用提升法小波分析进行地震信号的噪声衰减
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摘要
提升小波的基本思想是建立在双正交小波和完全可恢复滤波器组的理论基础上,在保持小波双正交特性的条件下,通过所谓提升和对偶提升过程,来改善小波及其对偶的性能,以满足各种应用的需要。文章简单介绍了基于提升方案小波分析的基本原理和方法,建立了一维和二维地震信号进行提升小波分解和重构的基本流程,分析了提升法小波变换相对于第一代小波变换的各种优点,最后结合具体实例,将基于提升格式的小波变换与重构用于地震数据的噪声压制。根据噪声与信号的特点,在小波低频与高频系数中分别采用不同的软阈值进行量化处理,取得了较好的压噪效果,提高了地震资料的信噪比。实际资料的应用效果表明,该方法易于实现,计算效率高,具有较好的应用前景。
The basic concept of wavelet lift is based on the dual orthogonal wavelet and complete recoverable filter bank theories. It is to improve wavelets and their duality to meet the requirements of various applications through the so-called lifting and dual lifting while keeping the dual orthogonality of wavelet. This paper briefly introduces the basic principles and methodologies of lifting wavelet analysis, establishes the basic flow charts for decomposition and reconstruction of lifting wavelet of 1D and 2D seismic signals, and analyzes the advantages of lifting wavelet transformation vs. wavelet transformation of the first generation. Finally, application of lifting wavelet transformation and reconstruction in noise suppression of seismic data is introduced in combination with the specific examples. According to the characteristics of noise and signal, different soft thresholds are used in the low frequency and high frequency coefficients of wavelet domain respectively for quantitative processing. The effect of noise suppression is good and the signal-to-noise ratio is improved. Application to real data shows that this method is characterized by easy realization and high calculation efficiency, thus it has a good prospect of application.
The basic concept of wavelet lift is based on the dual orthogonal wavelet and complete recoverable filter bank theories. It is to improve wavelets and their duality to meet the requirements of various applications through the so-called lifting and dual lifting while keeping the dual orthogonality of wavelet. This paper briefly introduces the basic principles and methodologies of lifting wavelet analysis, establishes the basic flow charts for decomposition and reconstruction of lifting wavelet of 1D and 2D seismic signals, and analyzes the advantages of lifting wavelet transformation vs. wavelet transformation of the first generation. Finally, application of lifting wavelet transformation and reconstruction in noise suppression of seismic data is introduced in combination with the specific examples. According to the characteristics of noise and signal, different soft thresholds are used in the low frequency and high frequency coefficients of wavelet domain respectively for quantitative processing. The effect of noise suppression is good and the signal-to-noise ratio is improved. Application to real data shows that this method is characterized by easy realization and high calculation efficiency, thus it has a good prospect of application.
引文
[1]SWELDENSW.Theliftingscheme:Aconstructionof secondgenerationwavelets[R].DepartmentofMathe matics,UniversityofSouthCarolina,1995.
[2]MALLATSG.Atheoryformultiresolutionsignalde composition:Thewaveletrepresentation[J].IEEETrans onPAMI,1989,11(7):927938.
[3]DAUBECHIESI,SWELDENSW.Factoringwavelet transformsintoliftingsteps[J].JFourierAnalApp,1998,4(3):245267.
[4]姜弢,刘庆普,胡留军.地震信号去噪的小波方法研究[J].哈尔滨工程大学学报,2002,23(4):8690.
[5]陈科贵,高伟,利霞,等.小波分析在测井储层识别和划分中的应用[J].天然气工业,2005,25(7):3840.
[6]王长龙,傅君眉,徐章遂,等.天然气管道漏磁检测中的信号处理[J].天然气工业,2005,25(6):100101,112.
[7]DONOHODL.De noisingbysoftthresholding[J].IEEE TransOnInformationTheory,1995,41(3):613627.
[2]MALLATSG.Atheoryformultiresolutionsignalde composition:Thewaveletrepresentation[J].IEEETrans onPAMI,1989,11(7):927938.
[3]DAUBECHIESI,SWELDENSW.Factoringwavelet transformsintoliftingsteps[J].JFourierAnalApp,1998,4(3):245267.
[4]姜弢,刘庆普,胡留军.地震信号去噪的小波方法研究[J].哈尔滨工程大学学报,2002,23(4):8690.
[5]陈科贵,高伟,利霞,等.小波分析在测井储层识别和划分中的应用[J].天然气工业,2005,25(7):3840.
[6]王长龙,傅君眉,徐章遂,等.天然气管道漏磁检测中的信号处理[J].天然气工业,2005,25(6):100101,112.
[7]DONOHODL.De noisingbysoftthresholding[J].IEEE TransOnInformationTheory,1995,41(3):613627.
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