Fourier Reconstruction of Nonuniformly Sampled, Aliased Seismic Data

There are numerous methods for interpolating uniformly sampled, aliased seismic data, but few can handle the combination of nonuniform sampling and aliasing. We combine the principles of Fourier reconstruction of nonaliased, nonuniformly sampled data with the ideas of frequency-wavenumber (f-k) interpolation of aliased, uniformly sampled data in a new two-step algorithm. In the first step, we estimate the Fourier coefficients at the lower nonaliased temporal frequencies from the nonuniformly sampled data. The coefficients are then used in the second step as an a priori model to distinguish between aliased and nonaliased energy at the higher, aliased temporal frequencies. By using a nonquadratic model penalty in the inversion, both the artifacts in the Fourier domain from nonuniform sampling and the aliased energy are suppressed. The underlying assumption is that events are planar; therefore, the algorithm is applied to seismic data in overlapping spatiotemporal windows.

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