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Wave equation migration of VSP data
Brad Artman Jeff Shragge .edu
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brad@sep.stanford .edu jeff@sep.stanford.edu
“Geologic complexity” Time migration Kirchhoff migration Wave equation migration Inversion “Imaging operator complexity” .edu
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brad@sep.stanford .edu jeff@sep.stanford.edu
Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries .edu
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Wavefield extrapolation
data = W(x, z, w) W(x, z+Dz, w) = W(x, z, w) e – i k Dz z kz2 = w2s2 – kx2 .edu
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Wavefield extrapolation
data = W(x, z, w) W(z, x+Dx, w) = W(x, z, w) e – i k Dx x kx2 = w2s2 – kz2 .edu
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brad@sep.stanford .edu jeff@sep.stanford.edu
Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries .edu
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Shot-profile migration
Seed source and receiver wavefields x t Extrapolate to all model levels Compare wavefields via an Imaging Condition t z I (x, z)=Σ U (w, x, z) D (w, x, z) ω IFT & zero lag extraction correlation Reflectors are imaged when energy in both U and D is co-located in x and z, at t=0. D U .edu
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brad@sep.stanford .edu jeff@sep.stanford.edu
X or Z * Dz or Dx e + i k Dz e - i k Dx z x .edu
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brad@sep.stanford .edu jeff@sep.stanford.edu
Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries .edu
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* Reflection imaging V (x, z) Back-scattered P to P reflection p
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Converted reflection imaging
V (x, z) and V (x, z) p s * p-wave s-wave Back-scattered P to S mode conversion .edu
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Converted transmission imaging
V (x, z) and V (x, z) p s * Forward-scattered P to S mode conversion .edu
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brad@sep.stanford .edu jeff@sep.stanford.edu
Image spaces Forward scattering Compressional down – shear down Backscattering Compressional down – compressional up Compressional down – shear up Shear down – shear up (?) .edu
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brad@sep.stanford .edu jeff@sep.stanford.edu
Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries .edu
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Deviated well geometries
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