Effective diffraction separation using the improved optimal rank-reduction method

Seismic diffractions encoding subsurface small-scale geologic structures have great potential for high-resolution imaging of subwavelength information. Diffraction separation from the dominant reflected wavefields still plays a vital role because of the weak energy characteristics of the diffractions. Traditional rank-reduction (RR) methods based on the low-rank assumption of reflection events have been commonly used for diffraction separation. However, these methods using truncated singular-value decomposition (TSVD) suffer from the problem of reflection-rank selection by singular-value spectrum analysis, especially for complicated seismic data. In addition, the separation problem for the tangent wavefields of reflections and diffractions is challenging. To alleviate these limitations, we have developed an effective diffraction separation strategy using an improved optimal RR (ORR) method to remove the dependence on the reflection rank and improve the quality of separation results. The improved RR method adaptively determines the optimal singular values from the input signals by directly solving an optimization problem that minimizes the Frobenius-norm difference between the estimated and exact reflections instead of the TSVD operation. This improved method can effectively overcome the problem of reflection-rank estimation in the global and local RR methods and adjusts to the diversity and complexity of seismic data. The adaptive data-driven algorithms indicate good performance in terms of the trade-off between high-quality diffraction separation and reflection suppression for the ORR operation. Applications of our strategy to synthetic and field examples demonstrate the superiority of diffraction separation in detecting and revealing subsurface small-scale geologic discontinuities and inhomogeneities.