Wavelet Transform And Its Application In Enhancing S/N Ratio Of Seismic Data

Fourier transform and short time Fourier transform are the chief methods in signal analysis, however, they suffer inherent limit: they can analysis a signal only 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 geophysics is a complement and advancement of existing processing and interpreting methods.Theory of continuous wavelet transform is discussed in this paper. The continuous wavelet transform is compared with the Fourier transform and short time transform, and it is approved to have the ability of time-frequency analysis and have the characters of band-pass filter. Based on the frame, the wavelet transform has some redundancy, and the redundant frame makes the computing stable but enlarging the work remarkably. Discrete wavelet transform can reduce the redundancy of continuous wavelet transform, the typical form of discrete wavelet transform is discrete dyadic wavelet transform. The theory of discrete dyadic wavelet transform and the construction of orthogonal wavelet is discussed on the base of multi-resolution analysis. This article discusses the algorithm of decomposition and reconstruction, which is approved to be self-contained.The scaling function and wavelet function can express the signal with the form of approximate and detailed components in some multi-scaled space, and the approximate and detailed components correspond to separate band of frequency. The de-noising methods are based on the speciality of frequency sharing of wavelet.This article studies on the S/N ratio quantitatively and discusses the de-noising methods of single-frequency interference wave, random noise and surface interference wave. If the spectrum of single-frequency interference wave and the spectrum ofsignal are separated, then the noise can be eliminated by the means of wavelet composition; if the spectrum of single-frequency interference wave and the spectrum of signal mix, it is hard to separate the signal and noise entirely. For threshold de-noising random noise in decomposition components, the most important work is to compute and set the threshold rightly. Through the test model processing, it is concluded that different threshold de-noising methods lead to different results, and the hard threshold is suitable for higher S/N ratio, on the other hand, the soft threshold is suitable for lower S/N ratio. It is also flnded that if the spectrum of signal and the spectrum of surface interference wave mix, it's impossible for wavelet decomposition to eliminate surface interference wave without harming the signal. We use wavelet decomposition and singular value decomposition to suppress the surface interference wave, the result is better than former method since it can suppress the noise effectively and maintain the dynamic character of the seismic signal.At last, through the processing of real seismic data, it is approved that the wavelet transform is effective and correct in suppressing noise.