MIGRATION IN TERMS OF SPATIAL DECONVOLUTION*

Publisher Website
Google Scholar
Abstract
The relationship between two finite‐difference schemes (15° and 40°) and the Kirchhoff summation approach is discussed by using closed form solutions of Claerbout's approximate versions of the wave equation. Forward extrapolation is presented as a spatial convolution procedure for each frequency component. It is shown that downward extrapolation can be considered as a wavelet deconvolution procedure, the spatial wavelet being given by the wave theory. Using this concept, a three‐dimensional model for seismic data is proposed.The advantages of downward extrapolation in the space‐frequency domain are discussed.Finally, it is derived that spatial sampling imposes an upper limit on the aperture and a lower limit on the extrapolation step.