F‐xy eigenimage filtering works by replacing constant‐frequency slices with the sum of their first few weighted eigenimages, and can be used to remove random noise from stacked 3D seismic volumes. It performs equally well on flat or dipping events, and has no effect on noiseless data when the number of dips is no more than the number of summed eigenimages. It is also independent of many x‐ and y‐consistent effects such as reordering, statics, and filtering. One consequence is that it tends to do a good job along the boundaries of the 3D grid. Execution time is comparable to f‐xy prediction filtering, but can be greatly reduced using approximations based on Lanczos bidiagonalization.

In previous papers we described a family of multidimensional filters to suppress random noise based on matrix-rank reduction of constant-frequency slices. Here we extend these filters to perform multidimensional trace interpolation. This requires rank reduction when some, perhaps most, of the matrix elements are unknown, a procedure called matrix completion or matrix imputation. We show how this new interpolator improves the spatial resolution of 3D data when applied prior to prestack migration.

Cadzow filtering has previously been applied along constant-frequency slices to remove random noise from 2-D seismic data. Here I extend Cadzow filtering to two or more spatial dimensions. The resulting method is superior to both f-xy prediction (deconvolution) and projection filtering, especially for very noisy data. In particular, it preserves signal better and can be made much harsher.

Rank-reduction filters operating on constant-frequency slices are highly effective at removing Gaussian random noise. Prestack seismic data, however, often contains spatially erratic noise which is far from Gaussian, sometimes causing these filters to give poor results. Here we describe new robust rank-reduction filters which can handle both Gaussian and erratic noise, and we present examples using synthetic and real data.

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