基于正则化理论的时频分析方法及应用
A regularization theory-based method for time-frequency analysis and its applications
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摘要: 时频分析方法在地震勘探中有广泛的应用,因而获得具有良好时频分辨率的时频分析算法至关重要。传统的时频分析方法存在着一定的局限性,为克服这些局限性,提出了基于正则化理论的时频分析方法。该方法认为,短时窗信号是不同频率谐波的叠加,应从求解反问题的角度考察时频分析问题。在此视角下,时频分析问题具有不适定性,为得到有意义的时频谱,需要在正则化理论框架下进行时频分析。考察了正则化理论中常用的L1范数约束、L2范数约束以及最小支撑约束条件下的求解方法,并将3种约束函数的求解方法统一到同一个求解框架中。通过数值分析表明,最小支撑约束的时频分析方法具有较高的时频分辨率。将方法系统应用于一个特定研究区的实际资料,获得了具有较高时频分辨率的时频数据体,并利用单频数据体清晰刻画了储层的平面展布范围,展示了方法良好的应用前景。Abstract: Time-frequency analysis (TFA) has been widely used in seismic exploration,thus it is crucial to develop a TFA algorithm with high time-frequency resolution.Given the limitations of conventional TFA methods,this study proposed a TFA method based on the regularization theory.The proposed method considers the signal in a short-time window as a superposition of harmonics with different frequencies and takes the TFA problem as an inverse problem.From this perspective,the TFA problem is ill-posed and needs to be solved based on the regularization theory to get a significant time-frequency spectrum.The solution methods under the conditions of L1 and L2 norm constraints and the minimum support constraint are commonly used in the regularization theory.This study investigated these solution methods and unified them into the same solution framework.Numerical analysis shows that the TFA method under the condition of the minimum support constraint yielded high time-frequency resolution.This method was systematically applied to the actual data of a specific study area,producing a time-frequency data volume with high time-frequency resolution.Moreover,the planar reservoir distribution was clearly characterized using a single-frequency data volume,demonstrating the promising application prospect of the method.
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