子空间分析方法在地震勘探等信号处理中的初步应用研究
摘要
计算机技术的发展使得现代信号处理技术同样得到了快速的发展；由于信号的特点和采集仪器的限制，采集得到的信号几乎都是时空域的数据，尽管在时空域对信号有非常直观的解释，但其处理手段有限；鉴于此，现代信号处理技术往往是将信号作某种形式的变换，以便于将信号从时空域变换到其他特定的子空间域内。在所有的信号变换中，傅立叶变换几乎可以说是现代信号处理的基础，其他的变换技术方法要么来源于傅立叶变换的扩展形式，要么或多或少有些联系。
从数学的角度来看，信号变换可以统一的视为信号（函数）与变换函数（我们统一称为基函数）之间的内积运算，这种内积运算等价于将信号从原始的样本空间投影（变换）到另一个特征子空间中，例如频域子空间或者核函数子空间，以便在这个特征子空间中能检测到信号在原样本空间中无法体现的模式，可以简言之―换一个角度看问题，可以更容易发现事物的本质‖；这就是本文选题的根本目的，子空间方法可以分为线性子空间方法和非线性子空间方法，线性子空间方法以某种正交变换为基础，其变换函数通常是某种正交基函数，鉴于此原因，线性子空间具有等维变换或降维变换的效果；而非线性子空间方法则是主要以核函数为主的与线性子空间方法对应的技术方法，这些非线性变换通常具有升维的效果，将数据从低维的样本空间经过非线性投影到一个更高维的核子空间，使数据变稀疏或者体现线性模式，以便在核子空间中使用业已成熟的线性技术对数据进行处理。
总体来说，本论文以子空间相关方法为主导，探索多种子空间方法在地球物理信号处理中的应用，分别从主成分分析，三维主成分分析，核主成分分析，独立成分分析，支持向量机等方面将这些子空间技术应用到地球物理信号的处理、解释等方面，本文的主要创新点和成果体现在以下几个方面：
（1）提出了一种将2D-PCA用于提高地球物理信号剖面的信噪比的方法。在2D-PCA中，地震剖面矩阵经特征分解之后得到特征值和特征图像，将特征值从大到小排序并对特征图像做同样的操作，这些特征图像被称为主成分，它们具有相互正交且方差依次减小的性质，分别代表地震剖面中的某些能量成分。通过选择不同的主成分组合来重构数据，对随机噪声、相干噪声和工业单频噪声的祛除分别进行实验，均获得了较好的效果。
（2）提出了一种基于3D-PCA融合RGB技术识别浊积扇的方法。用于处理地震切片，对特定层位上多个频率的地震切片，在保证结构信息不损失的情况下，将其从三维数据排列成二维并用PCA方法进行变换分解，得到特征切片，再将特定的特征切片映射到RGB颜色子空间。该方法用于对古河道的识别和预测，查明河道砂体的展布规律，得到了比较满意的结果，为后期的布井钻探提供相应的依据。
（3）提出了一种基于KPCA处理地震剖面非线性同向轴的方法。由于PCA技术实质上是一种线性变换，对于数据中的非线性特征提取效果较差；而地震剖面数据中往往存在非线性的同相轴，因此使用这种基于核函数的KPCA非线性的技术，将数据变换到核子空间中再利用PCA进行分解重构。仿真实验表明，KPCA在重构非线性同向轴的地震数据上，效果较好，可适用于地质目标提取和波场分离等问题。
（4）将独立成分分析技术用于子波提取，仿真实验结果表明该方法可行，为数据精细解释提出一个新的思路。
（5）将非线性支持向量机用于油气预测，通过对某工区碳酸盐岩储层数据进行模型训练和检验，实验结果令人满意，与其他预测技术比较，可作为油气预测技术的重要补充。
One has observed the rapid development of modern signal processing withprogress of computer technology. Signals are with the distribution in time-spacedomain thanks to limitation of instrument. There is an intuitive interpretation of signalin time-space domain, but its processing methods are limited. So, we often transformthe signal from time-space domain to the specific sub-space domain using somemethods from modern signal processing field. Fourier transform may be said as thebasis of modern signal processing because other transform methods are either linkedwith or derived from the Fourier transform.
From a mathematical point of view, the signal transform may be unified as theinner product between a signal (function) and the transformation function (referred toas the base function). In fact, for obtaining the detection of signal pattern in featuresubspace other than original space, this inner product is to transform the signal fromthe original space to feature subspace such as frequency subspace, kernel functionsubspace, etc. In short, it is easier to find the intrinsic feature of things from anotherangle of view. It is also the reason selecting the transform subspace as the topic of thisthesis. Subspace method may be general classified as linear subspace and nonlinearsubspace, which linear subspace uses the orthogonal basis as the transform function toachieve the destination of dimension reduction when kernel function of nonlinearsubspace is applied to arrive at the object of dimension increase. Specifically, data aretransformed from sample space with low dimensions to kernel subspace with higherdimensions by a nonlinear function to obtain sparse or linear separation.
On the whole, this paper presents the study of many kinds of subspace methodsin the application of geophysical signal processing or geophysical interpretation, forexample, principal component analysis (PCA), three-dimensional principalcomponent analysis (3D-PCA), independent component analysis (ICA), supportvector machine(SVM), and so on. In detail, the main research contents are concluded as follows.
(1) To improve the signal-to-noise ratio of the geophysical signal, this thesispresents a two-dimensional principal component analysis method (2D-PCA) whichcan obtain features of seismic section matrix with corresponding feature vectors bysingular value decomposition (SVD), then these feature vectors with higher featurevalues are reconstructed for decreasing the effect of noise. The experiments oneliminating rand noise, random noise, coherent noise and industrial noise withsingle-frequency show that the2D-PCA method is a good denoising tool.
(2) This thesis proposes a feature extraction method based on3D-PCA andcombines it with RGB to identify turbidite fan from seismic sections. Moreover, themethod proposed may be applied to the recognition or the prediction of the ancientriver and the distribution of sand body. Firstly, seismic slices with multiple frequencyin the specific layer are transformed to feature space on the condition of without lossof structure information; then, these feature slices are mapped to RGB color subspace;finally, the recognition information of seismic section may be obtained by combining3D-PCA and RGB subspace. The experiments in seismic section provide thecorresponding foundation for process seismic sections for the well drilling.
(3) The thesis shows a recognition method of event based on kernel PCA(KCPA). The linear PCA only can utilize first-order and second-order information ofdata. However, as a kind of high-order statistical tool, the KPCA can obtain nonlinearinformation. In general, there exist the nonlinear events in seismic section, so theKPCA method proposed may be applied to the geological targets extraction andseparation of wave field. The experiments show that the PCA method is with theexcellent performance.
(4) A wavelet extraction method based on ICA is presented. Simulation results show thatthe proposed method in the thesis is feasible. It is a novel way to the fine interpretation of data.
(5) A hydrocarbon prediction method based on nonlinear SVM is also shown inthis thesis. The experimental results are satisfactory when the proposed method isapplied to the carbonate reservoir data in the special exploration area. So, theprediction method proposed may be said as an alternative of the oil and gasforecasting.
从数学的角度来看，信号变换可以统一的视为信号（函数）与变换函数（我们统一称为基函数）之间的内积运算，这种内积运算等价于将信号从原始的样本空间投影（变换）到另一个特征子空间中，例如频域子空间或者核函数子空间，以便在这个特征子空间中能检测到信号在原样本空间中无法体现的模式，可以简言之―换一个角度看问题，可以更容易发现事物的本质‖；这就是本文选题的根本目的，子空间方法可以分为线性子空间方法和非线性子空间方法，线性子空间方法以某种正交变换为基础，其变换函数通常是某种正交基函数，鉴于此原因，线性子空间具有等维变换或降维变换的效果；而非线性子空间方法则是主要以核函数为主的与线性子空间方法对应的技术方法，这些非线性变换通常具有升维的效果，将数据从低维的样本空间经过非线性投影到一个更高维的核子空间，使数据变稀疏或者体现线性模式，以便在核子空间中使用业已成熟的线性技术对数据进行处理。
总体来说，本论文以子空间相关方法为主导，探索多种子空间方法在地球物理信号处理中的应用，分别从主成分分析，三维主成分分析，核主成分分析，独立成分分析，支持向量机等方面将这些子空间技术应用到地球物理信号的处理、解释等方面，本文的主要创新点和成果体现在以下几个方面：
（1）提出了一种将2D-PCA用于提高地球物理信号剖面的信噪比的方法。在2D-PCA中，地震剖面矩阵经特征分解之后得到特征值和特征图像，将特征值从大到小排序并对特征图像做同样的操作，这些特征图像被称为主成分，它们具有相互正交且方差依次减小的性质，分别代表地震剖面中的某些能量成分。通过选择不同的主成分组合来重构数据，对随机噪声、相干噪声和工业单频噪声的祛除分别进行实验，均获得了较好的效果。
（2）提出了一种基于3D-PCA融合RGB技术识别浊积扇的方法。用于处理地震切片，对特定层位上多个频率的地震切片，在保证结构信息不损失的情况下，将其从三维数据排列成二维并用PCA方法进行变换分解，得到特征切片，再将特定的特征切片映射到RGB颜色子空间。该方法用于对古河道的识别和预测，查明河道砂体的展布规律，得到了比较满意的结果，为后期的布井钻探提供相应的依据。
（3）提出了一种基于KPCA处理地震剖面非线性同向轴的方法。由于PCA技术实质上是一种线性变换，对于数据中的非线性特征提取效果较差；而地震剖面数据中往往存在非线性的同相轴，因此使用这种基于核函数的KPCA非线性的技术，将数据变换到核子空间中再利用PCA进行分解重构。仿真实验表明，KPCA在重构非线性同向轴的地震数据上，效果较好，可适用于地质目标提取和波场分离等问题。
（4）将独立成分分析技术用于子波提取，仿真实验结果表明该方法可行，为数据精细解释提出一个新的思路。
（5）将非线性支持向量机用于油气预测，通过对某工区碳酸盐岩储层数据进行模型训练和检验，实验结果令人满意，与其他预测技术比较，可作为油气预测技术的重要补充。
One has observed the rapid development of modern signal processing withprogress of computer technology. Signals are with the distribution in time-spacedomain thanks to limitation of instrument. There is an intuitive interpretation of signalin time-space domain, but its processing methods are limited. So, we often transformthe signal from time-space domain to the specific sub-space domain using somemethods from modern signal processing field. Fourier transform may be said as thebasis of modern signal processing because other transform methods are either linkedwith or derived from the Fourier transform.
From a mathematical point of view, the signal transform may be unified as theinner product between a signal (function) and the transformation function (referred toas the base function). In fact, for obtaining the detection of signal pattern in featuresubspace other than original space, this inner product is to transform the signal fromthe original space to feature subspace such as frequency subspace, kernel functionsubspace, etc. In short, it is easier to find the intrinsic feature of things from anotherangle of view. It is also the reason selecting the transform subspace as the topic of thisthesis. Subspace method may be general classified as linear subspace and nonlinearsubspace, which linear subspace uses the orthogonal basis as the transform function toachieve the destination of dimension reduction when kernel function of nonlinearsubspace is applied to arrive at the object of dimension increase. Specifically, data aretransformed from sample space with low dimensions to kernel subspace with higherdimensions by a nonlinear function to obtain sparse or linear separation.
On the whole, this paper presents the study of many kinds of subspace methodsin the application of geophysical signal processing or geophysical interpretation, forexample, principal component analysis (PCA), three-dimensional principalcomponent analysis (3D-PCA), independent component analysis (ICA), supportvector machine(SVM), and so on. In detail, the main research contents are concluded as follows.
(1) To improve the signal-to-noise ratio of the geophysical signal, this thesispresents a two-dimensional principal component analysis method (2D-PCA) whichcan obtain features of seismic section matrix with corresponding feature vectors bysingular value decomposition (SVD), then these feature vectors with higher featurevalues are reconstructed for decreasing the effect of noise. The experiments oneliminating rand noise, random noise, coherent noise and industrial noise withsingle-frequency show that the2D-PCA method is a good denoising tool.
(2) This thesis proposes a feature extraction method based on3D-PCA andcombines it with RGB to identify turbidite fan from seismic sections. Moreover, themethod proposed may be applied to the recognition or the prediction of the ancientriver and the distribution of sand body. Firstly, seismic slices with multiple frequencyin the specific layer are transformed to feature space on the condition of without lossof structure information; then, these feature slices are mapped to RGB color subspace;finally, the recognition information of seismic section may be obtained by combining3D-PCA and RGB subspace. The experiments in seismic section provide thecorresponding foundation for process seismic sections for the well drilling.
(3) The thesis shows a recognition method of event based on kernel PCA(KCPA). The linear PCA only can utilize first-order and second-order information ofdata. However, as a kind of high-order statistical tool, the KPCA can obtain nonlinearinformation. In general, there exist the nonlinear events in seismic section, so theKPCA method proposed may be applied to the geological targets extraction andseparation of wave field. The experiments show that the PCA method is with theexcellent performance.
(4) A wavelet extraction method based on ICA is presented. Simulation results show thatthe proposed method in the thesis is feasible. It is a novel way to the fine interpretation of data.
(5) A hydrocarbon prediction method based on nonlinear SVM is also shown inthis thesis. The experimental results are satisfactory when the proposed method isapplied to the carbonate reservoir data in the special exploration area. So, theprediction method proposed may be said as an alternative of the oil and gasforecasting.
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