Sparse Bayesian Learning-Based Seismic High-Resolution Time-Frequency Analysis

Abstract

Time-frequency (TF) analysis is a useful tool for seismic data processing and interpretation. We introduce sparse Bayesian learning (SBL) to TF analysis and propose a new SBL-based high-resolution TF method. The method decomposes the seismic trace into a series of Ricker wavelets using SBL-based sparse representations and subsequently implements Wigner-Ville distribution (WVD) on the decomposed wavelets to produce TF spectra. By iteratively solving a Bayesian maximum posterior and a type-II maximum likelihood, SBL-based decomposition can sequentially obtain an optimal number of Ricker wavelets with different peak frequencies or phases from a preset wavelet dictionary, and can simultaneously invert for the associated sparse TF pseudoreflectivity with the prediction uncertainty. The WVD of SBL-based decomposed wavelets can assemble TF distribution of the reconstructed signals to approximately characterize WVD of the original data. Therefore, the linear stack of WVD of all decomposed independent wavelets is immune from both the notorious cross-term interferences of the traditional WVD and random noise. Synthetic data example involving thin beds and laboratorial physical modeling data example involving several known multicave combinations are used to demonstrate the effectiveness of the proposed SBL-based TF analysis method and illustrate its advantages over WVD and the orthogonal matching pursuit-based TF analysis method. The 3-D real seismic data example is adopted to test its application potential for interpreting deep channels and the karst slope fracture zone. The results show that the proposed SBL-based TF method is a potentially effective, stable and high-resolution seismic TF analysis tool even in the presence of thin beds.