HR: 0830h
AN: NS51A-04    [Abstracts]
TI: The Application Of Second-Generation Wavelets In Seismic Data Denoising
AU: * Cao, S
EM: csy@bjpeu.edu.cn
AB: In 1994 Swelden first proposed the wavelet transform based on lifting steps. Lifting scheme is a kind of flexible method of wavelet construction and it uses linear or nonlinear operators to implement wavelet transform and make sure the transform is reversible. Lifting theme is independent of Fourier transform and the wavelet transform based on lifting theme is also called Second-generation wavelet transform. Its features include: Keep the multi-resolution feature of first-generation wavelet; Independent of Fourier Transform; Fast arithmetic is easily to be achieved; Reverse transform is easier; Non-linear wavelet transform is available, etc. The paper discusses the principle and procedures of second-generation wavelet transform and apply it to the de-noising of seismic data. Examples on synthetic as well as field data prove that it is a new effective de-noising method. Assuming that the original signal c_j is decomposed into low frequency approximate signal c_j-1 and high frequency detail signal d_j-1 by lifting steps. The transform includes three steps: split, predict and update: (1)Split: The original signal is split into two non-intersectant subsets c_j-1 and d_j-1. The more correlative c_j-1 and d_j-1 are, the better the split effect is. Commonly, we divide a signal sequence into even sequence and odd sequence. (2) Predict: By means of the correlativity of the data, we can predict d_j-1 from c_j-1 by using a predict operator P. The resulting difference is the wavelet coefficient d[n], and it reflects the approaching degree of the two data sequences. (3) Update: After the two steps above, some characters of the resulting data sequence c_j-1 are not consistent with the original data, so update step is necessary. We can use an update operator U to generate a better data sequence c[n], and make it keep the characters of the original data sequence. The three steps above constitute a lifting step, and by iterative lifting steps we can obtain approximate signal c_j-n and high frequency detail signal d_j-n. After n times of decompositions, the original data can be represented as c_j-n, d_j-n, d_j-n+1, d_j-1. By changing operation orders and signs, we can get the reconstruction formulas very conveniently. The de-noising by second-generation wavelet transform is divided into three steps: wavelet decomposition, wavelet coefficient reduction and data reconstruction. The common wavelet de-noising methods include soft threshold and hard valve methods. Soft valve method is used in this paper. In the paper, wavelet Deslauriers-Dubuc(4, 2) is used to make wavelet transform. Based on the transform methods above, we can get different levels of approximation and detail signals. At each level, we use soft threshold method to reduce wavelet coefficients, and then reconstruct data. As a consequence, the noise can be reduced apparently. Second-generation wavelet transform is the further development of traditional wavelet theory. The research about its theory and application should be done more deeply. In the paper, we discuss the principles and transform process of Second-generation wavelet, and apply it to seismic data de-noising. Examples on synthetic as well as real data prove that it is a new effective de-noising method.
DE: 0910 Data processing
DE: 0935 Seismic methods (3025)
DE: 3025 Marine seismics (0935)
SC: Near-Surface Geophysics [NS]
MN: 2005 Joint Assembly