The Study On Attenuating Seismic Random Noise With Curvelet Combinatorial Method

With the development of exploration, the depth of exploration becomes deeper and situation becomes more complex, so that the seismic signal from deep zone will be distorted and distrubed, the seismic record today has the feature of low signal-to-noise ratio, complex noise categories and weak effective signal, which would severely restrict the latter programmes, like high signal-to-noise ratio, exact image and property inversion. In order to settle these problems, the operator of seismic processing would like to find more effective methods in the area of signal processing.The foundation of wavelet transform is Fourier transform, wavelet transform has obtained big development in data processing area because that it has very good ablity on time-frequency analysis and superiority to express linear dimension limited function. Unfortunately, linear dimension discrete wavelet just has few derections, so that is can not express high uygur functions which contain line singularity and surface singularity. In order to overcome this limitation, schorlars propose the Ridgelet transform, however, the redundant property of Ridgelet transform, it is difficulty to process the field data. Curvelet transform, developed in recent years, has made big breakthrough in the area of image processing and analysis, and it became the favor of geophysicst.In 1999 ,Candes and Donoho put forward the first generation curvelet transform, its initial application domain includes: Computer image denoising, image fusion, SAR denoising, deconvolution and so on. At first these applications generally uses the digital curvelet transform, which is based on the tranditional structure, it firstly carries on the pretreatment to the image, then uses the Ridgelet transform. This algorithm has the high redundance, low computational efficiency. In last ten years, the research of curvelet transform focus on its understanding and application. In 2002, Candès et al. proposed the new curvelet frame construction, we called it the second generation curvelet transform. The new theory is divided from Ridgelet transform, and enhances the computational efficiency of curvelet transform, so that it proviede the possibility of application in the field data processing. After this, they proposed two kinds algorithms based on the second generation curvelet transform in 2006, USFFT algorithm and Wrap algorithm respectiveley. Compared the original discrete method, these two methods are simpler, faster, and reduced the redundancy which tradition algorithm brought. This has built the solid foundation of curvelet transform into the area of seismic data processing. This article uses the Wrap algorithm of second generation curvelet transform, with this help the actual operation becomes simple and easy.This article introduces and summaries the curvelet thresholding iterative method systematically. Curvelet thresholding iterative method has good result in suppressing seismic random noise, it fully uses the sparsity of curvelet transform. It takes the problem of suppressing seismic random noise into the complex L1-optimization problem, Solving this problem we use the thresholding iterative method, and finally achieve the result of suppressing random noise. The thresholding iterative method is an essential method of solving the sparse restraint optimization inversion. It has good theoretical principle, and obtained scholars'confirmation of it continuity, the astringency and the stability. The curvelet thresholding iterative method also makes the satisfying result in seismic field processing. However, the curvelet thresholding iterative method faces a question that it has low computational efficiency when the times of iterative is high.This article uses the difference of correlation between effective signal and random noise in seismic record. In order to suppressing random noise, I design the Curvelet Combinatorial Method, the methods which combine with curvelet transform are median filter and Radon transform. The basic theory of Curvelet Combinatorial Method is that separate frequency to process seismic data, and use the correlation of effective signal to enhance the continuty of them, finally we will have the result of suppressing the seismic random noise in the record. The article use the Curvelet Median Method, fx deconvolution and curvelet thresholding method on the modeling, and obtain the follow conclusion: the fx deconvolution could enhance the data signal-to-noise ratio, however it also could lose some effective signal and the degree of enhancement is not high; curvelet thresholding method is really good on suppressing seismic random noise, enhance the signal-to-noise ratio and it almost does not lose any effective signal; Curvelet Median Method could suppress the most random noise among these methods and largely enhance the signal-to-noise ratio of data. The denoising effect is obvious along with the data's signal-to-noise ratio reduction, but Curvelet Median Method will lose some effective signal when the events are high inclination angle. In view of the shortcome of Curvelet Median Method, the article designs the Curvelet Radon Method, it makes up the flaw of Curvelet Median Method to a certain extent. Finally, the article applies the Curvelet Combinatorial Method into the seismic field data, and it has very good results on supressing seismic random noise.