Kirchhoff Inversion in Image Point Coordinates Recast as Source/Receiver Point Processing

Kirchhoff inversion theory tells us that reflection data provides information about the Fourier transform of the reflectivity function at each point in the illuminated subsurface. Thus, inversion formulas expressed as integrals in image point coordinates that closely characterize that Fourier domain are attractive for their relative simplicity. On the other hand, integrals over source/receiver coordinates are more natural to implement on seismic data. We propose a general principle for seismic migration/inversion (MI) processes: think image point coordinates; compute in surface coordinates. This principle allows the natural separation of multiple travel paths of energy from a source to a reflector to a receiver. Furthermore, the Beylkin determinant is particularly simple in this formalism, and transforming to surface coordinates transforms deconvolution-type imaging and inversion operators into convolution-type operators with the promise of better numerical stability.