Radon变换去噪方法的保幅性理论分析
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摘要
本文在对比常规抛物线Radon变换、最小二乘抛物线Radon变换和高分辨率抛物线Radon变换的保幅性的基础上,重点分析了影响高分辨率抛物线Radon变换去噪方法保幅性的各种因素,认为对于最小二乘Ra-don变换和高分辨率Radon变换而言,信号在变换域中的分辨率都依赖于信号模型的"标准同相轴"假设,地震数据处理中各种实际因素导致信号同相轴偏离该假设,进而导致分辨率降低,影响Radon变换去噪方法的保幅能力。文中给出了波场分解类去噪方法的保幅性理论分析思路以及评价标准,然后以Radon变换去除多次波为例,具体分析了Radon变换的各种实现方式对信号的操作过程,并进行了保幅性理论评价。理论分析以及数值试验结果表明:常规Radon变换不满足保幅性处理的要求;最小二乘Radon变换算子满足保幅性要求,但变换域中信号分辨率仍然有待提高;逼近"标准同相轴"假设条件时,高分辨率Radon变换去噪方法在一定精度范围内可以认为是保幅的。
Based on the amplitude preservation analysis of conventional parabolic Radon transform,least squares parabolic Radon transform and high resolution parabolic Radon transform,various factors influencing the amplitude preservation of high resolution parabolic Radon transform are analyzed specifically.It is noted that for least squares Radon transform and high resolution Radon transform,the signal resolution in transform domain depends on the "standard event" assumption of signal model.But in the actual processing,due to various factors,the events deviate from the assumption,which leads to a lower signal resolution,and influences the amplitude-preserving ability of Radon transform de-noising method.In this paper,the way of amplitude preservation theoretical analysis of the wave field decomposition class de-noising methods is provided,as well as evaluation standards.Then,taking removing multiples by Radon transform as a case,we make a detailed analysis of the signal operation process for several implementations of Radon transform,and a theoretical amplitude preservation assessment.The following observations from theoretical analysis and numerical experiments are obtained: Firstly,conventional Radon transform does not meet the requirements of amplitude-preserved processing;secondly,least squares Radon transform operator satisfies amplitude preservation requirements,but signal resolution in transform domain still need to be improved;finally,under the approximation to the "standard event" assumption,high resolution Radon transform de-noising method can be considered to be amplitude-preserved in a certain precision range.
Based on the amplitude preservation analysis of conventional parabolic Radon transform,least squares parabolic Radon transform and high resolution parabolic Radon transform,various factors influencing the amplitude preservation of high resolution parabolic Radon transform are analyzed specifically.It is noted that for least squares Radon transform and high resolution Radon transform,the signal resolution in transform domain depends on the "standard event" assumption of signal model.But in the actual processing,due to various factors,the events deviate from the assumption,which leads to a lower signal resolution,and influences the amplitude-preserving ability of Radon transform de-noising method.In this paper,the way of amplitude preservation theoretical analysis of the wave field decomposition class de-noising methods is provided,as well as evaluation standards.Then,taking removing multiples by Radon transform as a case,we make a detailed analysis of the signal operation process for several implementations of Radon transform,and a theoretical amplitude preservation assessment.The following observations from theoretical analysis and numerical experiments are obtained: Firstly,conventional Radon transform does not meet the requirements of amplitude-preserved processing;secondly,least squares Radon transform operator satisfies amplitude preservation requirements,but signal resolution in transform domain still need to be improved;finally,under the approximation to the "standard event" assumption,high resolution Radon transform de-noising method can be considered to be amplitude-preserved in a certain precision range.
引文
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[15]Claerbout J F.Earth Soundings Analysis Processingversus Inversion.Blackwell Scientific Publications,Inc,2004
[16]Claerbout J F.Image Estimation by Example:Geo-physical Soundings Image Construction Multidimen-sional Autoregression.Blackwell Scientific Publica-tions,Inc,2011
[17]Trad D,Ulrych T and Sacchi M.Latest views of thesparse Radon transform.Geophysics,2003,68(1):386～399
[2]陈新荣,尚新民,李继光等.地震资料振幅保持影响因素分析.地球物理学进展,2009,24(4):1411～1419Chen Xinrong,Shang Xinmin,Li Jiguang et al.Ana-lysis on influence factors of preserved amplitude pro-cessing.Progress in Geophysics,2009,24(4):1411～1419
[3]郭树祥.地震资料保幅处理的讨论.油气地球物理,2009,7(1):1～3Guo Shuxiang.Discussion on preserved amplitudeprocessing of seismic data.Petroleum Geophysics,2009,7(1):1～3
[4]芮拥军.地震资料处理中相对保幅性讨论.物探与化探,2011,35(3):371～374Rui Yongjun.An Analysis of relative amplitude-pres-ervation in seismic data processing.Geophysical andGeochemical Exploration,2011,35(3):371～374
[5]刘喜武,刘洪,李幼铭.高分辨率Radon变换方法及其在地震信号处理中的应用.地球物理学进展,2004,19(1):8～15Liu Xiwu,Liu Hong,Li Youming.High resolutionradon transform and its application in seismic signalprocessing.Progress in Geophysics,2004,19(1):8～15
[6]张军华,吕宁,雷凌等.抛物线拉冬变换消除多次波的应用要素分析.石油地球物理勘探,2004,39(4):398～405Zhang Junhua,Lv Ning,Lei Ling et al.Analysis ofapplied factors for using parabolic Radon transform toremove multiple.OGP,2004,39(4):398～405
[7]Thorson R and Claerbout J.Velocity stack and slantstack-stochastic inversion.Geophysics,1985,50(12):2727～2741
[8]Hampson D.Inverse velocity stacking for multipleelimination.J Can Soc Expl Geophys,1986,22(1):44～55
[9]Sacchi M and Ulrych T.High resolution velocitygathers and offset space reconstruction.Geophysics,1995,60(4):1169～1177
[10]Cary P.The simplest discrete Radon transform.SEGTechnicalProgram Expanded Abstracts,1998,17:1999～2002
[11]Foster Douglas J and Mosher Charles C.Suppressionof multiple reflections using the Radon transform.Geophysics,1992,57(3):386～395
[12]Zhou B and Greenhalgh S A.Linear and parabolicτ-ptransforms revisited.Geophysics,1994,59(7):1133～1149
[13]Kabir M N N and Marfurt K J.Toward true ampli-tude multiple removal.The Leading Edge,1999,18(1):66～73
[14]Nowak Ethan J and lmhof Matthias G.Amplitudepreservation of Radon-based multiple-removal filter.Geophysics,2006,71(5):V123～V126
[15]Claerbout J F.Earth Soundings Analysis Processingversus Inversion.Blackwell Scientific Publications,Inc,2004
[16]Claerbout J F.Image Estimation by Example:Geo-physical Soundings Image Construction Multidimen-sional Autoregression.Blackwell Scientific Publica-tions,Inc,2011
[17]Trad D,Ulrych T and Sacchi M.Latest views of thesparse Radon transform.Geophysics,2003,68(1):386～399
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