多小波方法及其在深地震测深数据去噪中的应用
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摘要
在宽角反射/折射地震测深数据处理中,仍多用基于傅里叶变换的滤波方法和小波去噪方法。鉴于傅里叶方法对稳态信号很有效但对非稳态的地震信号效果不佳的状况以及小波不能同时具有正交性、紧支性、对称性,本文给出了基于多小波的去噪方法,多小波具有正交性、对称性、紧支性,克服了传统小波的缺陷。编写了多小波去噪方法的人机交互软件。该软件可以方便快捷地显示宽角反射/折射地震记录截面,进行多小波域的阈值去噪。实例计算结果表明,本文所述方法和编写的软件有效且可行。
In wide angle reflection/refraction seismic sounding data processing, filtering and denoising methods based on Fourier transform and wavelet denoising method are still used. In view of the problem that there are inherent defects using the Fourier transform to process non-steady state seismic signal and that there not are the orthogonality, tight branch, and symmetry in wavelet transform at the same time, multi-wavelet denoising method is given, which has orthogonality, symmetry, compact, and overcomes the defect of traditional wavelet. Graphical user interface software is written based on the multi-wavelet in this paper. The software can show quickly and easily wide angle reflection/refraction seismic record section, can do adaptive threshold denoising in the multi-wavelet domain. Examples show that the methods and software in this paper are effective and feasible.
In wide angle reflection/refraction seismic sounding data processing, filtering and denoising methods based on Fourier transform and wavelet denoising method are still used. In view of the problem that there are inherent defects using the Fourier transform to process non-steady state seismic signal and that there not are the orthogonality, tight branch, and symmetry in wavelet transform at the same time, multi-wavelet denoising method is given, which has orthogonality, symmetry, compact, and overcomes the defect of traditional wavelet. Graphical user interface software is written based on the multi-wavelet in this paper. The software can show quickly and easily wide angle reflection/refraction seismic record section, can do adaptive threshold denoising in the multi-wavelet domain. Examples show that the methods and software in this paper are effective and feasible.
引文
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[16]樊计昌,刘明军,王夫运,等.小波包节点域和空间域倾角扫描高阶相关去噪技术[J].石油地球物理勘探,2009,44(6):695-699.Fan JC,Liu MJ,Wang FY,et al.Denoise by dip-angle sweeping higher-order correlation in wavelet-packets node and space domains[J].Oil Geophysical Prospecting,2009,44(6):695-699.
[17]Donoho DL,Jonstone IM.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994(81):425-455.
[18]刘英霞,王欣.最佳软门限去噪[J].电子学报,2006,34(1):167-169.Liu YX,Wang X.Optimal soft thresholding for signal denoising[J].Acta Electronica Sinica,2006,34(1):167-169.
[2]张军华,吕宁,田连玉,等.地震资料去噪方法综合评述[J].石油地球物理勘探,2005,40(S1):121-127.Zhang JH,Lv N,Tian LY,et al.Review on denoise for seismic data[J].Oil Geophysical Prospecting,2005,40(Sl):121-127.
[3]付燕.人工地震信号去噪方法研究[D].西安:西北工业大学,2002.Fu Y.Study on denoise for seismic signal[D].Xi'an:Northwestem Polytechnic University,2002.
[4]崔丽鸿,程正兴.多小波和平衡多小波的理论和设计[J].工程数学学报,2001,18(5):105-116.Cui LH,Cheng ZX.Multiwavelet and balanced multiwavelet theory and design[J].Journal of Engineering Mathematics,2001,18(5):105-116.
[5]Donoho DL.De-noising by soft thresholding[J].IEEE Tram on IT,1995,41(3):613-627.
[6]赵瑞珍.小波理论及其在图像、信号处理中的算法研究[D].西安:西安电子科技大学,2001.Zhao RZ.Wavelet theory and algorithm for image and signal processing[D].Xi'an:Xidian University,2001.
[7]Bruce AG,Gao HY.1995b understanding wave Shrink:Variance and Bias estimation[J].Technical Report,Stat Sci Division,Math Soft,Inc,1700 Westlake Ave.N,Seattle,WA98109-9891.
[8]Goodman TN,Lee SL,Tang WS.Wavelets in wandering snbspaces[J].Trans.American Math Soc,1994,338:639-654.
[9]Geronimo JS,Hardin DP,Massopust PR.Fractal functions and wavelet expansions based on several scaling functions[J].Journal of Approximation Theory,1994,78:373-401.
[10]阎晓红,刘贵忠,刘峰.分形信号的多小波基表示[J].自然科学进展,2004,14(3):453-458.Yan XH,Liu GZ,Liu F.Multi-wavelet base representation of fractal signal[J].Natural Science Progress,2004,14(3):453-458.
[11]程正兴,张玲玲.多小波分析与应用[J].工程数学学报,2001,18(1):99-107.Cheng ZX,Zhang LL.Multi-wavelet analysis and application[J].Journal of Engineering Mathematics,2001,18(1):99-107.
[12]Cotronei M,Montefusco LB,Puccio L.Multi-wavelet analysis and signal preprocessing[J].IEEE Trans.Circuits SystⅡ,1998,45:970-987.
[13]张随征,张建宇,高立新,等.面向一维信号分析的多小波预处理方法研究[J].机械设计与制造,2012,52(10):91-93.Zhang SZ,Zhang JY,Gao LX,et al.Research on multiwavelet preprocessing methods for one dimensional signal analysis[J].Machinery Design&Manufacture,2012,52(10):91-93.
[14]刘志刚,何正友,钱清泉.多小波的研究进展及其在电力系统中应用的展望[J].电力系统自动化,2004,28(11):90-96.Liu ZG,He ZY,Qian QQ.The research progress of multi-wavelet and its application prospect in the power system[J].Power System Automation,2004,28(11):90-96.
[15]樊计昌,王夫运,刘明军,等.小波尺度域和空间域倾角扫描高阶相关去噪技术[J].石油地球物理勘探,2008,43(5):514-517.Fan JC,Wang FY,Liu MJ,et al.Denoise by dip-angle sweeping higher-order correlation in wavelet scale and space domains[J].Oil Geophysical Prospecting,2008,43(5):514-517.
[16]樊计昌,刘明军,王夫运,等.小波包节点域和空间域倾角扫描高阶相关去噪技术[J].石油地球物理勘探,2009,44(6):695-699.Fan JC,Liu MJ,Wang FY,et al.Denoise by dip-angle sweeping higher-order correlation in wavelet-packets node and space domains[J].Oil Geophysical Prospecting,2009,44(6):695-699.
[17]Donoho DL,Jonstone IM.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994(81):425-455.
[18]刘英霞,王欣.最佳软门限去噪[J].电子学报,2006,34(1):167-169.Liu YX,Wang X.Optimal soft thresholding for signal denoising[J].Acta Electronica Sinica,2006,34(1):167-169.
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