摘要
We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.
本文利用分数阶傅里叶变换(FrFT)的时频旋转性,设计基于广义时间带宽积准则的最优窗函数,从而实现自适应分数域最优Gabor变换,达到提高时频聚集性的目的。该算法首先找到最优旋转因子,然后对信号做该阶次下的FrFT,将经过FrFT后的信号做频谱成像,最后反方向旋转到原时频位置,从而解决了时频轴在旋转中失去物理意义的问题,这将推进FrFT在高精度储层预测领域的应用。另外,本文从分数域Parseval定理角度提出一种自适应搜索最优旋转因子的方法,降低了算法整体运算复杂度。地震信号谱分解结果表明本文算法获得的谱分解瞬时频率切片显著优于传统Gabor变换。这种自适应时频分析对于复杂地震信号处理具有重大意义。
基金
supported by national natural science foundation of China(No.41274127,41301460,40874066,and 40839905)
