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By Thang Ha & Yuji Kim University of Oklahoma, 2016

Seismic Reprocessing: Constrained Conjugate Gradient Least-Squares Migration and Migration-Driven 5D Interpolation: Application to Jeju Basin Marine Data. By Thang Ha & Yuji Kim University of Oklahoma, 2016. Motivation. What do we do to get high quality images?. Expensive.

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By Thang Ha & Yuji Kim University of Oklahoma, 2016

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  1. Seismic Reprocessing:Constrained Conjugate Gradient Least-Squares Migration and Migration-Driven 5D Interpolation:Application to Jeju Basin Marine Data By Thang Ha & Yuji Kim University of Oklahoma, 2016

  2. Motivation

  3. What do we do to get high quality images? Expensive • Acquire and process new data • Reprocess old data with new techniques

  4. With the not-so-promising present…

  5. Seismic Reprocessing • Consist of many steps, including velocity refinement, advanced static correction, noise suppression, and migration • The last step, migration, is the actual “engine” to convert the acquired data to seismic images. Some migration algorithm requires regularized input data • Two methods are shown in this project to address migration and regularization issues: • Constrained Conjugate Gradient Least-Squares Migration (LSM) and • Migration-Driven 5D Interpolation

  6. Outline • Theory behind Constrained Conjugate Gradient Least-Squares Migration • Theory behind Migration-Driven 5D interpolation • Application to Jeju Basin Data (South Korea) • Conclusions • Acknowledgement

  7. Constrained Conjugate GradientLeast-Squares Migration • 4 elements: • Migration • Least-Squares • Conjugate Gradient • Constraint

  8. Migration • Work by “swiping” trace data along ellipsoidal surfaces • “swiped” images constructively interfered at reflection events • Focus diffraction • Move reflectors to their correct location • Shape of ellipsoids depend on velocity model image from xsgeo.com

  9. Least-Squares • Migration can be understood as a filter – an operator – applied on acquired data, to produce images. • Similarly, a reverse filter – an operator to convert seismic reflectivity images to acquired data is commonly known as “demigration” or forward modeling operator L • d=Lm, where • + d: acquired data • + L: forward modeling (demigration) operator • + m: seismic reflectivity images

  10. Least-Squares • We want to get seismic reflectivity image m, so we have to calculate the inverse of L: L-1 • However, in practice, it’s impossible to invert L • Yet, we can approximate L-1 by LT, the transpose of L, which is basically migration operator • m=LTd

  11. Least-Squares • In short, we can never have the exact solution to the equation d=Lm • The next best thing: find m so that the magnitude of the difference (d-Lm), or the squaresof the difference, (d-Lm)2, is the least • Thus “Least-Squares”

  12. Conjugate Gradient Method • Developed by Hestenes and Stiefel (1952) • Among the first-order iterative methods to solve Least-Squares problem, Conjugate Gradient method is the fastest (i.e. has the highest rate of convergence) • Detail of math-to-geophysics translation of the Conjugate Gradient method is provided in a 10-page single-spaced appendix.

  13. Let’s keep things simple, otherwise…

  14. Constraint • Beware that the acquired data contains both signal AND noise • If we try to solve for the reflectivity model m too exactly, then we also try to make m represent the noise in our data! • Constraint is used to enhance signal and reduce noise • We use Structure-Oriented Filter (SOF) as the constraint for Least-Squares Migration. SOF works by smoothing data where we have strong coherent reflectors while keeping faults sharp

  15. Too complicated to be represented by a flow chart m0=SOF(m0)=0 Original Data (d0=r0) Migrated Data Migrate SOF Update residual: r1=r0-α1*Lh0 α1=<g0.g0>/<Lh0.Lh0> Lh0 (g0=h0) Demigrate Update model: SOF(m1)=α1*h1 Update directional vector: v1=SOF(m1)/α1 α1 r1 Update conjugate gradient: h1=g1+β1v1 β1=<g1.g1>/<g0.g0> g1 Migrate v1 h1

  16. Better be represented by a step-by-step workflow

  17. LSM workflow is in AASPI Prestack Utility

  18. Outline • Theory behind Constrained Conjugate Gradient Least-Squares Migration • Theory behind Migration-Driven 5D interpolation • Application to Jeju Basin Data (South Korea) • Conclusions • Acknowledgement

  19. What are 5 Dimensions and what is interpolation for? Migration-Driven • Inline, Xline, Offset, Azimuth, Time • Source-X, Source-Y, Rec-X, Rec-Y, Time • Inline, Xline, Offset Tile X, Offset Tile Y, Time • Interpolation helps balance amplitude across seismic survey • Some advanced migration algorithm, such as wave-equation migration, required regularized input, which can only be archived through interpolation Conventional

  20. Conventional 5D Interpolation (Trad, 2005) Acquisition before interpolation Acquisition after interpolation

  21. Conventional 5D Interpolation: Coherence Map High Coherence Low 2 km Migrated image with 5D interpolation Migrated image without 5D interpolation (Chopra and Marfurt, 2013)

  22. 2D simple fault model Distance (km) 10 0 0 Sedimentary rock: v=2500m/s d=2200kg/m3 Depth (m) Basement rock: v=5000m/s d=2750kg/m3 1000

  23. Shot gather before NMO Distance (m) 0 10000 Amplitude Positive 0 Negative 0.5 Time (s) 1.0 1.5

  24. Shot gather after NMO Distance (m) 0 10000 Amplitude Positive 0 Negative 0.5 Time (s) 1.0 1.5

  25. Shot gather after NMO, decimated Distance (m) 0 10000 Amplitude Positive 0 Negative 0.5 Time (s) 1.0 1.5

  26. Shot gather after NMO, decimated, FFT interpolated Distance (m) 0 10000 Amplitude Positive 0 Negative 0.5 Time (s) 1.0 1.5

  27. Migration-Driven 5D Interpolation • Use Demigration (the reverse of migration, i.e. forward modeling) as the “engine” for interpolation • Defocus diffraction events into hyperboloids • With appropriate parameters, ONE iteration may already be enough

  28. Original CDP gathers Amplitude Positive 0 0.2 Negative 0.4 Time (s) 0.6 0.8 1.0

  29. Demigrated CDP gathers Amplitude Positive 0 0.2 Negative 0.4 Time (s) 0.6 0.8 1.0

  30. Migrated original data Amplitude Positive 0 0.2 Negative 0.4 Time (s) 0.6 0.8 1.0

  31. Migrated result of demigrated data Amplitude Positive 0 0.2 Negative 0.4 Time (s) 0.6 0.8 1.0

  32. Stacked image of migrated original data 0.2 Amplitude Positive 0 Negative 0.4 Time (s) 0.6 0.8 1.0

  33. Stacked image of migrated result of demigrated data 0.2 Amplitude Positive 0 Negative 0.4 Time (s) 0.6 0.8 1.0

  34. The Math Behind The Scene… • Inspired by Projection Onto Convex Sets (POCS) • Abma and Kabir (2006) followed POCS approach for 2D interpolation using Fourier Transform

  35. Projection Onto Convex Sets Abma and Kabir (2006)

  36. Projection Onto Convex Sets Abma and Kabir (2006)

  37. Projection Onto Convex Sets Abma and Kabir (2006)

  38. New Migration-Driven 5D Interpolation Workflow Looking good? Structural Oriented Filtering Original Data No Migrate Yes Merge Demigrate into interpolated locations 5D interpolated migrated result Looking good? 5D interpolated result

  39. Outline • Theory behind Constrained Conjugate Gradient Least-Squares Migration • Theory behind Migration-Driven 5D interpolation • Application to Jeju Basin Data (South Korea) • Conclusions • Acknowledgement

  40. Application to Jeju Basin Data (South Korea) • Introduction Regional map of the East China Sea.

  41. Application to Jeju Basin Data • Acquisition parmeters Phase 1-3 seismic survey areas. 3rd phase 1st, 2nd phase

  42. Application to Jeju Basin Data Total Energy • Phase 1-2 fold map High Low 5 km Feathering • Phase 3 fold map Phase 1-3 seismic survey areas. 3rd phase 1st, 2nd phase

  43. Application to Jeju Basin Data Total Energy • Feathering, sparse sampling in cross-line direction High • Total energy • Amplitude Low

  44. Application to Jeju Basin Data • Preconditioning workflow NO Surface Related Multiple Elimination Add Navigation data & Merge SEGD’s PSTM Migration and Stacking Resampling & Bandpass filtering Velocity Analysis (1km x1km) Geometry Applied Data PSTM Seismic Volume Import Individual SEG-D Generate Attribute Volume Detailed Velocity Analysis Are Surface Related Multiple Present? Attribute Volume Least-squares migration Deconvolution Brute Stack YES

  45. Application to Jeju Basin Data (Least-squares migration) • Migration and demigration

  46. Application to Jeju Basin Data (Least-squares migration) • Migration and demigration

  47. Application to Jeju Basin Data (Least-squares migration) • LSM workflow • Residuals from each iteration Acquisition footprint Sobel-filter similarity • 3rd iteration • 1st iteration • 2nd iteration High Low

  48. Application to Jeju Basin Data (Least-squares migration) Kirchhoff migration Least-squares migration Amp Pos (a) Amplitude Neg

  49. Application to Jeju Basin Data (Least-squares migration) Kirchhoff migration Least-squares migration Sobel-filter similarity (b) Coherence High Direction of acquisition (45 degree) Low

  50. Application to Jeju Basin Data (Least-squares migration) • Conclusion • Least squares migration reduces artifacts resulted from incomplete data (e.g. poor sampling). • Constrain factor reduces the number of iterations to converge. • The LSM on marine data effectively alleviates acquisition footprint, which is shown in slices through coherence and curvature attributes.

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