raypath Cancels Key Point #2: Every Bounce Pt on Surface Acts a New Virtual Source Key Point #3: Summation over Sources Picks out Specular Contribution Key Point #4: Kills Source Statics and no need to know src location or excitation time Key Point #5: Huge increase in Illumination Area

  25. Outline • Background for Non-geo types • What is Seismic Interferometry? • Reciprocity Equation Correlation Type • Classification Matrix • Applications: VSP->SWP • Conclusions

  26. 3x3 Classification Matrix SSP VSP SWP SSP SSP SSP SSP VSP SSP SWP VSP VSP SSP VSP VSP VSP SWP SSP SWP SWP SWP VSP SWP SWP

  27. Motivation Problem: Overburden+statics defocus VSP migration Solution: VSP -> SWP Transform Redatum sources below overburden Local VSP migration

  28. SWP VSP { { Im G(B|A) + S S 0 0 0 0 Reciprocity Correlation Equation Far-field VSP -> SWP Transform = kG(B|x)* G(A|x) S0 x S A 0 B

  29. 0 Time (s) Reflection wavefield 3 Depth (m) 3500 1500 VSP Geometry 1500 Depth (m) 3500 Offset (m) 1000 0

  30. Reduced Form GSM Ray tracing of line source (picked direct wave) Reduce form GSM result 1500 ? Depth (m) 3500 0 Offset (m) 1000 0 Offset (m) 1000

  31. Reduced Form GSM Ray tracing of line source (picked direct wave) Reduce form GSM result 1500 Lesson: Super-resolution ? Depth (m) 3500 0 Offset (m) 1000 0 Offset (m) 1000

  32. 120 shots ? 98 geophones Poor image of flank by standard migration VSP Salt Flank Imaging (BP Hornby et al, 2006) Overburden

  33. Interferometric Migration Result 0 2000 ft

  34. VSP->SWP Summary ! 1. Redatum sources below overburden 2. Local VSP migration 3. Kills Source Statics and no need to know src location or excitation time 4. Super-resolution 5. Instead of redatuming receivers to surface, we redatum sources to depth.

  35. Outline • Background for Non-geo types • What is Seismic Interferometry? • Reciprocity Equation Correlation Type • Classification Matrix • Applications • Conclusions

  36. 3x3 Classification Matrix SSP VSP SWP SSP SSP SSP SSP VSP SSP SWP VSP VSP SSP VSP VSP VSP SWP SSP SWP SWP SWP VSP SWP SWP

  37. SSP SSP SSP A B A B A B x x x Seabed Seabed Seabed Reflectors Reflectors Reflectors Natural , Extrapolated Data Natural Green’s Function Green’s Function SSP Extrapolation Model based

  38. 0 Z (km) 4.5 0 X (km) 6.0 SSP Extrapolation SIGSBEE 2B velocity model 200 shots dx = 30 m 300 receivers aperture: 2.4 km dx = 7.62 m

  39. Real CSG Original CSG Extrapolated CSG 0.8 0.8 0.8 6.0 6.0 6.0 X (km) X (km) X (km) 0 0 0 Time (s) Time (s) Time (s) 4.0 4.0 4.0 SSP Extrapolation We can improve the results by a matching filter but we do not have enough time

  40. 0 Z (km) 4.5 6.0 0 X (km) SSP Extrapolation Migration of extrapolated SSP data 300 receivers aperture: 2.4 km dx = 7.62 m 200 shots dx = 30 m

  41. 0 Z (km) 4.5 6.0 0 X (km) SSP Extrapolation Migration of extrapolated SSP data

  42. Field Data Test Acquisition geometry demenstration Mahogony OBS Data 800 Shots beneath free surface 180 receivers on sea floor Sea floor depth: about 120m Shots and receivers interval: 25 m Time sample interval: 4ms 0 800 shots dx = 25 m 120 Sea floor 180 receivers dx =25 m Z (m) 0 X (m) 20000

  43. 0 0 Time (s) Time (s) 3.0 3.0 250 250 0 0 1200 1200 X (m) X (m) OBS Extrapolation Original CSG Virtual CSG virtual traces real traces

  44. 0 0 Time (s) Time (s) 3.0 3.0 250 250 0 0 1200 1200 X (m) X (m) OBS Extrapolation Virtual CSG by 1 iteration Virtual CSG by 5 iterations

  45. 0 0 Time (s) Time (s) 3.0 3.0 500 0 1200 X (m) 500 0 1200 X (m) OBS Extrapolation Original CSG Virtual CSG virtual traces real traces

  46. 0 0 Time (s) Time (s) 3.0 3.0 500 0 1200 X (m) 500 0 1200 X (m) OBS Extrapolation Virtual CSG by 1 iteration Virtual CSG by 5 iterations

  47. Summary Natural redatuming no need to know velocity model, statics Uses natural mirrors in the earth -> Enlarge illumination+aperture Problems: Finite Aperture-> Partial G(A|B) Attenuation, Field Approximation SSP VSP SWP SSP SSP SSP SSP VSP SSP SWP VSP VSP SSP VSP VSP VSP SWP SSP SWP SWP SWP VSP SWP SWP Partial cures: Deconvolution, Adapt. Filters

  48. Narrow aperture Wide aperture Sparse OBS Dense OBS Conclusions Future Work Field data test 3D test Helpful for OBS and SSP survey design Helpful for survey design in environmentally sensitive areas: receivers in town, sources out of town, e.g., Dhahran, Saudi Arabia Problems: attenuation ?

  49. G(A|x)* G(B|x) = G(A|B) x Correlation Redatuming VSP ->SSP ! k Standard VSP Primary VSP -> SSP

  50. Arbitrary Unknown Src V(z) V(x,y,z) W(t) Location Claerbout, Katz, 70’s xx xx xy Migrate Utah+LLNL 1997 Claerbout, Rickett 1999 xy Migrate SELECTIVE HISTORY SEISMIC INTERFEROMETRY Validity NO YES YES YES Earthquake 1900’s NO YES/NO YES NO YES NO YES YES YES YES/NO YES NO? YES YES YES YES Delft, Shell, Stanford, Utah

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