The Application Of Wiener Filtering Method Based On Kernel Function Principal Component Analysis In Seismic Signal Processing

In recent years, as global oil industry developing rapidly, which high-speed development relies on the theory of oil and gas exploration and the technology to solve difficult production. With the deepening of the oil and gas exploration, seismic exploration, as a main tool for subsurface hydrocarbon exploration, is more complicated for the problems that the exploration geophysics seismology theory and practical research development face today. The seismic data got from seismic exploration always have a lot random noise which significant influence the whole quality of the seismic exploration, even make seismic data unavailable. Therefore, using the method of suppressing noise to improve SNR is very necessary. So far, many methods was proposed by researchers to reduce the random noise, which have some effect, but when the strong noise existing in data, the noise suppression is not completely removed or effective signal energy is also loss.Classical Wiener filtering as we have known is widely used in processing stationary signal. But as the least square method has the problem in solving ill-conditioned matrix, which leads to the Wiener filtering meeting the same problems and let the result of filtering inaccurate. Through research, this ill-conditioned matrix can be solved by the method, which is the algorithm ideas in there paper, of the principal component analysis and Mercer kernel functions. Principal component analysis is a linear dimension-reduction methods, which main idea is ruled out the overlapping information in numerous coexistence ones to achieve the purpose of dimension reduction. In order to extract more nonlinear characteristics data from principal component, we can add the Mercer kernel functions based on the method of PCA in it, which we call KPCA. The basic principle of it is mapping the input data into high dimension space from original one, this allows data in high dimension space linear separable. Such mapping using kernel functions to instead the inner product, will reduce the computation complexity, and the data after mapping using PCA to extract for the further application of data.In conclusion, this paper proposed to utilize kernel principal component Wiener filter (KWPC) to process seismic data disturbed by random noise. The method first uses linear kernel functions to process the data, which mapped onto high-dimension space, with kernel function transference, then reduces dimension by using principal component analysis. Last using the principal component extracted to Wiener filtering processing, such treatment can improve the problem of ill-conditioned matrix in processing of Wiener filtering solving under low SNR.This paper introduces in detail the theories about the algorithm and derivation, in order to validate the effectiveness and practicality of the algorithm which will be used both in the processing of simulated seismic signal and real seismic data. In simulation experiment, by changing the important parameter of simulated signal the effectiveness is verified, including change wavelet first break, wavelet initial phase, wavelet amplitude, noise types, noise power and etc. The experimental results prove this algorithm has good effect on random noise suppression in seismic records processing. In order to have a further step about its effectiveness of the method, we will use it to deal with a region real seismic data, the results further prove its good effect.Suppressing random noise in real seismic records without losing the effective signal is one of the key technologies of seismic signal processing. Using this method to remove the random noise in practical seismic data proves the good effect of the noise suppression. The combination of kernel function and PCA algorithm, reduce the ratio of the problem about ill-conditioned matrix after the processing of Wiener filter, which make the results more accurate, also improve filtering. After a lot of simulation experiments, we have some experiment on how to choose the kernel function and the parameters, which will be a guide on choosing kernel function in seismic signal processing in the future.