Stanford Exploration Project VSP Migration Wave equation migration

Stanford Exploration Project VSP Migration Wave equation migration of VSP data Brad Artman Jeff Shragge brad@sep. stanford. edu jeff@sep. stanford. edu 1

Stanford Exploration Project VSP Migration “Geologic complexity” Time migration Kirchhoff migration Wave equation migration “Imaging operator complexity” brad@sep. stanford. edu Inversion jeff@sep. stanford. edu 2

Stanford Exploration Project VSP Migration • Wavefield extrapolation • Shot-profile migration – Surface reflection – VSP experiment • Scattering modes – Reflection – Transmission • Deviated well geometries brad@sep. stanford. edu jeff@sep. stanford. edu 3

Stanford Exploration Project VSP Migration Wavefield extrapolation data = W(x, z, w) W(x, z+Dz, w) = W(x, z, w) e – i kz Dz kz 2 = w 2 s 2 – kx 2 brad@sep. stanford. edu jeff@sep. stanford. edu 4

Stanford Exploration Project VSP Migration Wavefield extrapolation data = W(x, z, w) W(z, x+Dx, w) = W(x, z, w) e – i kx Dx kx 2 = w 2 s 2 – kz 2 brad@sep. stanford. edu jeff@sep. stanford. edu 5

Stanford Exploration Project VSP Migration • Wavefield extrapolation • Shot-profile migration – Surface reflection – VSP experiment • Scattering modes – Reflection – Transmission • Deviated well geometries brad@sep. stanford. edu jeff@sep. stanford. edu 6

Stanford Exploration Project VSP Migration Shot-profile migration • Seed source and receiver wavefields x • Extrapolate to all model levelsz • t Compare wavefields via an Imaging Condition t I (x, z)=Σω U (w, x, z) D (w, x, z) correlation IFT & zerowhen lag extraction Reflectors are imaged 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 7

Stanford Exploration Project VSP Migration X or Z * Dz e + i k z. Dz brad@sep. stanford. edu or Dx e - i k x. Dx jeff@sep. stanford. edu 8

Stanford Exploration Project VSP Migration • Wavefield extrapolation • Shot-profile migration – Surface reflection – VSP experiment • Scattering modes – Reflection – Transmission • Deviated well geometries brad@sep. stanford. edu jeff@sep. stanford. edu 9

Stanford Exploration Project VSP Migration Reflection imaging Vp (x, z) * Back-scattered P to P reflection brad@sep. stanford. edu jeff@sep. stanford. edu 10

Stanford Exploration Project VSP Migration Converted reflection imaging Vp(x, z) and Vs (x, z) * p-wave s-wave Back-scattered P to S mode conversion brad@sep. stanford. edu jeff@sep. stanford. edu 11

Stanford Exploration Project VSP Migration Converted transmission imaging Vp(x, z) and Vs (x, z) * Forward-scattered P to S mode conversion brad@sep. stanford. edu jeff@sep. stanford. edu 12

Stanford Exploration Project VSP Migration 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 13

Stanford Exploration Project VSP Migration • Wavefield extrapolation • Shot-profile migration – Surface reflection – VSP experiment • Scattering modes – Reflection – Transmission • Deviated well geometries brad@sep. stanford. edu jeff@sep. stanford. edu 14

Stanford Exploration Project VSP Migration Deviated well geometries * brad@sep. stanford. edu jeff@sep. stanford. edu 15