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MIGRATION IN TERMS OF SPATIAL DECONVOLUTION *
Author(s) -
BERKHOUT A. J.,
PALTHE D. W. VAN WULFFTEN
Publication year - 1979
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1979.tb00970.x
Subject(s) - extrapolation , deconvolution , convolution (computer science) , limit (mathematics) , wavelet , mathematical analysis , mathematics , sampling (signal processing) , algorithm , geology , computer science , physics , optics , machine learning , artificial intelligence , detector , artificial neural network
A bstract 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.