High-resolution time-frequency analysis based on l1-l2 norm and its application

In this paper, we proposed a sparse time-frequency analysis method based on the l(1)-l(2) norm to improve the accuracy of the time-frequency analysis. To enhance the resolution of time-frequency spectrum, sparse constraint-based time-frequency analysis methods apply inverse transform of time-frequency analysis to construct inversion equation and use sparse norm to constrain the spectrum of each time point. Representative constraints include l(1) norm and l(p) norm. In recent years, the l(1)-l(2) norm has been proved to be more sparse than the l(p) norm, which is widely used in seismic data processing, resolution enhancement, and inversion. Based on the compressive sensing, we applied the l(1)-l(2) norm to constraint the spectrum and solved the inversion problem using Alternating Direction Method of Multipliers (ADMM). Then the high-resolution time-frequency analysis based on the l(1)-l(2) norm will be obtained, which can be used to extract the dispersion parameters. Synthetic tests demonstrate that the proposed time-frequency analysis method has higher time-frequency concentration and better noise resistance. Application to field data shows that combining with the proposed method and P-wave dispersion parameters, we can clearly describe the scope of the reservoir and accurately indicate the gas reservoir.