Seismic spectrum decomposition based on sparse time-frequency analysis

Abstract

Time-frequency analysis is widely used in many engineering fields. However, the traditional time-frequency analysis methods suffer from issues such as low resolution or the interference of cross terms. To solve the above issues, this paper proposes a sparse time-frequency analysis by using an L1-norm constraint, fitting the sparse prior of a signal's spectrum. This process begins with the relationship between the sparse spectrum and the short-time measurement in order to propose the short-time sparse spectrum inversion model. Then, the first-order primal-dual method is employed to solve the proposed model. In this way, the reconstructed spectrum is constrained to be sparse. On the one hand, the concentration of the proposed algorithm is high due to the adoption of the L1-norm constraint. On the other hand, cross terms are avoided because the proposed method is based on the short-time Fourier transform and convex optimization technology. To show the performance of the proposed method, experiments based on both the theoretical signal and the real seismic signal are then conducted and compared with state-of-the-art time-frequency methods. The results show that the proposed method can obtain more accurate time-frequency distributions than other algorithms. Finally, we apply the proposed method in the decomposition of a seismic signal spectrum. The experiments show that the proposed method is capable of obtaining high-resolution frequency slices and more precisely exploring the spatial distribution of a reservoir than traditional time-frequency methods.