Seismic signal sparse time–frequency representation by Lp-quasinorm constraint

Abstract

Time–frequency representation has been applied successfully in many fields. However, the traditional methods, like short time Fourier transform and Cohen distributions, commonly suffer from the low resolution or the interference of the cross terms. To solve these issues, we put forward a new sparse time–frequency representation model by using the Lp-quasinorm constraint, which is capable of fitting the sparsity prior knowledge in the frequency domain. In the proposed model, we regard the short time truncated data as the observation of the sparse representation and design a dictionary matrix, which builds up the relationship between the short time measurement and the sparse spectrum. Based on the relationship and the sparsity constraint described by the Lp-quasinorm, the sparse time–frequency representation model is established. The alternating direction method of multipliers (ADMM) is adopted to solve the proposed model. Experiments are then conducted on several synthetic signals and applied to a seismic signal and a seismic profile crossing the gas reservoir. These examples indicate that the proposed method is able to obtain a time–frequency distribution with higher resolution than state-of-the-art time–frequency methods. Thus, the proposed method is of great importance to seismic exploration.