基于l_(1)-l_(2)范数的高分辨率时频分析方法及应用

High-resolution time-frequency analysis based on l_(1)-l_(2) norm and its application

本研究提出一种基于l_(1)-l_(2)范数的稀疏约束类时频分析方法,以提高信号时频分析的精度.稀疏约束类时频分析方法通过窗口类时频分析的逆变换构造反演方程,使用稀疏范数约束每个时间点的频谱,从而提高时频谱的分辨率;常用约束包括l_(1)范数、l_(p)范数等,近几年l_(1)-l_(2)范数被证明稀疏约束能力强于l_(p)范数,被广泛的应用于地震数据处理高分辨率、反演等问题中.本文基于压缩感知理论,使用l_(1)-l_(2)范数约束频谱,基于交替方向乘子法(ADMM)进行反问题的求解,得到基于l_(1)-l_(2)范数的高分辨率时频分析方法,并将其应用于地震频散属性的计算中.模型分析表明,本研究提出的基于l_(1)-l_(2)约束时频分析具有高时频聚焦性,高抗噪性,适用于地震信号的时频分析.实际数据表明,基于l_(1)-l_(2)范数的时频分析具备高时频分辨率,联合纵波频散属性,使得该方法可以清晰刻画储层的范围,准确指示气藏.

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.