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Prestack Migration

Prestack Migration. Intuitive. Least Squares. Green’s Theorem. Migration. 3D Prestack Diffraction Stack Migration. Motivation: ZO only good if no lateral vel change. s. g. x. . =. d(x’ ,  +  ). x g. s x. s, g. 3D Prestack Diffraction Stack Migration.

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Prestack Migration

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  1. Prestack Migration Intuitive Least Squares Green’s Theorem Migration

  2. 3D Prestack Diffraction Stack Migration Motivation: ZO only good if no lateral vel change s g x

  3. = d(x’,  +  ) xg sx s,g 3D Prestack Diffraction Stack Migration m(x) = Trial image pt x s g x

  4. Prestack DS Migration Theory Outline RTM RTM vsPoststackvsPrestack MATLAB Code

  5. Question: Why Prestack when poststack migration seems good enough? Prestack Migration Answer: Stacking to get stacked section assumes layered medium assumption. Solution: Migrate shot gathers so no layer assumption needed. This is prestack migration.

  6.  + sx xg    + T(s,g) = s,g sx xg g s   sx xg d(s,g, ) x Diffraction Stack Migration: Prestack Up time Down time Where is scatterer? Narrow band case: direct wave correlated with data

  7. m = L d T  x ~ ~ W( ) m(x) 2 w 115. Diffraction Stack Modeling: Prestack d= L m     i i ~ sx e xg e d(s,g) = A(s,x) A(g,x)

  8. m = L d T  d  d s,g s,g ~ ~ W( ) W( )=1 ò ò Broadband case d(s,g,  +  ) = sx xg A(x,g) A(s,x) 2 w 115. Diffraction Stack Migration: Prestack - -     i i * sx ~ e xg e ~ m(x) = d(s,g) A(s,x) A(g,x) .. m(x) Narrow band case: direct wave correlated with data

  9. Prestack DS Migration Theory Outline RTM RTM vsPoststackvsPrestack MATLAB Code

  10. Prestack RTM vs One-way Wave Equation Migration

  11. Prestack RTM vs One-way Wave Equation Migration

  12. m(x) = d (g, )  xg g traces ZO Diffraction Stack Migration Trial image pt x g x

  13. m(x) = d (g, )  xg g traces ZO Diffraction Stack Migration Trial image pt x 2D dot product of migration Operator and d(g,t) g Migration Image x

  14. m(x) = d (g, )  xg g traces ZO Reverse Time Migration Trial image pt x ~Scattered RTM g Super-resolution x x

  15. m(x) = d (g, )  xg g traces ZO Reverse Time Migration Trial image pt x ~Scattered RTM g Super-resolution x x

  16. Prestack RTM vs One-way Wave Equation Migration

  17. Prestack DS Migration Theory Outline RTM RTM vsPoststackvsPrestack MATLAB Code

  18. Shortest path ray Maximum energy ray Shortest traveltime ray Shortest Traveltime or Shortest Raypath Maximum Energy Traveltimes Types of Traveltimes

  19. Poststack vs Prestack Migration

  20. Poststack vs Prestack Migration

  21. RRTM vs KM Migration

  22. RRTM vs KM Migration

  23. Prestack RTM vs One-Way Mig.

  24. Prestack RTM vs One-Way Mig.

  25. Prestack DS Migration Theory Outline RTM RTM vsPoststackvsPrestack DS MATLAB Code

  26. MATLAB Prestack Migration

  27. MATLAB Inefficient Prestack Migration for isx=1:nx % Loop over shot for igx=1:nx % Loop over receivers for ix=1:nx % Loop over model x for iz=1:nx % Loop over model z t=timer(ix,iz,isx)+timer(ix,iz,igx) sample=gather(isx,igx,t) % Shot gather has 2 time derivatives mig(ix,iz)=mig(ix,iz)+sample end end end end

  28. MATLAB Prestack Migration

  29. 1. No assumption about velocity model Prestack Migration 2. More sensitive to velocity model errors compared to poststack migration 2 6 3. More than 10 – 10 times slower than poststack migration 4. More sensitive to velocity model than time migration

  30. Poststack vs Prestack Migration

  31. PoststackvsPrestack Migration

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