Research On Least Squares Support Vector Regression Based On Ricker Wavelet Kernel And Its Applications In Seismic Exploration Data Denoising

Seismic exploration is an important tool for coal fields and oil-gas resources. With the development of seismic exploration technology and increasing demands for oil-gas, the prospecting has turn to research the complex structures and deep crusted structures. The seismic exploration data obtained from the complex earth's surface, such as desert, hill and boondocks etc., is rather complex with the strong random noise. It is possible that the number of the unqualified data, the signal-to-noise ratio(SNR) of which is below 1:1, is increasing so that the higher demands are needed for the seismic data processing,that is to extract the weak effective signal from the background of the strong noise, remove the noise and improve the SNR and resolution of the seismic data. However, some traditional processing methods, such as Wiener filtering, can not complete the goal of design when the SNR is under 0.5dB. Obviously, the improvement of SNR of the seismic exploration data with the poor SNR is a focus and difficulty in the fields of seismic exploration, in which an important task is to suppress the random noise in the seismic data with the poor SNR. This is helpful for researching the structure of subsurface and for prospecting oil-gas reservoirs.The development of data mining technology arose from analyzing data and mining the natural meaning of mass data by machine learning. Support vector machine (SVM) is a new method of data mining. It is a universal learning machine based on statistic learning theory (SLT). SVM is proposed based on the principle of structure risk minimization rather than empirical risk minimization used by the traditional methods such as neural network. So the generalization of SVM is superior to the neural network. At the same time, SVM uses the idea of kernel mapping so that it overcomes the dimensional disaster and local minimization. And it shows its advantages when processing nonlinear problems. So recently it has attracted the international scientific fields and is applied in the classification and regression, text recognition, face recognition, speech recognition, fault diagnoses and time sequence predict, etc. Because the signal denoising may be considered as a problem of function regression, SVM with good generalization is introduced to process the seismic exploration data for suppressing the noise in this paper.SVM integrates several technologies including the maximal margin super-plane, Mercer kernel, convex quadratic planning, sparse solve and slackness variable, etc. The main contents of support vector regression (SVR) are summarized in this paper, including SLT, optimization theory and kernel feature spaces. The section of SLT generalizes the definition of VC, consistency theorem and structure risk minimization which is a vital idea of SVM. The section of optimization theory refers to the problem of quadratic planning, Wolfe duality theory and KKT condition. The section of kernel feature spaces gives the decision theorem of kernel and the principle of kernel skill. Based on the upper theoretical fundamentals, the inference processes of standard SVR and least squares SVR (LS-SVR) are given. By the comparative analysis of their denoising experiments, it is showed that SVR is slight better than LS-SVR at the cost of slower speed of solving and more parameters, so LS-SVR for its simplicity and effectiveness is used by this paper.Aiming at the application of SVM in the seismic exploration signal processing, a new admissible kernel - Ricker wavelet kernel which is appropriate for the seismic data, is proposed and proved. Then the selection methods of its parameters including the kernel parameter f and regularization parameterγare discussed. The experiments show that the kernel parameter f may be selected as the dominant frequency of the seismic data, and the regularization parameterγmay be selected in a wide range only not excessive small. This paper uses the method of Cherkassky. The experiments about the denoising processing of the single channel data with different noise intensity show that regardless of strong noise or weak noise, the denoising performance of Ricker wavelet LS-SVR in terms of the smoothness of wave, phase shift and high frequency components exceed or proximate the conventional methods such as Wiener filtering and the new methods such as TFPF.In the simulation experiments of the seismic theoretical models denoising, from simplicity to complication, we construct the changeable single event data on noise intensity, layer velocity, dominant frequency and phase-amplitude ratio, and the complicated multi-events data with fault, thick layer and incomplete events. The results of the processing show that the denoising performance of Ricker wavelet LS-SVR method is hardly impacted on the change of the wave shape, dominant frequency and layer velocity. And the experiments of the seismic data with the multi-events, fault and thick layer also get good effects of suppressing the random noise even in the case of poor SNR(such as -0.4dB). So this method has the capability of suppressing the random noise in the seismic exploration data no supposition for the wave shape and the pattern of event.The results of processing the practical common seismic reflected data of the sunken zone of some basin show that the whole qualities are improved by Ricker wavelet LS-SVR. For example, the effective wavelets in the practical seismic data are enhanced and the wave shape is smoother, most of the random noise is almost suppressed completely, the continuance of events are improved, the effective spectrum in the range from 10Hz to 30Hz are remained and their distributions are more reasonable. From the above, we can conclude that Ricker wave LS-SVR may be used to suppress the random noise of the practical common seismic data and can improve the quality of data.On the base of the theoretical simulation and the practical data processing, several basic problems are discussed. By computing the eigenvalues of Ricker wavelet kernel matrix, we find the fact not satisfied Mercer condition. This shows that the applied condition of Mercer theorem may be loosed, that is, the kernel matrix may approximate the condition of positive semi-definite(has non-negative eigenvalues), or up to 10 13 ~1016? ? ? ? rather than rigidly satisfying with the condition. The theoretical denoising mechanism of LS-SVR is analyzed, that is, the kernel function acts as a band-pass, but not only a simple band-pass. In frequency domain, the double functions of the spectrum of signal multiplied by the spectrum of kernel and convolution by the deforming of kernel spectrum are used to filter the signal. If the kernel parameter is selected as the dominant frequency of the effective signal, the results gained are the best that suppress the high frequency and remain the effective frequency. Considering the frequency attenuation of the seismic wavelet in the propagation, using variant parameters seems more rational, so LS-SVR with the variant parameters is proposed in this paper. The results of the theoretical and the practical experiments show that it is more effective that LS-SVR with invariant parameters under the special conditions.SVR is introduced in the applied study of the seismic signal denoising processing in this paper. Though the theoretical and the practical experiments show its availability, some questions, for example, its adaptability for all kinds of practical seismic data, or it stability and robustness, the selection of most appropriate kernel, the development of two or multi-dimensional SVR using the strong correlation between the individual channel data, etc., need be further discussed and researched.