Robust Seismic Attenuation Compensation Based on Generalized Minimax Concave Penalty Sparse Representation

Abstract Deep hydrocarbon resources have become more and more important nowadays. However, owing to the affection of long-distance propagation and stratigraphic absorption, seismic data coming from deep beds generally suffer from weak energy, low resolution, and low signal-to-noise ratio (SNR), which seriously influence the reliability of seismic interpretation. Generally, inverse Q (quality factor) filtering (IQF) is used for absorption compensation, but it may amplify noise at the same time. Although compensation methods based on inversion overcomes the instability, it is still difficult to obtain high-SNR results. To address this issue, under the framework of sparse representation theory, we proposed a single-channel attenuation compensation method constrained by generalized minimax concave (GMC) penalty function. It takes the modified Kolsky model to describe seismic absorption and combines sparse representation theory to create objective function. Furthermore, a GMC penalty function is utilized to promote sparsity. It allows more accurate estimates of sparse coefficients from noise-contaminated seismic data. Although the GMC penalty itself is concave, the objective function remains strictly convex. Therefore, globally optimal sparse solutions can be obtained through an operator-splitting algorithm. Even in the presence of noise, this method can obtain stable and accurate compensation results through reconstruction. Synthetic data tests and field seismic data application showed that this method has high robustness to noise. It can stably and effectively compensate for the energy loss of seismic data, as well as maintain high SNR.