Seismic signal sparse time-frequency analysis by Lp-quasinorm constraint
For geophysicists and reservoir engineers, this method enhances seismic signal analysis for better reservoir exploration, though it is an incremental improvement over existing sparse time-frequency approaches.
The authors propose a sparse time-frequency analysis model using Lp-quasinorm constraint to improve resolution and reduce cross-term interference, achieving higher time-frequency distribution than state-of-the-art methods in seismic signal decomposition.
Time-frequency analysis has been applied successfully in many fields. However, the traditional methods, like short time Fourier transform and Cohen distribution, suffer from the low resolution or the interference of the cross terms. To solve these issues, we put forward a new sparse time-frequency analysis 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 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 Lp-quasinorm feasible domain, the proposed model is established. The alternating direction method of multipliers (ADMM) is adopted to solve the proposed model. Experiments are then conducted on several theoretical signals and applied to the seismic signal spectrum decomposition, indicating that the proposed method is able to obtain a higher time-frequency distribution than state-of-the-art time-frequency methods. Thus, the proposed method is of great importance to reservoir exploration.