中文摘要：

提出了一种基于分数域自适应滤波的地震信号去噪方法.先论述了分数阶傅立叶变换（FrFT）的基本原理及分数域滤波的采样与信号重构定理.根据FrFT具有时频旋转特性,分析了时频域信噪重叠情况下实现噪声分离的可行性.通过时频面旋转交互方式求取最佳阶数以及滤波器的带宽,最后利用理想信号与处理结果的相关系数来验证该方法的有效性.合成记录及实际资料的处理结果表明,分数域滤波与常规Fourier变换相比,具有良好的去噪性能,可有效解决时频域信噪重叠的信噪分离难题,达到信号保真与去除噪声的目的.

英文摘要：

The paper presents a de-noising method of seismic signal based on adaptive filtering in fractional domain. Firstly, we introduce the fundamental principals of the fractional Fourier transform （FrFT） theory and describe the sampling and reconstruction theorem in fractional domain. According to the rotational attribute of FrFT, we analyze the feasibility of separating signals and noises, which overlapped both in time and frequency domain. The optimal order of the FrFT and the bandwidth in the fractional domain can be obtained by interactive approach. Finally, we validate it by calculating the correlation coefficient between the ideal signals and filtered signals. Several illustrative results of the synthetic data and real data verify that filtering in fractional domain posses better performance, compared with ordinary Fourier domain filtering. The proposed method can solve the difficult how to effectively remove noise from signals when coupling in t-f domain and also can keep the good fidelity after de-noising.