Research Of Seismic Data Denoising Methods Based On Sparse Transform

With the improvement of seismic data requirements, denoising method is becoming more and more important, common denoising methods have their own limitations, to looking for a better method that can remove the noise in a greater degree and reserve more effective signal also adapt to the seismic signal, this article combine sparse representation theory which developed fast in recent years with seismic signal denoising. Under many circumstances, the effective signal and the noise signal in the temporal domain is difficult to directly isolated. But after a special conversion, due to the differences in the transformed domain between the characteristics of the effective signal and noise, they become easily to be separated. In this article we use the sparsity of coefficients of a signal in the sparse transform domain to deal with the the coefficients in the sparse domain. Extracte large coefficients which represents the effective signal and suppress the small coefficients which represents noise, in order to achieve the goal of denoising noisy original data.At the same time, the paper by the research of discrete Fourier transform, discrete cosine transform, wavelet transform and curvelet transform four commonly used sparse transform meticulous, and achieve the sparse representation of the seismic data with these sparse transform. Find the best proportion of the sparse representation coefficients. On the basis of the sparse representation theory we proposed a new definition named transform sparsity concept of seismic data, and measured sparse ability to transform the target seismic data’s sparsity of the four methods. We use this concept to manage the coefficients in sparsity region to extract the effective signal and suppress random noise. In addition, we focuses on the curvelet transform with threshold of seismic data denoising in this article, and proposed an improved single threshold strategy. On the other hand, we gave the process and the algorithm to enforce the curvelet transform method in denoising under this threshold. The correctness and effectiveness of this method on seismic data denoising had been proved by the numerical experiments. Compared with the results of other sparse transform, the multiple scales and directions of curvelet transform make it much better than others in adapting to the seismic data.Finally, we proposed a new seismic data denoising method in this paper by processing the coefficients of curvelet transform which called cascading curvelet transform method. The method make use of the characteristics that the coefficients of curvelet transform has a sparse representation of seismic signal, and the coefficients of noisy signal has the same characteristics with the seismic data that they both have events. Make these coefficients as new target signal, do curvelet transform on them in each direction and each scale. Denoise on the coefficients at first then use these new coefficients to reduct the seismic signal. It will be the final result of denoising. Numerical examples to verify the correctness of the method, and compare the results to the result from making use of discrete cosine transform and wavelet transform to deal with the curvelet coefficients. Results showed that using curvelet transform to manage the coefficients of curvelet transform is much better than the other two methods in denoising, at the same time it improved on the signal-to-noise ratio in comparasion with doing curvelet transform only one time.