基于局部频率的W变换方法  

W-transform based on local frequency

作　　者：武国宁[1] 周鑫 郑意腾 张子昂 顾亚鑫 吴春勇 WU Guoning;ZHOU Xin;ZHENG Yiteng;ZHANG Ziang;GU Yaxin;WU Chunyong(College of Science,China University of Petroleum(Beijing),Beijing 102249,China)

机构地区：[1]中国石油大学(北京)理学院,北京102249

出　　处：《石油地球物理勘探》2025年第1期177-184,共8页Oil Geophysical Prospecting

基　　金：油气资源与工程全国重点实验室项目“基于深度学习的地震信号检测及其应用研究”(PRP/DX‑2305)的资助。

摘　　要：时频分析是一种能够揭示信号频谱随时间变化规律的重要方法,在地震信号处理和特征分析等领域具有重要意义。为提高时频分析的精度,文中提出了一种基于局部频率的W变换时频分析方法。该方法借助局部频率获得信号的平滑主频率,然后将该平滑主频率应用于W变换,进而得到信号的时频谱。通过局部频率对主频率进行平滑处理,有效减少了噪声的干扰,获得更为精确的主频率,从而提高了时频分析的可靠性。与传统的S变换相比,这种基于局部频率的W变换在一定程度上克服了高频段的频散现象,在低频段能够获得更高的时间分辨率。相较于W变换,该方法使信号的频谱能量更好地聚集在能量中心,具有较好的聚焦性。引入局部频率对W变换进行改进,提高了时频分析的精度。最后,本文通过数值试验验证了方法的有效性和优越性。Time‑frequency analysis is an important method that reveals the change regularity of signal spectrum over time.It is of great significance in the fields of seismic signal processing and feature analysis.To improve time‑frequency analysis accuracy,this paper proposes a time‑frequency analysis method based on local frequency by using the W‑transform.The method uses local frequency to obtain the smooth dominant frequency of the signal,which is then applied to the W‑transform to obtain the time‑frequency spectrum of the signal.By smoothing the dominant frequency using the local frequency approach,this method effectively reduces the impact of noise,yielding a more accurate dominant frequency and improving the reliability of time‑frequency analysis.In comparison to the traditional S‑transform,this W‑transform based on local frequencies partially overcomes dispersion at high frequencies and achieves higher time resolution at low frequencies.Compared with the W‑transform,this method makes the spectral energy of the signal better concentrated in the energy center,having better focusing capability.The introduction of local frequencies enhances the W‑transform,contributing to increased accuracy in time‑frequency analysis.Finally,the effectiveness and superiority of the method are validated through numerical experiments.

关 键 词：时频分析 W 变换 局部频率 频散 低频阴影 

分 类 号：P631[天文地球—地质矿产勘探]