第二代小波变换及其在地震信号去噪中的应用

Second generation wavelet transform and its application in the denoising of seismic data

（石油大学CNPC物探重点实验室，北京102249）

Key Laboratory of Geophysical Exploration, CNPC, University of Petroleum, Beijing 102249, China

第二代小波变换是从传统小波理论发展起来的一个分支，与第一代小波变换相比它有如下特点：① 继承了第一代小波的多分辨率特性；② 不依赖于傅里叶变换；③易实现快速算法；④ 逆变换易实现；⑤可实现非线性小波变换等。目前对第二代小波的研究还处于起步阶段，其应用主要是在图像处理领域。讨论了第二代小波变换的基本原理和变换过程，并将第二代小波变换引入到地震资料去噪处理中，通过对模拟数据和实际资料的处理，证明了它对地震信号去噪具有很好的效果。

Secondgeneration wavelet transform is a branch derived from traditional wavelet theory. Compared with the firstgeneration wavelet transform, its features include: ①keep the multiresolution feature of firstgeneration wavelet. ②Independent of Fourier Transform ③Fast arithmetic is easily to be achieved.④Reverse transform is easier.⑤Nonlinear wavelet transform is available, etc. At presently, the research for secondgeneration wavelet transform is on the earlier stage and its application is mainly limited to image processing field. The principle and procedures of secondgeneration wavelet transform and application in the denoising of seismic data are discussed in the paper. Examples on synthetic as well as field data prove that it is a new effective squelch method.