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Migration

Migration. Intuitive. Least Squares. Green’s Theorem. Migration. ZO Migration Smear Reflections along Fat Circles. . . x x. + T. x x. o. 2-way time. x. Thickness = c*T /2. x. o. . 2. 2. ( x - x ) + y. =. x x. c. d ( x , ). Where did reflections

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Migration

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  1. Migration Intuitive Least Squares Green’s Theorem Migration

  2. ZO Migration Smear Reflections along Fat Circles   xx + T xx o 2-way time x Thickness = c*T /2 x o  2 2 (x-x ) + y = xx c d(x , ) Where did reflections come from?

  3. ZO Migration Smear Reflections along Fat Circles  xx & Sum  2-way time x Hey, that’s our ZO migration formula d(x , )

  4. ZO Migration Smear Reflections along Circles & Sum  2-way time x In-Phase Out-of--Phase  d(x , ) xx m(x)=

  5. ZO Migration Resolution Intersection of Fresnel Zones Intersection of Fresnel Zones Vertical Res. = Near-Offset Traces

  6. ZO Migration Resolution Intersection of Fresnel Zones Intersection of Fresnel Zones Horiz. Res. = Far-Offset Traces

  7. Why is Pt. Scatterer Response of Migration a Blurred Version of Point? Lr d = Lr but Migration: Migration Section = Blured Imageof r Migrated Section Data T m = L d

  8. Seismic Section 12 km Time

  9. 0 km 3 km 0 km 7 km

  10. ZO Data Migration ZO Data 0 km 3 km 0 km 7 km

  11. ZO Migration: Smear Trace Sample over Circle  g m(x) = Loop over x in model Loop over z in model d (g, )  xg Loop over data for ixtrace=1:ntrace; for ixs=istart:iend; for izs=1:nz; r = sqrt((ixtrace*dx-ixs*dx)^2+(izs*dx)^2); time = 1 + round( r/c/dt ); mig(ixs,izs) = mig(ixs,izs)/r + data(ixtrace,time); end; end; end; Traveltime Smear over circle

  12. ZO Migration: Sum Trace Samples along migration hyperbola into m(x) Loop over x in model Loop over z in model for ixtrace=1:ntrace; for ixs=istart:iend; for izs=1:nz; r = sqrt((ixtrace*dx-ixs*dx)^2+(izs*dx)^2); time = 1 + round( r/c/dt ); mig(ixs,izs) = mig(ixs,izs)/r + data(ixtrace,time); end; end; end; (x,z) (x’,z’) Sum samples along hyperbola Loop over data

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

  14. 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

  15. m(x) = d (g, )  xg g ZO Diffraction Stack Migration: C(x,z) Trial image pt x Ray tracing

  16. m(x) = d (g, )  xg g 3D ZO Diffraction Stack Migration Trial image pt x Impulse Response of Mig. Op.

  17. 3D Prestack Diffraction Stack Migration Motivation: ZO only good if no lateral vel change s g x

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

  19. Migration Forward Problem: d=Lm Intuitive Least Squares T m=L d Green’s Theorem Migration

  20. = d(x’,  +  ) xg sx s,g  m(x) = d (g, )  xg g Summary Migration Motivation: diffractions, dipping layers, conflicting dips, out-of-plane reflections 3D ZO Diffraction Stack Migration Trial image pt x 3D Prestack Diffraction Stack Migration m(x) = Trial image pt x

  21. Migration Interpretation Sum Trace Samples along migration hyperbola into m(x) Smear Trace Sample over Circle RTM Dot product of hyperbola & data (x’,z’) Migration Spatial Resolution Horiz. Res. = Far-Offset Traces Vertical Res. = Near-Offset Traces

  22. Homework 1. Write pseudo-Matlab code for poststackmig. 2. Write pseudo-Matlab code for pretstackmig. 3. Which has better x-resolution, wide aperture or narrow aperture ZO migration? L Z 4. GOM Rayleigh Resolution Formula: dx = 0.5 l Z/(4L) vsdz = l/4 dz dx

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