Blind Source Separation Theory And Its Application In Geophysical Exploration

It is difficult to get the exact information from the abundant complicated data derived from reality. Under some assumptions and circumstances, we can pick up the just signal by means of several proper transformations or filtering algorithms with the information known to us. Whereas, if the information is all or partially unknown, we can not make use of the traditional method to achieve the just signal. So, the theory of blind source separation comes into being.The problem of blind source separation (BSS) is arising from blind signal processing. In blind source separation, signals from multiple sources arrive simultaneously at a sensor array, so that each sensor output contains a mixture of source signals. Sets of sensor outputs are processed to recover the source signals from the mixed observations. The term blind refers to the fact that specific source signal values and accurate parameter values of a mixing model are not known as a priori. BSS is developed from the last ten years of the twenties, and it includes a wide range of applications, such as radar and communication system, seismic exploration, speech enhancement, biomedical image, data mining and so on.In the history of BSS, the early research focusd on linear mixing problem derived from algebra, and the recent work concentrates on extending area of application beside embedded in the research on the theory of BSS itself. The goal of this thesis is probing into blind algorithms which require little or no prior information about source signal or mixing system parameter values and developing BSS's applications in the field of geophysical exporation. The blind source separation techniques proposed in this thesis are based on instantaneous mixing model and the result is as following:1) So far there's been a class of adaptive mature algorithms for blind source separation that implements traditional theory and presents dependable results. And in these algorithms, the step-size plays a key role on their convergence rates and stability conditions. In view of the adaptive selection of step-size factor in sequential blind source separation, a novel variable step-size algorithm is presented based on the correspondence between separating performance index and step-size. The proposed algorithm restructures the performance index by adopting an auxiliary separation system with some restriction and attains the adaptive updating rule of step-size in the light of the index descending in an exponential form. Simulation results show that the convergence and steady-state performance of the proposed method outperforms the fixed step-size and the recently proposed adaptive step-size algorithms in both stationary and non-stationary environments.Because the adaptive algorithms are more superiore in nonstationary data processing, they have important values for real applications.2) The linear system identification is a theory and method that investigates and sets up mathematical model by utilizing the input data and output data. Several common methods, such as least-square method, maximum likelihood method and so on, are all have unqualified results under additive colorful noise especially low signal-noise-rate circumstances.A novel noise subtraction method is proposed and investigated for estimating the parameters of a linear system with additive noisy output. This method treats the problem of system identification as the instantaneous mixing model defined in blind source separation. The proposed method works in two stages. First, a BSS model involed in FastICA algrithm is derived, and then the least-square approach is employed to estimate the parameters of the unknown system whose noise is canceled. Independent upon the statistics of the noise, the proposed method separates and subtracts the noise using some special characters of the mixing matrix. Computer simulations utilizing a variety of additive noises indicate that the proposed method gives superior identification performance even at low SNR conditions.3) This thesis presents a new approach for acoustic gas influx detection based on linear system identification with additive noisy output. It treats the model of acoustic gas influx detection system as a blind source separation problem with source signals received by several observed signals so that the estimation of noise can be obtained from the observed signals. And a modified on-line algorithm is applied in order to cost less time for identification. This proposed approach does not rely on any statistic characteristics of the additive noise and can work well under low SNR conditions. Synthetic data are applied to validate the effectiveness of the proposed method and improved performance is obtained.4) According to the non-gaussianity of the primary and the multiple in seismic exploration, this thesis presents an instantaneous BSS model and a novel algorithm for multiple wave subtraction, which achieved the separation of primary from multiple by accounting for the different scale coefficients of each predictive multiple corresponding to its real multiple in amplitude. The algorithm settled the two ambiguities of the separated primary that were inherent in BSS by using some special characters of the mixing matrix. Synthetic seismic data set derived from the time-distance equation is applied to validate the effectiveness of the proposed algorithm and experimental results indicate the improved performance of our algorithm.