The Study On Seismic Data Denoising And Interpolation With Curvelet Thresholding Iterative Method

This paper combines the curvelet transform that developed in recently years with the thresholding iterative method that solves optimizational inversion problem. The primary study is the application of curvelet-based thresholding iterative method in seismic data random noise attenuation and missing trace interpolation. Especially, we discuss detailedly seismic data random noise attenuation, and we compare it with traditional median filter, FX deconvolution and wavelet threshold methods, and finally, we know that curvelet thresholding iterative method not only increases sufficiently signal noise ratio, but also damages the least effective signal. Then, we make direction controlling after curvelet thresholding iterative denoising, this further increases signal noise ratio. In the aspect of seismic data missing trace interpolation, we interpolate respectively for uniform missing trace modeling data and nuniform missing trace modeling data, and proved the feasibility of this method.Fast Discrete Curvelet Transform is a basic tool in this paper's research. Curvelet transform was proposed firstly by Candès and Donoho in 1999. Its initial application fields contain computer image denoising, image fusion, SAR denoising, deconvolution and so on. The digial curvelet transform used in these initial applications was generally based on tranditional structure, that is, it was achieved by pre-processing image firstly and then ridgelet transform. This algotiehm is more redundant. In the past several years, making curvelet transform become easier use and understanding was its primary research content. Candès et al proposed new curvelet transform frame system in 2002, and it was called second generation curvelet transform. This new theory frame system provides the possibility for increasing the speed of curvelet transform. From then, they proposed two fast discrete realization methods based on second curvelet transform in 2006. These methods become easier and more rapid and decrease the redundancy of traditional algorithm. It is a solid basis for curvelet-based seismic data processing. Our paper makes use of this transform and it makes practical operation easy to realize.Thresholding iterative method is a basic theory in our paper's research. It is used to solve sparsity constraint optimization inversion problems. Daubechies et al have derived strictly equation, and described detailedly its continuity, convergence and stability. This method assumpts that signal is sparse. We verify that curvelet transform has much better sparsity than Fourier and wavelet transform on seismic data. So we know that curvelet-based thresholding interative method has better solving precision. Moreover, we describe seismic data denoising and interpolation problems as a one-norm optimization problem, and then solve it with curvelet-based thresholding iterative method.Seismic data random noise attenuation is the main study content. We compare curvelet thresholding iterative method with conventional median filter, FX deconvolution and wavelet threshold methods in the modeling experiment, and finally, come to the conclusions: median filter could not obtain satisfied denoising result, and it damages much signal. This phenomenon will become worse, especially when noisy data have low signal noise ratio; FX deconvolution have good denoising result for seismic data random noise, however, it damages seriously high frequency signal, and when signal noise ratio of data is low, it losses more effective signal; Wavelet threshold method can obtain well denoising result that could be close to FX deconvolution method, but the denoised seismic data become fuzzy because of defect of wavelet transform itself, this decreases the resolution in seismic data. Also, this method damages much signal. Curvelet-based thresholding iterative method is very effective for seismic data random noise attenuation. It not only attenuates a lot noise, but also damages less signal. So it is a effective method to denoising. In addition, direction controlling which based on the result of curvelet thresholding iterative denoising increases signal noise ratio of data, this is a highlight in the paper. Finally, we realize curvelet thresholding iterative denoising in field data, and obtain fine result.We realize seismic data missing trace interpolation based on curvelet thresholding iterative in the last part of the paper. We compare the interpolation results of uniform missing trace with nonuniform missing trace, and vetify that interpolation result is much better in the condition of nonuniform missing trace. This is because that the sparsity of nonuniform missing trace is better than uniform missing condition in Fourier domain. In addition, interpolation result is not perfect for 2D data when the percentage of missing trace is big, so we prospect a method of curvelet thresholding iterative in focus domain. Focus transform will increase furtherly the sparsity of data, and this will obtain much better interpolation result in theory.