# Translations:Mathematical foundation of 3-D migration/101/en

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Now, we want to design a complex Wiener prediction filter to interpolate data in the spatial direction. Consider a CMP-stacked data set *P*(*x, t*), where *x* is the CMP axis and *t* is the two-way zero-offset time axis. Apply Fourier transform in the *t* direction to decompose this 2-D data set to its frequency components *P*(*x, ω*). For each frequency component, define a complex array **P** : *P*(*x, ω*) in the *x* direction. Specifically, we want a filter **F** : *F*(*x*) such that, when applied to the input data array **P** : *P*(*x, ω*), it yields an estimate of the input array **D** : *P*(*x + Δx*/2, *ω*), at *x* + Δ*x*/2, where **D** is the desired output array and Δ*x*/2 is the prediction lag ^{[1]}.

- ↑ Spitz, 1991, Spitz, S., 1991, Seismic trace interpolation in the
*f − x*domain: Geophysics, 56, 785–794.