Seismic trace interpolation in the Fourier transform domain

A data adaptive interpolation method is designed and applied in the Fourier transform domain (f-k or f-k(x)-k(y)) for spatially aliased data. The method makes use of fast Fourier transforms and their cyclic properties, thereby offering a significant cost advantage over other techniques that interpolate aliased data. The algorithm designs and applies interpolation operators in the f-k (or f-k(x)-k(y)) domain to fill zero traces inserted in the data in the t-x (or t-x-y) domain at locations where interpolated traces are needed. The interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data. This operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies, and corresponds to the f-k (or f-k(x)-k(y)) domain version of the well-known f-x (or f-x-y) domain trace interpolators. The Method is applicable to 2D and 3D data recorded sparsely in a horizontal plane. The most common prestack applications of the algorithm are common-midpoint domain shot interpolation, source-receiver domain shot interpolation, and cable interpolation.