1 / 48

Reverse Time Migration =

Reverse Time Migration =. Generalized Diffraction Migration. Outline. 1. RTM = GDM. 2. Implications. Superresolution. Filtering. Target Oriented RTM. Fast LSM. Diffraction Selective. Perfect Migration Operators. , r,s. w. Direct wave. B ackpropagated traces.

nat
Download Presentation

Reverse Time Migration =

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. Reverse Time Migration = Generalized Diffraction Migration

  2. Outline 1. RTM = GDM 2. Implications Superresolution Filtering Target Oriented RTM Fast LSM Diffraction Selective Perfect Migration Operators

  3. ,r,s w Direct wave Backpropagated traces Reverse Time Migration Generalized Diff. Migration Calc. Green’s Func. By FD solves Trial image pt x d(r)= m(x) * * [ ] G(s|x) G(x|r) = dot product data with hyperbola Generalized Kirchhoff kernel Convolution of G(s|x) with G(x|r) T=0 QED: RTM can now enjoy: Anti-aliasing filter Obliquity factor Angle Gathers UD Separation Decomplexifyback&forward felds according 2 taste Etc. etc. s r x Expensive to store Calc. Green’s Func. By FD solves

  4. ,r,s w Most Kirchhoff Tricks for Kirchhoff Migration can be Implemented for RTM Direct wave Backpropagated traces Reverse Time Migration Generalized Kirch. Migration Calc. Green’s Func. By FD solves Trial image pt x d(r)= m(x) * * [ ] G(s|x) G(x|r) = dot product data with hyperbola Generalized Kirchhoff kernel Convolution of G(s|x) with G(x|r) T=0 QED: RTM can now enjoy: Anti-aliasing filter Obliquity factor Angle Gathers UD Separation Decomplexifyback&forward felds according 2 taste Etc. etc. s r x Expensive to store Calc. Green’s Func. By FD solves

  5. Outline 1. RTM = GDM 2. Implications Superresolution Filtering Target Oriented RTM Fast LSM Diffraction Selective Perfect Migration Operators

  6. Multiples time time Primary Primary Multiples Resolution of KM vs GDM Kirchhoff Mig. vs GDM 1. Low-Fold Stack vs Superstack 2. Poor Resolution vsSuperresolution 3. Caution: RTM sensitive to mig. vel. errors

  7. time Rayleigh Resolution L migrate Dx = 0.25lz/L

  8. Is Superresolution by RTM Achievable? Tucson, Arizona Test This is highest fruit on the tree..who dares pick it? 60 m ~Kirchhoff Mig. Poststack Migration ~Scattered RTM (Hanafy et al., 2008)

  9. Can Scatterers Beat the Resolution Limit? • Recorded Green’s functions G(s|x) divided into: • Shot gathers with direct arrivals only • Shot gathers with scattered arrivals only

  10. Outline 1. RTM = GDM 2. Implications Superresolution Filtering: 1st Arrival Filtering Target Oriented RTM Fast LSM Diffraction Selective Perfect Migration Operators

  11. Phase Shift, Beam, Kirchhoff Migrations are Special Cases of True RTM S de (x) = [G(s|x)G(x|g)]* d(s|g) Frechet Derivative 1. RTM: ds s,g S [{} { } ]* d(s|g) G(x|g) G(x|g) G(x|g) = + + s,g S { * } ~ d(s|g) True RTM G(s|x) G(s|x) G(s|x) s,g First Arrival Filter & U p+Down filter First Arrival Filter Early Arrival Filter Super-wide Angle Phase Shift Migration Single Arrival Kirchhoff w/o high-freq. appox Multiple Arrival Kirchhoff w/o high-freq. appox (or Super beam migration)

  12. FD only in expanding box Efficient RT Migration Operators SALT

  13. Example (Min Zhou, 2003) Standard FD Wavefront G(s|x) Early Arrival FD Wavefront G(s|x) Standard RTM vs Early Arrival RTM

  14. Efficient RT Migration Operators Standard FD 0 1.5 km 0 4.5 km Wavefront FD

  15. FD/ Wavefront FD Cost 45 5 FD/ Wavefront FD Cost 500 3000 # Gridpts along side

  16. Model 0 1.5 km 1.5 km/s 2.2 km/s 1.8 km/s Wavefront Migration Image 0 1.5 km 0 4.5 km

  17. Reverse Time Migration 0 1.5 km 1.5 km/s 2.2 km/s 1.8 km/s Wavefront Migration Image 0 1.5 km 0 4.5 km

  18. Outline 1. RTM = GDM 2. Implications Superresolution Filtering: 1st Arrival Filtering Target Oriented RTM Fast LSM Diffraction Selective Perfect Migration Operators

  19. Filtering of Wave Equation Migration Operators Truncation: anti-aliasing SALT SALT

  20. Slant stack Filtering of Wave Equation Migration Operators SALT

  21. 0 km 4.5 km 0 km 4.5 km X (km) X (km) Filtering of Wave Equation Migration Operators COG Mig. Op. Filtered COG Mig. Op. 0 s 1.0 s Z=70 m 0 s 1.0 s Time (s) Z=270 m 0 s 1.0 s Z=1190 m

  22. Outline 1. RTM = GDM 2. Implications Superresolution Filtering: 1st Arrival Filtering Target Oriented RTM Fast LSM Diffraction Selective Perfect Migration Operators

  23. Datum Standard Reverse Time Redatuming Special case:10 Shot Gathers at the Surface, 3 Receivers at Depth Procedure:Compute 10 FD Solves, one for each shot at z=0 Cost = 10 FD Solves to get G(x|x)

  24. Datum Target Oriented Reverse Time Redatuming Special case:10 Shot Gathers at the Surface, 3 Receivers at Depth Trick:By ReciprocityG(x|x)=G(x|x) Procedure:Compute 3 FD Solves, one for each shot at z=datum Cost = 3 FD Solves to get G(x|x) Benefit: Several orders magnitude less expensive

  25. Kirchhoff Migration Redatum + KM Offset (km) 0 3.5 3D Synthetic Data (Dong) W E 0 Depth (Km) 1.24 2.0 0 Offset (km) 3.5 A slice of 3D SEG/EAGE model at x=2.0 km

  26. Interval velocity model km/s 0 5.5 Z (km) 8.0 0 y (km) 12 x (km) 6.0 0 New Datum 1.5 3D Field Data Test OBC geometry: 50,000 shots 180 receivers per shot Datum depth: 1.5 km RVSP Green’s functions: 5,000 shots 180 receivers per shot

  27. Redatumed CSG Original CSG 0 0 Time (s) Time (s) 6.0 6.0 y (km) y (km) 4.5 4.5 0 0 3D Field Data Test

  28. x (km) 0 KM of redatumed data 12 0 Z (km) 8 KM of original data 0 0 y (km) 5 Z (km) 8 0 12 y (km) x (km) 5 0 3D Field Data Test KM of RTD data

  29. 0 0 Z (km) Z (km) 8.0 8.0 0 0 X (km) X (km) 12 12 3D Field Data Test ( Inline No. 61 ) KM of original data KM of RTD data

  30. 0 0 Z (km) Z (km) 8.0 8.0 0 0 Y (km) Y (km) 5.0 5.0 3D Field Data Test ( Crossline No. 41 ) KM of original data KM of RTD data

  31. 0 0 Z (km) Z (km) 8.0 8.0 0 0 Y (km) Y (km) 5.0 5.0 3D Field Data Test ( Crossline No. 61 ) KM of original data KM of RTD data

  32. 0 0 Y (km) Y (km) 5.0 5.0 0 0 X (km) X (km) 12 12 3D Field Data Test ( Depth 2.0 km ) KM of original data KM of RTD data

  33. 0 0 Y (km) Y (km) 5.0 5.0 0 0 X (km) X (km) 12 12 3D Field Data Test ( Depth 2.5 km ) KM of original data KM of RTD data

  34. 0 0 Y (km) Y (km) 5.0 5.0 0 0 X (km) X (km) 12 12 3D Field Data Test ( Depth 4.0 km ) KM of original data KM of RTD data

  35. Computational Costs

  36. Outline 1. RTM = GDM 2. Implications Superresolution Filtering: 1st Arrival Filtering Target Oriented RTM Fast LSM Diffraction Selective Perfect Migration Operators

  37. Motivation (Ge Zhan) • Kirchhoff (diffraction-stack) migration is efficient but with a high-frequency approximation. • WEM method (RTM)is accurate but computationally intensive compared to KM. • Problem • Conventional RTM suffers from imaging artifacts. • Solution • Compressed generalized diffraction-stack migration (GDM) . • Wavelet compression of Green’s functions (10x or more). • Least squares algorithm.

  38. Theory 2D Wavelet Transform appropriate threshold 10x compression r s Migration Operator G(s|x)G(x|g) (5 dimensions) x Size = nx*nz*ns*ng*nt = 645*150*323*176*1001*4 = 20 TB Too big to store.

  39. Theory trace Green’s Function Can Scatterers Beat the Resolution Limit ?

  40. km/s 4.5 3.5 0 0 2.5 1.5 Z (km) Z (km) 3 3 0 0 15 15 X (km) X (km) Zoom View Numerical Results SEG/EAGE Salt Model 323 shots 176 geophones peak freq = 13 Hz dx = 24.4 m dg = 24.4 m ds = 48.8 m nsamples = 1001 dt = 0.008 s

  41. Trace Comparison 1.5 0 Time (s) Time (s) 4 1 101 201 301 401 Trace# 4 1 401 Trace # Numerical Results Wavelet Transform Compression Calculated GF Reconstructed GF 1 401 Trace # 200 MB 20 MB

  42. Multiples 0 Time (s) 1 401 Trace# 4 1 401 Trace# Numerical Results Early-arrivals

  43. 0 0 (a) GDM using Early-arrivals (b) GDM using Full Wavefield Z (km) Z (km) 3 3 0 0 15 15 X (km) X (km) 0 15 X (km) (c) GDM using Multiples (d) Optimal Stack of (a) and (c) 0 15 X (km) Numerical Results

  44. Outline 1. RTM = GDM 2. Implications Superresolution Filtering: 1st Arrival Filtering Target Oriented RTM Fast LSM Diffraction Selective Perfect Migration Operators

  45. IMPLICATION #2 Exact Migration Operators from VSP SALT g(s|x)

  46. IMPLICATION #2 * g(s|x) Exact Migration Operators from VSP * g(r|x) SALT

  47. Exxon RVSP Data Direct Reflections Multiples Focusing Operator g(s|x) g(x|r) 0 s 0.5 s Z = .18 km X 0 km 0.2 km

  48. Prim Refl. Kirchhoff Operator Interbed Multiple Refl. Kirchhoff Operator Exxon RVSP Data Prim Refl. Focusing Operator 0.2 s 0.28 s X 0 km 0.2 km Interbed Multiple Refl. Focusing Operator 0.31 s 0.37 s X 0 km 0.2 km

More Related