应用组稀疏正则化反演的高分辨率自适应Gabor时频分析方法

地震信号频率成分随时间的变化规律(时频特性)对油气检测具有重要意义,且Gabor变换作为最简便的时频分析技术在地震资料解释中得到了广泛应用。然而常规Gabor变换所得时频谱的时间分辨率低,相邻反射子波频谱信息混叠严重,不利于开展高分辨率地震资料解释。为了提高Gabor时频谱的时间分辨率,首先基于Gabor反变换的定义将Gabor时频谱的计算归结为求解反演问题; 然后以相同时刻频谱分入同一组的策略加入组稀疏正则化约束项; 最终利用投影快速软阈值迭代算法实现上述目标函数求解并获得Gabor时频谱。同时,还给出一种利用地震信号瞬时质心频率自适应地构造Gabor时频分析所需高斯窗函数的方法。理论信号实验及实际数据应用表明,该方法可在时间方向上对Gabor时频谱的能量团进行显著压缩,低频端和高频端的时间分辨率获得同步提高,进而在低频和高频剖面上同时清晰揭示薄储层顶、底界面,便于精细对比解释。

High-resolution self-adaptive Gabor time-frequency analysis method based on group-sparse regularized inversion

Time-varying property of the frequency components, i.e., the time-frequency characteristic, in seismic signals plays a significant role in hydrocarbon detection. The simplest time-frequency analysis technique,Gabor transform,has been widely used in seismic data interpretation. However,the time resolution of time-frequency spectra obtained via traditio-nal Gabor transform is poor because the spectra of adjacent reflection wavelets are seriously aliased with each other. This defect is unfavorable for high-resolution seismic data interpretation. To improve the time resolution of Gabor time-frequency spectra,we first express the calculation of a Gabor time-frequency spectrum as inversion problem solving according to the definition of inverse Gabor transform. Then,a group-sparse regularization constraint is introduced with the strategy of grouping the spectra of the same moment. Finally,the objective function is solved using the projected fast iterative soft-thresholding algorithm,and the Gabor time-frequency spectrum can be obtained. In addition,an adaptive method for constructing Gaussian window functions required by Gabor time-frequency analysis is developed with the instantaneous centroid frequency of the seismic signal. Theoretical signal tests and field data applications show that the proposed method can significantly compress the energy groups of Gabor time-frequency spectra in the time direction,simultaneously improve the time resolution of both low- and high-frequency components. Therefore,the top and bottom interfaces of thin reservoirs can be clearly revealed on both low- and high-frequency sections,which facilitates fine comparison and interpretation.