Preliminary Application Of The Subspace Analysis Methods In Signal Processing, Such As Seismic Exploration

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.