Independent Component Analysis And It's Application On Multiple Attenuation

Independent component analysis (ICA) derived from blind source separation (BSS) is a new method for finding underlying factors or components from multivariate (multidimensional) statistical data. The goal of ICA is to recover the unobserved source signals without any prior information given only the sensor observations that are unknown linear mixtures of the independent sources. Recently, because of a few assumptions on surroundings, ICA has become one of the exciting new topic, both in the field of data mining and more generally in image processing, feature extraction, telecommunications, financial time series analysis. ICA defines a generative model for the observed multivariate data, which is typically given as a large database of samples. In the model, the data variables are assumed to be linear or nonlinear mixtures of some unknown latent variables, and the mixing system is also unknown. The latent variables are assumed nongaussian and mutually independent and they are called the independent components of the observed data. These independent components, also called sources or factors, can be found by ICA. It can be seen as an extension to principal component analysis and factor analysis. ICA is a much more powerful technique, however, capable of finding the underlying factors or sources when these classic methods fail completely. Compared with the spatial decorrelations techniques which are only based on second-order (SOS), ICA can not only eliminate the first-or second-order correlations among the components, but also do the same to the high-order ones. In chapter 2, the basic ICA model is covered and solved. This is the linear instantaneous noise-free mixing model that is classic in ICA, and forms the core of the ICA theory. Then the preprocessing stage and the two ambigurities are represented in the following. After that, several common principles of ICA estimation are given and corresponding algorithms are discussed in connection with each principle. Especially, the emphasis is on the representation of algorithms based on the second-order statistics and the information theory, which include of AMUSE (Algorithm for Multiple Unknown Signals Extraction), Infomax (Information maximization) algorithm, MLE (Maximum Likelihood Estimation) algorithm, MMI (Mimimum Mutual Information) algorithm. At last, it introduces the concepts of not only delay and convolution mixing model, but also non-liner mixing one in the rough. The seismic data is an improtant information source for seismic exploitation. And the multiple reflections are often one of the most serious problems in seismic suveying which influence the authenticity and the reliability of seismic imaging badly and intefere the seismic interpretation, so as to increase the cost of seismic exploitation. At the present time, the methods of the multiple attenuation are divided into two categories. One is the filtering approaches based on the differences between the primary and the multiple. The other is the prediction and subtraction approaches based on wave-equation. Without any a priori information and neither structural nor material information about the subsurface geology, the latter become an effective method and the main developing trend in the field of attenuating the multiple, and that, more and more scholars realized that the subtraction step in the prediction and subtraction approaches based on wave-equation is the sticking point. The effective method of subtraction can not only solve the disaccordance between the predictive multiple and the real multiple, but also reduce the complex of calculation during the course of prediction largely. However, the energy minimum criterion (least-squares criterion) which is based on the second-order statistics is adopted by the almost existing multiple subtraction methods. From a theoreticalpoint of view, only if the primary and the multiple are normal, the multiple can be removed totally. But in general, the above assumption is invalid in the real seismic data, so that there will remain survival multiple in the primary which is induceded by the optimal criterion based on second-order statistics. After working over a variety of the existing multiple attenuation methods and the ICA theory, we try to use the ICA technique for sovling the problem of the multiple subtraction in order to hurdle the obstacle in the energy fuction based on second-order statistics. We view the seismic data and the predictive multiples as the observed signals, the primary and the real multiples as the source signals, so the subtraction can be treated as a processing of blind source separation. Because of no normal assumption in ICA technique, accordingly, we can settle the problem appeared in the second-order statistics method. In this paper, the free-surface related multiple and the internal multiple are depicted for making out that the major amount of the multiple energy in sesmic data is related to the large reflectivity of the free-surface. Next, it demonstrates the rationality of BSS equivalent to multiple substraction theoretically and brings forwards general ICA model for the real seismic data. Nevertheless, for the sake of accomplishing this BSS problem, we have to master the ICA technique and are provided with mathematical and high-order statistical theory. But what the most depressing thing is that the present ICA technique is still on the way of exploring for the case when the quantity of the source is more than that of the mixture. For this reason, the paper makes assumption on the general ICA model. It is assumed that there are different coefficients between the each real multiple and the corresponding predictive multiple on amplitude, and there is no time-delay between them. Because the any order of the free-surface related multiple can be predicted by wave-equation, the paper simplifies the BSS problem of two observed signals...