Application Of Wavelet Analysis On Seismic Data De-Noising

Fourier transform and short time Fourier transform are the chief methods in signal analysis,however,they suffer inherent limit:they can analysis a signal on the whole spectrum,but not on multi-resolution. Wavelet transform is a great advancement in the harmonic analysis field. It gets over the limit of Fourier transform and short time Fourier transform.The wavelet function is not unique,which makes the wavelet transform adaptive and stable.Applying the wavelet transform in De-noising Of seismic data is a complement and advancement of existing processing methods.In this paper,the basic theory of wavelet de-noising and its application in de-noising of seismic data are mainly researched.The main achievements of this study could be summarized as follows:Firstly,as the emerging discipline,the development situation of the wavelet analysis is briefly reviewed.The basic theory of wavelet,the progress of research at home and abroad,and the objectives,research methods of this articleare introduced.Secondly,the wavelet analysis theory is introduced,including a detailed analysis of the differences and relation between the wavelet transform and Fourier transform,continuous wavelet transform,and discrete wavelet transform.The mathematics properties of wavelet basis, including orthogonality,regularity,vanishing moments,and the symmetry, are systematically discussed.Then we discussed the most important theory of the wavelet—multi-resolution analysis theory and Mallat algorithm.Three wavelet de-noising methods for one-dimensional signal are introduced in detail,including the principles of wavelet transform modulus maximum de-noising method,the de-noising method based on wavelet threshold,and the spatially selective noise filtration(SSNF) method.We programmed these methods,and the simulation testing has proved correctness.Comparing the de-noising results,the advantages and disadvantages of each method and existing problems are pointed out.Finally,three kinds of wavelet de-noising method is applied to the field of seismic signal de-noise.We quantitatively,analyzed the selection problem of seismic signal wavelet bases function and decomposition scale by compared with the calculation error of reconstruction.After analyzed and compared the results of three de-noise methods,we found that most of the high-frequency noise can be removed using the spatially selective noise filtration(SSNF) method,but the amplitude of the signal has changed.However,based on wavelet transform modulus maxima and the threshold method of seismic signal can remove the high-frequency noise very well,it can also retained effectively high-frequency signals.