Translations:Mathematical foundation of 3-D migration/54/en
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Methods to obtain hn such that the actual Fourier transform H(k) given by equation (G-17) closely approximates the actual Fourier transform D(k) given by equation (G-16) is described by Holberg [1] and Hale [2]. The former is based on least-squares and the latter is based on a modified Taylor series. The Hale method is described in Section D.5. Since the desired amplitude spectrum is |D(k)| = 1 for all k, then we require the actual amplitude spectrum to be |H(k)| ≤ 1 for all k. This will ensure that the operator is stable — that is, amplitudes of the extrapolated wavefield will not grow from one depth level to another.