基于MATLAB的小波分析用于地震信号的去噪研究
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摘要
信号与信号处理是近二十年来发展最为迅速的学科，而信号去噪是信号处理中最常见的处理过程，经典的信号去噪方法如纯时域法，纯频域法，Fourier变换，等各自都有其应用的局限性。傅里叶变换是一种全局变换，即对信号的表征要么在时域，要么在频域。作为频域表示的频谱或功率谱并不能告诉我们其中的某种频率分量出现在什么时候以及它的变化情况，所以这对于非平稳信号的处理来说是远远不够的。
小波变换作为一种出色的数学分析工具，在很多工程应用领域已经取代传统傅里叶变换的作用。因为小波变换的时间－尺度分析方法具有多分辨率的特点，所以它在时间和频率域都具有良好的局部化性质，它可以对任何频率成分进行精细的描述，有“数学显微镜”之称。本文旨在探讨小波变换理论，并结合专业中的地震信号去噪展开研究。
本文以小波变换为核心，并对其原理做出了深入的分析。不仅包括连续小波，离散小波，多分辨率分析方法还包括与传统傅氏变换的对比，从而在理论上明确其性能特点的优越性。在对信号噪声特点研究的基础上，特别是地震信号的噪声特点，分析研究了小波去噪的过程框图。对于信号去噪过程中的分解重构进行了理论讲述，并采用二次函数和反正切函数的组合方法，构造出新的阈值函数，用matlab模拟实验仿真，结果表明，新的阈值函数达到的去噪效果比常用的几种阈值函数的去噪效果好，可以用于地震信号去噪的处理与分析。
Signal and signal processing is the fastest growing disciplines in the last twodecades, signal de-noising is the most common signal processing process, the classicsignal de-noising methods, such as pure time-domain method, pure frequency domainmethod, Fourier transform, etc. , each has its application limitations. The Fouriertransform is a global transformation, that is, the characterization of the signal either inthe time domain or frequency domain. Expressed as a frequency domain spectrum orpower spectrum, frequency domain does not tell us of a certain frequency componentsappear at what time and how it changes, so this is not enough for the non-stationarysignal processing
As an excellent mathematical analysis tool，Wavelet transform is being more andmore important in engineering practice and has replaced the role of the conventionalFourier transform in many research fields. The wavelet transform-scale analysis methodhas the characteristics of multi-resolution, which in the time and frequency domainhave a good localized nature it can be carried out on any frequency components finedescription of a "mathematical microscope," This study aims to explore wavelettransform theory, and the combination of professional study of seismic signalde-noising.
This text regards the wavelet transform as the core explains its principles in detail,which leads to the wavelet transform theory. This includes not only the continuouswavelet, multire solution analysis methods also include the comparison of traditionalFourier transform clear the superiority of its performance characteristics in theory.Noise in the signal, on the basis of characteristics, so we can particularly the noisecharacteristics of the seismic signal is given wavelet de-noising diagram of the process.The signal de-noising decomposition in the process of remodeling on the theoreticalmethod, and the combination with a quadratic function and the inverse tangent function,construct a new threshold function using matlab simulation simulation results show that the new thresholddenoising function to achieve better than the commonly usedfunctions of several threshold denoising can be used for the processing and analysis ofthe seismic signal denoising.
小波变换作为一种出色的数学分析工具，在很多工程应用领域已经取代传统傅里叶变换的作用。因为小波变换的时间－尺度分析方法具有多分辨率的特点，所以它在时间和频率域都具有良好的局部化性质，它可以对任何频率成分进行精细的描述，有“数学显微镜”之称。本文旨在探讨小波变换理论，并结合专业中的地震信号去噪展开研究。
本文以小波变换为核心，并对其原理做出了深入的分析。不仅包括连续小波，离散小波，多分辨率分析方法还包括与传统傅氏变换的对比，从而在理论上明确其性能特点的优越性。在对信号噪声特点研究的基础上，特别是地震信号的噪声特点，分析研究了小波去噪的过程框图。对于信号去噪过程中的分解重构进行了理论讲述，并采用二次函数和反正切函数的组合方法，构造出新的阈值函数，用matlab模拟实验仿真，结果表明，新的阈值函数达到的去噪效果比常用的几种阈值函数的去噪效果好，可以用于地震信号去噪的处理与分析。
Signal and signal processing is the fastest growing disciplines in the last twodecades, signal de-noising is the most common signal processing process, the classicsignal de-noising methods, such as pure time-domain method, pure frequency domainmethod, Fourier transform, etc. , each has its application limitations. The Fouriertransform is a global transformation, that is, the characterization of the signal either inthe time domain or frequency domain. Expressed as a frequency domain spectrum orpower spectrum, frequency domain does not tell us of a certain frequency componentsappear at what time and how it changes, so this is not enough for the non-stationarysignal processing
As an excellent mathematical analysis tool，Wavelet transform is being more andmore important in engineering practice and has replaced the role of the conventionalFourier transform in many research fields. The wavelet transform-scale analysis methodhas the characteristics of multi-resolution, which in the time and frequency domainhave a good localized nature it can be carried out on any frequency components finedescription of a "mathematical microscope," This study aims to explore wavelettransform theory, and the combination of professional study of seismic signalde-noising.
This text regards the wavelet transform as the core explains its principles in detail,which leads to the wavelet transform theory. This includes not only the continuouswavelet, multire solution analysis methods also include the comparison of traditionalFourier transform clear the superiority of its performance characteristics in theory.Noise in the signal, on the basis of characteristics, so we can particularly the noisecharacteristics of the seismic signal is given wavelet de-noising diagram of the process.The signal de-noising decomposition in the process of remodeling on the theoreticalmethod, and the combination with a quadratic function and the inverse tangent function,construct a new threshold function using matlab simulation simulation results show that the new thresholddenoising function to achieve better than the commonly usedfunctions of several threshold denoising can be used for the processing and analysis ofthe seismic signal denoising.
引文
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[2]Burt P J ,Adelson E，The Laplacian Pyramid as a compact images code，IEEETrans on Communications，2007,32（4），532-540
[3]Le Heron,D.P.and Thusu,B.Prospects in Libya’s mature and frontierbasins[J].First Break,2007, 25(2),73-79
[4]Application of wavelet multi-resolution analysis for correction of seismicacceleration records .Journal of Geophysics and Engineering, 2007,(4) :362-377 .
[5]胡昌华，李国华，周涛.基于MATLAB的系统分析与设计——小波分析[M]．西安：西安电子科技大学出版社，2008
[6]郭蓉,郭丽,马启哓.428XL地震数据采集站原理分析[J].石油仪器,2009,23(3):28-30
[7]赵殿栋.高精度地震勘探技术发展回顾与展望[J].石油物探,2009,48(5):425-435
[8]Jose M Bioucas-Dias. Bayesian Wavelet-Based Image Deconvolution: A GEMAlgorithm Exploiting a Class of Heavy-Tailed Priors[A] .Image Processing IEEETrans, 2007, l5(4) :937-951 .
[9]Xuanchao Liu,Xiaolong Liu.Weak Signal Detection Research Based on DuffingOscillator Used for Downhole Communication[J].JOURNAL OF COMPUTERS,2011,6(2):359-367
[10]Somanath Misra,Satinder Chopra.Phase stability via nonlinearoptimization:A case study[J].The Leading Edge,2010,11:1338-1343
[11]王正蕾.基于小波变换的微地震信号检测方法研究[J].勘探地球物理进展,2009,32(3):182-185
[12]张恒磊,刘天佑,张云翠.基于高阶相关的Curvelet域和空间域的倾角扫描噪声压制方法[J].石油地球物理勘探,2010,45(2):208-214
[13]张军华.地震资料去噪方法——原理、算法、编程及应用(M).中国石油大学出版社.2011
[14]吴逍,纪国宜.基于谐波小波包理论检测微弱信号的研究[J].电子测量技术,2010,33(6):1-3
[15]包乾宗,陈文超,高静怀.基于第二代Curvelet变换的地震资料随机噪声衰减[J].煤田地质与勘探,2010,38(1):66-70
[16]张恒磊,张云翠,宋双,等.基于Curvelet域的叠前地震资料去噪方法[J].石油地球物理勘探,2008,5:508-513
[17]吴爱弟,赵秀玲.基于曲波变换的地震信号去噪方法[J].中国石油大学学报(自然科学版).2010,34(3):30-33
[18]王小品,贺振华,熊晓军.基于小波变换与奇异值分解的地震资料去噪新方法[J].石油天然气学报，2010,32(1):232-236
[19]黄中敏,游洪文,孟小红.阿曼36、38区块低信噪比地震资料处理技术[J].石油天然气学报,2007,29(1):63-651
[20]沈鸿雁，李庆春.频域奇异值分解（SVD）地震波场去噪.石油地球物理勘探,2010,45(2):185-189
[21]冯毅，王香华,小波变换降噪处理及其MATLAB实现,2007,21(12),37-39.
[22]李敏,张小英,毛捷.基于邻域方差加权平均的小波图像融合.理论与方法，2008,27(1):5-7
[23]YangYi，Han Chong-Zhao，Han De-Qiang．A structure information based imagefusion algorithm using IHS and discrete wavelet transform.InternationalConferen on Wavelet Analysis and Pattern Recognition,2008，2：859—864
[24]QiaoLi-Hong，PengLi-Zhong,Guo Wei,Yuan Wei-Tao.A novel image fusionalgorithm based on 2D EMD and HIS.International Conference on Machine Leanangand Cybernetics,2008,7：4040_4044
[25]Morler J, Wave propation and sampling theory and complex waves,Geophysics,2006,47(2):222-236
[26]Shen H Y,Li Q C.Seismic wave fields sparation and noise attenuation infrequeccy dommain var singular value decomposition.Near Surface Geop hysics andHuman Activity,2008,178～181
[27]Anooshiravan Ansad,Assadollah Noorzad,Mehdi Zare.Application of waveletmulti-resolution analysis for correction of seismic accelerationrecords .Journal of Geophysics and Engineering, 2007, (4) :362-377 .
[28]Jianhong Yao, Binkun Gao，Xiaohua Wang; Optimal Configuration of the ActivePower Filter in Distribution Network of Single/Multi Harmonic Sources 1stInternational Conference on Sustainable Power Generation and Supply（EI）2009.
[29]Jianhong Yao, Binkun Gao;The Realization of A Passive Identification TagTransmitter Based on SAW wicom 2008（EI）2008.1
[30]LIU Wei-dong,LIU Shang-he.A New Modified Method Based on Wavelet Thre sholdDe-Noising functions[J].Chinese Journal of Electron Devices.2007,30:58-62.
[31]张荣标，胡海燕，冯友兵．基于小波熵的微弱信号检测方法研究[J]．仪器仪表学报，2007，28(11)：2078-2083．
[32]姚胜利．地震信号的小波去噪方法研究[D]．中南大学，2007，22-37．
[33]吴勇．基于小波的信号去噪方法研究[D]．武汉理工大学，2007，5：44-56．
[34]兰芸，樊可清.基于小波阈值去噪方法的研究.山东.科技信息.2008(2).209一210
[35]刘霞，潘洪屏，高晓春，吴伟龙.基于小波阈值的地震信号去噪处理[J]．科学技术与工程，2010.10 No.29.
[36]侯锐锋,郭科.基于小波变换新阈值函数的去噪方法[J].现代计算机,2009,301(2):42-44.
[37]李杏梅，陈亮.小波阈值去噪在图像去噪中的应用[J].现代计算机，2006(10):78-80
[38]李录明，李正文.地震勘探原理、方法和解释[M].北京：地质出版社2007.
[39]孙志新．小波分析在地震数据噪声处理中的应用研究[D]．中国地震局工程力学研究所，2008，12：51-56．
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