Regularized Low-Rank Approximation Method for Diffraction Enhancement

Abstract

The significance of seismic diffractions for the high-resolution imaging of subsurface discontinuities has been emphasized in recent years. Separating diffractions from strong specular reflected wavefields is a crucial process owing to the weak amplitude of diffractions. The low-rank characteristics of seismic data have been successfully implemented for diffracted wavefield isolation using rank-reduction methods. Traditional low-rank-based diffraction separation uses the optimal low-rank approximation of the Hankel matrix formulated from seismic data for predicting linear reflection events. However, without the Hankel structure in traditional low-rank approximation, the Hankel matrix of estimated reflections does not exhibit the expected low-rank properties, which may affect the predicted reflection accuracy. In this study, a regularized low-rank (RLR) approximation method that exploits the low-rank properties of reflection events and the corresponding Hankel structure was developed to enhance diffractions and eliminate reflections. The RLR approximation algorithm considered the low-rank constraint of the Hankel matrix for estimated reflections, leading to improved low-rank approximation. Synthetic and field examples were used to demonstrate the effectiveness of the proposed algorithm in separating diffractions and imaging small subsurface geological structures.