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Time vs Depth Migration

Time vs Depth Migration. CMP Gather. CMP Gather. time. time. Depth Migration. Time Migration. Insensitive to v(z) model. Sensitive to v(z) model. Incoherent summation if guess is wrong. Time migration uses best fit hyperbola. Coherent summation. Depth migration uses best

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Time vs Depth Migration

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  1. Time vs Depth Migration CMP Gather CMP Gather time time Depth Migration Time Migration Insensitive to v(z) model Sensitive to v(z) model Incoherent summation if guess is wrong Time migration uses best fit hyperbola Coherent summation Depth migration uses best guess moveout curve

  2.   g g g m(x,z) = 2-way vertical traveltime z 2 2 d (g, 4[(x-g)/c] + (2z/c) ) 2 2 d (g, 4[(x-g)/c] + T ) m(x,z(T)) = 2 2 d (g, 4[(x-g)/c] + T ) M(x,T) = Depth Migration -> Time Migration Depth Migration: Maps data into function(x,z) We know 2z/c=T so Time Migration: Maps data into function(x,T)

  3. g c(T) v1 v2 T v3 v4 v5 v6 Time Migration for c(T) Time Migration: Maps data into function(x,T) 2 2 M(x,T) = d (g, 4[(x-g)/c(T)] + T ) More generally, c(T) is a function of T!

  4. g m(x,z) = Loop over x in model Loop over z in model d (g, )  xg MATLAB ZO Depth Migration for ixtrace=1:ntrace; for ixs=istart:iend; for izs=1:nz; r = sqrt(4*(ixtrace*dx-ixs*dx )^2+(2*izs*dx)^2); time = 1 + round( r/c/dt ); mig(ixs,izs) = mig(ixs,izs)/r + data(ixtrace,time); end; end; end; Traveltime

  5. g 2 2 M(x,T) = Loop over x in model Loop over iT in model MATLAB ZO Time Migration d (g, 4[(x-g)/c(T)] + T ) for ixtrace=1:ntrace; for ixs=istart:iend; for iT=1:nT; time = sqrt(4*([ixtrace*dx-ixs*dx]/c(iT))^2+(iT*dt)^2); time = 1 + round( time/dt ); mig(ixs,iT) = mig(ixs,iT)/r + data(ixtrace,time); end; end; end; Traveltime Note: c(iT) or c(ixtrace,iT)

  6. Time Migration vs Depth Migration  2 2 M(x,T) = d (g, 4[(x-g)/c] + T ) Insensitive to c(z) model Time migration uses best fit hyperbola

  7. Time Migration vs Depth Migration  2 2 M(x,T) = d (g, 4[(x-g)/c] + T ) Insensitive to v(z) model Time migration uses best fit hyperbola

  8. Time Migration vs Depth Migration  2 2 M(x,T) = d (g, 4[(x-g)/c] + T ) Insensitive to v(z) model Time migration uses best fit hyperbola

  9. Time Migration vs Depth Migration  2 2 M(x,T) = d (g, 4[(x-g)/c] + T ) Insensitive to v(z) model Time migration uses best fit hyperbola

  10. Time Migration vs Depth Migration  2 2 M(x,T) = d (g, 4[(x-g)/c] + T ) =c/f  M(x,z) = d (g, t ) gx Insensitive to v(z) model Sensitive to v(z) model Incoherent summation if guess is wrong Time migration uses best fit hyperbola Coherent summation Depth migration uses best guess moveout curve Cheap: no ray tracing Expensive: ray tracing Stretched wavelet thickness Uniform wavelet thickness 1/f Best focusing if v(x,z) correct Best focusing if v(x,z) really wrong Good focusing if v(x,z) smooth

  11. Depth Migration in Deep GOM is only Way to Go if V(x,y,z) Correct Therefore, spend time to get v(x,y,z) Correct: Tomography, MVA, Waveform Inversion

  12. Velocity Analysis  2 2 M(x,T) = d (g, 4[(x-g)/c] + T ) CMP C(T) T Time x c

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