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

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 + Δx/2, where D is the desired output array and Δx/2 is the prediction lag .