Robust low-rank diffraction separation and imaging by CUR matrix decomposition

Diffractions from underground discontinuities, which appear as common wavefields in seismic records, contain rich geologic information regarding small-scale structures. As a result of their weak amplitude characteristics, a key preliminary task in imaging subsurface inhomogeneities using seismic diffractions is to simultaneously eliminate strong reflections and separate weak diffractions. Traditional low-rank diffraction separation methods predict linear reflections and separate diffractions by applying a low-rank approximation, such as truncated singular value decomposition (TSVD). However, these methods require the accurate estimation of the rank, which influences the separation and imaging quality of diffractions. A robust low-rank diffraction separation method is developed using CUR matrix decomposition rather than the TSVD calculation to avoid the rank estimate. CUR matrix decomposition expresses a data matrix as a product of the matrices C, U, and R by randomly selecting a small number of actual columns and rows from the matrix to achieve a low-rank approximation. A near-optimal sampling algorithm is used to randomly select columns and rows from the Hankelmatrix and calculate the CUR decomposition. Oversampling of columns and rows effectively eliminates the requirement for an accurate rank. Moreover, synthetic and field applications demonstrate the good performance of our CUR-based diffraction separation method in attenuating reflections and highlighting diffractions.