复小波变换在地震随机噪声衰减中的应用研究

发布时间：2019-03-31 09:10

【摘要】：提高地震资料的信噪比一直是地震勘探的关键，小波变换是目前地震勘探去噪过程中的主要方法，由于小波变换具有去相关性，多分辨特性以及层间和层内系数相关性等优点，如何利用这些特性进行去噪一直是研究的热点，在众多基于小波变换的去噪方法中，小波阈值去噪由于其简单实用的特性一直是生产中常用的方法，但是硬阈值函数的不连续性导致重构信号容易产生伪吉布斯现象，而软阈值函数虽然整体连续性有了改进，，但是其估计值与实际值之间总存在着一定偏差，局限性较大。随着勘探环境越来越多样，勘探目标越来越向深部转移，常规的小波去噪方法已经不能满足实际生产对于地震资料高信噪比的要求，阈值估计一直是阈值去噪的关键因素，本文对小波变换的地震勘探去噪方法进行了深入的研究，首先，本文从小波变换基本理论出发，给出了小波变换的基本概念、基本思想和基本结论，包括连续小波变换理论、二进小波、小波框架理论、多分辨分析与Mallat算法等,详细介绍了几种经典的小波变换去噪算法，并用线性回归的方法推导了比例萎缩去噪算法中原图像的噪声估计，接着对复小波的理论和性质进行了详尽的探讨，由于复数小波变换具有近似平移不变性，对地震信号具有良好的方向选择性，完全重构特性，有限的冗余度，较小的计算量等各种优点，使得它可以克服离散小波变换中存在的毛刺现象。常规的小波阈值去噪方法由于其自身的局限性不能充分的利用地震信号的特点，估计值与实际值之间总是存在一定的偏差。为此，本文从原始的BivaShrink12模型出发，给出了另外两个二元萎缩函数去噪模型（BivaShrink13,BivaShrink23）,并对其进行了双树复小波的改进，同时为了验证复小波变换相对于小波变换的优越性，本文以BivaShrink模型为基础，探讨了BivaShrink13,BivaShrink13,BivaShrink23,贝叶斯方差局部自适应等几种方法的小波变换及其复小波变换，最后基于双树复小波变换和子带相关去噪模型（TrivaShrink），兼顾小波系数层间和层内相关性，利用当前系数、父层系数、邻阈系数，通过这种3维萎缩函数共同确定局部自适应窗口，从而达到最优估计小波函数的萎缩因子，实现对地震记录的降噪功能。通过模型试算，证明了复数小波变换方法在对地震记录随机噪声的去除效果上优于一般的小波去噪方法。
[Abstract]:Improving the signal-to-noise ratio of seismic data has always been the key to seismic exploration. Wavelet transform is the main method in the process of seismic exploration de-noising at present. Because of the advantages of wavelet transform, such as de-correlation, multi-resolution and interlayer and intra-layer coefficient correlation, etc. How to use these characteristics to Denoise has been the focus of research. Among the many denoising methods based on wavelet transform, wavelet threshold de-noising has always been a common method in production because of its simple and practical characteristics. However, the discontinuity of the hard threshold function leads to the pseudo-Gibbs phenomenon of reconstructed signal, while the soft threshold function has improved global continuity, but there is always a certain deviation between the estimated value and the actual value, and the limitation is large. With the variety of exploration environment and the moving of exploration targets to the deep, the conventional wavelet de-noising method can not meet the requirement of high signal-to-noise ratio of seismic data in actual production, and threshold estimation is always the key factor of threshold de-noising. In this paper, the de-noising method of seismic exploration based on wavelet transform is deeply studied. Firstly, based on the basic theory of wavelet transform, the basic concept, basic thought and basic conclusion of wavelet transform are given, including the theory of continuous wavelet transform. Based on dyadic wavelet, wavelet frame theory, multi-resolution analysis and Mallat algorithm, several classical wavelet transform de-noising algorithms are introduced in detail, and the noise estimation of proportional atrophy denoising algorithm is derived by linear regression method. Then the theory and properties of complex wavelet are discussed in detail. Because the complex wavelet transform has approximate translation invariance, it has good directional selectivity, complete reconstruction property and limited redundancy. It can overcome the burr phenomenon in discrete wavelet transform because of its advantages such as small computation and so on. The conventional wavelet threshold de-noising method can not make full use of the characteristics of seismic signals because of its own limitations. There is always a certain deviation between the estimated value and the actual value. Based on the original BivaShrink12 model, the other two binary atrophy function de-noising models (BivaShrink13,BivaShrink23) are presented in this paper, and the double-tree complex wavelet transform is improved. At the same time, in order to verify the superiority of the complex wavelet transform over the wavelet transform, this paper presents the two binary atrophy function de-noising models (BivaShrink13,BivaShrink23). In this paper, based on the BivaShrink model, the wavelet transform and complex wavelet transform of BivaShrink13,BivaShrink23, Bayesian variance local adaptation are discussed. Finally, based on the double-tree complex wavelet transform and subband correlation denoising model (TrivaShrink), the wavelet transform and its complex wavelet transform are discussed. Taking into account the inter-layer and intra-layer correlation of wavelet coefficients, using the current coefficient, parent layer coefficient and neighborhood threshold coefficient, the local adaptive window is determined by this three-dimensional shrinkage function, so that the shrinkage factor of wavelet function can be estimated optimally. The noise reduction function of seismic records is realized. Through model trial calculation, it is proved that the complex wavelet transform method is superior to the general wavelet de-noising method in removing random noise of seismic records.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.4

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