A rigorous, explicit spatial antialias filter is designed and applied to spatially coarsely sampled seismic data by removing all energy above the first Nyquist wavenumber, and aliased energy that is folded back across the Nyquist, in the horizontal slowness-frequency domain. The spatial filtering in the slowness-frequency domain is explicit, free from any event linearity assumption, and does not require any interpolation. The spatially aliased energy is dispersive, and present at small and large slownesses. Comparison of the output data after antialias spatial filtering, with output data after conventional antialias frequency filtering, shows that the filter removes the spatially aliased frequencies selectively at each slowness; antialias low-pass frequency filtering under-or overcorrects for spatial aliasing at all slownesses. A seismic gather can be spatially dealiased only at the expense of wavelet spectral changes; dealiasing and preservation of amplitude variations with offset are not simultaneously possible.
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