# Translations:Mathematical foundation of 3-D migration/54/en

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Methods to obtain *h _{n}* 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.