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Goal: Learn about potential, principles and

Seismic Interferometry Course (Schuster, Cambridge Press). algorithms of seismic interferometry. Format : Lecture, sometimes followed by exercise. Course project. Goal: Learn about potential, principles and.

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Goal: Learn about potential, principles and

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  1. Seismic Interferometry Course (Schuster, Cambridge Press) algorithms of seismic interferometry Format: Lecture, sometimes followed by exercise. Course project. Goal:Learn about potential, principles and . Topics: Deterministic interferometry, stochastic interferometry, 3x3 classification matrix, reciprocity theorems, applications to VSP, SSP, OBS, and Xwell data.

  2. Seismic Interferometry:Instead of using just primary arrivals, you also use the multiples for a wider view

  3. Overview of Seismic Interferometry and Applications in Exploration Gerard Schuster KAUST & University of Utah

  4. What is Seismic Interferometry? Outline • Applications • VSP->SSP (surface seismic profile) • VSP->SWP (single well profile) • SSP->SSP • Conclusions

  5. 1968 1970s Claerbout V(z)+passive Berryhill model-based redatum Cole+Claerbout V(x,y,z)+passive? 1980s Scherbaum earthquake V(z)+passive 1990s 1999 Rickett+Claerbout V(z) Helioseismology , passive Daylight Imaging Utah: Stationary Phase Theory, SSP, and VSP 2001 Seismic Interferometric imaging, deterministic Wapenaar Recip. Thm. Correlation Type 2002-04 Gerstoft + others Surface Wave Interferometry Snieder Stationary Phase Redatuming SELECTIVE HISTORY SEISMIC INTERFEROMETRY ! redatum Shell Virtual Sources:Calvert+Bakulin

  6. SELECTIVE HISTORY SEISMIC INTERFEROMETRY ! redatum Earthquakes Passive Reservoir Nowack, Sheng, Curtis etc Shell, Draganov, Wapenaar, Snieder, Polleto Miranda, etc Engineering Xwell Minato, Onishi, Matsuoka etc Surface waves Volcanoes+Coda Snieder, Scales, Gret et al Shapiro, Derode, Larose, Dong, Xue, Halliday, Curtis, Van Mannen, Robertsson, Gerstoft,Sabra, Kepler, Roux, He, Ritzwoller, Campillo etc Model Tank Scales, Malcolm etc Interpolation Sheng, Curry, Berkhout, Wang, Dong, Hanafy, Cao, etc VSP Yu, Calvert, Bakulin, He, Jiang, Hornby, Xiao, Willis, Lu, Toksoz, Campman etc Extrapolation Dong, Hanafy, Cao, etc EM Slob, Wapenaar, Snieder Theory: Acoustic, EM, Elastic, Potential Refractions Exploration Curry, Guitton, Shragg, Yu, Artman Boise State Univ, Dong Fink, Wapenaar, Snieder, Papanicolaou, Blomgren, Slob, Thorbeck, van derNeut etc

  7. Point Source Response with src at B and rec at B G(B|x) G(B|x) = iwt xB e B virtual primary iw(t ) F.S. multiple direct xB e iw( ) t + t + t + t e Bz zB Bz zB z x Answer: Redatums data bycorrelationof trace pairs and stacking the result for different shot positions correlation stacking What is Seismic Interferometry? s * = G(B|B) VSP => SSP B virtual source z A z Assume a VSP experiment • No need to know src. location Phase of Common Raypath Cancels • No need to know src excitation time • Redatum source closer to target

  8. What is Seismic Interferometry? Point Source Response with src at B and rec at B = x iwt xB e iw(t ) xB e iw( ) t + t + t + t e Bz zB Bz zB z x Answer: Redatums data bycorrelationof trace pairs and stacking the result for different shot positions correlation stacking * G(B|x) G(B|x) = G(B|B) ~ ~ z A z • No need to know src. location x Phase of Common Raypath Cancels • No need to know src excitation time • Redatum source closer to target

  9. G(x|B)* G(x|A) = G(A|B) x SSP VSP VSP A A B B A x Old Multiples Become New Primaries! x Reciprocity Correlation Equation 2D Reflection Data k ~ ~ • No need to know VSP rec location at x Phase of Common Raypath Cancels • No need to know receiver statics

  10. n G(x|B)* G(x|A) = G(A|B) S x well 2 d x Reciprocity Correlation Equation 2D Reflection Data k (Wapenaar, 2004) Finite aperture leads to incomplete G(B|A) B A A A B x x Old Multiples Become New Primaries! Problems: Finitesource aperture Muting, Least squares or MDD Atten. Compensation No attenuation Deghostfilt.,U & D separation 1-way+ far-field approx. { } * * * - G(A|x) = G(A|B) - G(B|A) G(B|x) G(A|x) G(B|x)

  11. * A B B C A B C • Prediction Multiple by Convolution (SRME) • Prediction Primaries by Crosscorrelation • (Crosscorrelation migration interferometry)

  12. VSP Multiple (12 receivers 13 kft @ 30 ft spacing; 500 shots) 5000 Depth (ft) 13000 X (ft) 0 56000 TLE, Jiang et al., 2005

  13. Surface Seismic 5000 Depth (ft) 13000 X (ft) 0 56000 TLE, Jiang et al., 2005

  14. VSP Multiple (12 receivers 13 kft @ 30 ft spacing; 500 shots) 5000 Depth (ft) 13000 X (ft) 0 56000 TLE, Jiang et al., 2005

  15. Standard VSP vs Interferometric VSP Imaging Standard VSP Imaging Interferometric VSP Imaging Primary reflections Multiple reflections Small vs Huge Illumination Instead of using just primary arrivals, you also use the multiples for a wider/partialvision

  16. stellar interferometry, a team of French astronomers has captured one of the sharpest color images ever made. They observed the star T Leporis with the European Southern Observatory's Very Large Telescope Interferometer (VLTI; Cerro Paranal, Chile), which emulates a virtual telescope about 100 meters across, and which revealed a spherical molecular shell around the aged star. Stellar Interferometry An astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution.

  17. 3x3 Classification Matrix SSP VSP SWP out in SSP SSP SSP SSP VSP SSP SWP VSP VSP SSP VSP VSP VSP SWP SWP SWP SSP SWP VSP SWP SWP

  18. G(x|B)* G(x|A) Im[G(A|B)] x • Seismic Interferometry: imaginary Summary ~ ~ x x k AB AB G(B|x) G(A|x) G(A|B) • Merits: Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target , no velocity model needed (unlike Berryhill). • Challenges: Finite aperture and noise, attenuation, acoustic & farfield approximations , amplitude fidelity • Killer Apps in Earthquake: Surface wave interferometry • Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP

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

  20. Reciprocity Eqn. of Correlation Type * Free surface x 2 2 + k [ ] G(A|x) =- (x-A); B A * P(B|x) G(A|x) 2. Multiply by G(A|x) and P(B|x) and subtract 2 2 + k [ ] P(B|x) =- (x-B) * 2 2 + k P(B|x) [ ] G(A|x) =- (x-A) P(B|x) 2 2 * + k G(A|x) [ ] P(B|x) =- (x-B) * G(A|x) 2 2 2 2 - G(A|x) P(B|x) G(A|x) P(B|x) = (B-x)G(A|x) - (A-x)P(B|x) * * * [ * * * ] G(A|x) = { } G(A|x) P(B|x) P(B|x) ] [ * * ] [ * P(B|x) = P(B|x) G(A|x) G(A|x) P(B|x) G(A|x) - P(B|x) - G(A|x) 1. Helmholtz Eqns: *

  21. Reciprocity Eqn. of Correlation Type * Free surface x { } 2 2 + k [ ] G(A|x) =- (x-A); B A * P(B|x) G(A|x) 2. Multiply by G(A|x) and P(B|x) and subtract 2 2 + k [ ] P(B|x) =- (x-B) * 2 2 + k P(B|x) [ ] G(A|x) =- (x-A) P(B|x) 2 2 * + k G(A|x) [ ] P(B|x) =- (x-B) * G(A|x) 2 2 2 2 - G(A|x) P(B|x) G(A|x) P(B|x) = (B-x)G(A|x) - (A-x)P(B|x) * * * * * * G(A|x) = { } G(A|x) P(B|x) P(B|x) [ * * ] * P(B|x) = P(B|x) G(A|x) G(A|x) * * = (B-x)G(A|x) - (A-x)P(B|x) * G(A|x) P(B|x) - P(B|x) - G(A|x) - G(A|x) P(B|x) G(A|x) P(B|x) 1. Helmholtz Eqns: [ *

  22. Reciprocity Eqn. of Correlation Type - G(A|x) = G(A|B) - P(B|A) P(B|x) G(A|x) P(B|x) { } - G(A|x) = G(A|B) - P(B|A) P(B|x) G(A|x) P(B|x) n * * * { } * * * 2 3 d x d x Source line G(A|B) Free surface x B A Integration at infinity vanishes 3. Integrate over a volume 4. Gauss’s Theorem

  23. Reciprocity Eqn. of Correlation Type - G(A|x) = G(A|B) - P(B|A) P(B|x) G(A|x) P(B|x) n * * * { } 2 3 d x d x Source line Relationship between reciprocal Green’s functions G(A|B) Free surface x B A Integration at infinity vanishes 3. Integrate over a volume 4. Gauss’s Theorem { } * * * - G(A|x) = G(A|B) - G(B|A) G(B|x) G(A|x) G(B|x)

  24. Reciprocity Eqn. of Correlation Type n n r = 2i Im[G(A|B)] = 2i Im[G(A|B)] n n r iwr/c e |r| |r| iw/c G(A|x ) = ik (2a) Recall 2 2 d x d x Source line Source line n r -iwr/c n e -ik -iw/c (2b) G(B|x )* = G(B|x ) B X * * 2ik A G(B|x) G(A|x) (3) = G(A|B) - G(B|A) * 2 Neglect 1/r G(A|x ) { } (1) * * * - G(A|x) = G(A|B) - G(B|A) G(B|x) G(A|x) G(B|x) Plug (2a) and (2b) into (1)

  25. Far-Field Reciprocity Eqn. of Correlation Type n n r r ^ ^ n r k = 2i Im[G(A|B)] = 2i Im[G(A|B)] ~ n r 1 ~ A 2 2 d x d x k Source line Source line * * * * G(B|x) G(B|x) G(A|x) G(A|x) (3) (4) = G(A|B) - G(B|A) = G(A|B) - G(B|A) G(A|B) Free surface x B A

  26. Far-Field Reciprocity Eqn. of Correlation Type n n r r k = 2i Im[G(A|B)] = 2i Im[G(A|B)] ~ n r 1 ~ 2 2 d x d x k Source line Source line G(A|B) Free surface x B A * * * * G(B|x) G(B|x) G(A|x) G(A|x) (3) (4) = G(A|B) - G(B|A) = G(A|B) - G(B|A)

  27. Far-Field Reciprocity Eqn. of Correlation Type n r = 2i Im[G(A|B)] x x x 2 d x k Source line B A B A B A Virtual source G(B|x)* G(A|x) G(A|B) * * G(B|x) G(A|x) (4) = G(A|B) - G(B|A) Source redatumed from x to B

  28. What is Seismic Interferometry? Outline • Applications • VSP->SSP (surface seismic profile) • VSP->SWP (single well profile) • SSP->SSP • Conclusions

  29. 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 Challenge: Finite Receiver Aperture = Partial Reconstruction

  30. 3D SEG Salt Model Test (He, 2006)

  31. 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)

  32. Marine 3D VSP Field Data Application

  33. BP 3D VSP Survey Geometry (36 recs) ~ 11 km 1.6 km 4.0 km (He et al., 2007) 3 km

  34. VSP->SSP Summary x k G(A|x)* G(B|x) = Im[G(A|B)] A B A B A B x x x VSP VSP SSP ! Key Point #1: Every Bounce Pt on Surface Acts a New Virtual Source Key Point #2: Kills Receiver Statics Key Point #3: Redatuming = Huge Increase Illumination area Key Point #4: Liabilities: Finite Aperture noise, attenuation, loss amplitudes fidelity

  35. What is Seismic Interferometry? Outline • Applications • VSP->SSP (surface seismic profile) • VSP->SWP (single well profile) • SSP->SSP • Conclusions

  36. Motivation Problem: Overburden+statics defocus VSP migration Solution: VSP -> SWP Transform (Calvert, Bakulin) VSP VSP SWP Redatum sources below overburden Local VSP migration

  37. 0 Reflection wavefield Time (s) 3 VSP Geometry 1500 Depth (m) 3500 Offset (m) 1000 0 (He , 2006)

  38. 0 Reflection wavefield Time (s) 3 VSP Geometry 1500 Depth (m) superresolution 3500 Offset (m) 1000 0 China (He , 2006)

  39. 120 shots ? 98 geophones Poor image of flank by standard migration VSP Salt Flank Imaging (Hornby & Yu, 2006) Overburden

  40. Interferometric Migration Result 0 2000 ft

  41. 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.

  42. What is Seismic Interferometry? Outline • Applications • VSP->SSP (surface seismic profile) • VSP->SWP (single well profile) • SSP->SSP • Conclusions

  43. Surface Wave Interferometry G(A|x)* G(B|x) G(B|A) A B x A B x

  44. Surface Wave Interferometry G(A|x)* G(B|x) = G(B|A) x A B

  45. Surface Wave Interferometry x S-velocity distribution, surface wave predic.+elimination G(A|x)* G(B|x) = G(B|A) x A B Shear velocity Yao (2009)

  46. 3x3 Classification Matrix SSP VSP SWP out in SSP SSP SSP SSP VSP SSP SWP VSP VSP SSP VSP VSP VSP SWP SWP SWP SSP SWP VSP SWP SWP

  47. G(x|B)* G(x|A) Im[G(A|B)] x • Seismic Interferometry: Summary ~ ~ x x k AB AB • Merits: Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target , no velocity model needed (unlike Berryhill). G(B|x) G(A|x) G(A|B) • Challenges: Finite aperture and noise, attenuation, acoustic & farfield approximations , amplitude fidelity • Killer Apps in Earthquake: Surface wave interferometry • Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP

  48. UTAM sponsors Thanks • Min Zhou, ChaiwootBoonyasiriwat, Ge Zhan

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

  50. Saudi Land Survey overburden sandstone sandstone shale shale

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