5D Interpolation
Rank-Reduction-Based Interpolation
Multidimensional filters can be used to suppress random noise based on matrix-rank reduction of constant-frequency slices. We have extended 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 use a strategy called matrix-rank reduction (see, for example, Trickett, 2003), also called truncated singular-value decomposition, principal-component analysis, subspace filtering, and many other names. This new interpolator can be used to improve the spatial sampling of pre-stack seismic data, thus improving the resolution of the final seismic section. It seems particularly effective at suppressing the acquisition footprint.
Common-offset-vector gather before 5D interpolation
After 5D interpolation