Wave equation migration of VSP data Brad Artman Jeff Shragge brad@sep.stanford .edu jeff@sep.stanford.edu

brad@sep.stanford .edu jeff@sep.stanford.edu “Geologic complexity” Time migration Kirchhoff migration Wave equation migration Inversion “Imaging operator complexity” brad@sep.stanford .edu jeff@sep.stanford.edu

brad@sep.stanford .edu jeff@sep.stanford.edu Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries brad@sep.stanford .edu jeff@sep.stanford.edu

Wavefield extrapolation data = W(x, z, w) W(x, z+Dz, w) = W(x, z, w) e – i k Dz z kz2 = w2s2 – kx2 brad@sep.stanford .edu jeff@sep.stanford.edu

Wavefield extrapolation data = W(x, z, w) W(z, x+Dx, w) = W(x, z, w) e – i k Dx x kx2 = w2s2 – kz2 brad@sep.stanford .edu jeff@sep.stanford.edu

brad@sep.stanford .edu jeff@sep.stanford.edu Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries brad@sep.stanford .edu jeff@sep.stanford.edu

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 brad@sep.stanford .edu jeff@sep.stanford.edu

brad@sep.stanford .edu jeff@sep.stanford.edu X or Z * Dz or Dx e + i k Dz e - i k Dx z x brad@sep.stanford .edu jeff@sep.stanford.edu

brad@sep.stanford .edu jeff@sep.stanford.edu Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries brad@sep.stanford .edu jeff@sep.stanford.edu

* Reflection imaging V (x, z) Back-scattered P to P reflection p brad@sep.stanford .edu jeff@sep.stanford.edu

Converted reflection imaging V (x, z) and V (x, z) p s * p-wave s-wave Back-scattered P to S mode conversion brad@sep.stanford .edu jeff@sep.stanford.edu

Converted transmission imaging V (x, z) and V (x, z) p s * Forward-scattered P to S mode conversion brad@sep.stanford .edu jeff@sep.stanford.edu

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 (?) brad@sep.stanford .edu jeff@sep.stanford.edu

brad@sep.stanford .edu jeff@sep.stanford.edu Wavefield extrapolation Shot-profile migration Surface reflection VSP experiment Scattering modes Reflection Transmission Deviated well geometries brad@sep.stanford .edu jeff@sep.stanford.edu

Deviated well geometries * brad@sep.stanford .edu jeff@sep.stanford.edu