【作者】 仝中飞；

【导师】 王德利；

【作者基本信息】 吉林大学 ， 地球探测与信息技术， 2009， 硕士

【摘要】 .基于Curvelet变换的阈值迭代法在地震数据随机噪声衰减和缺失道插值中的应用是本文研究的重点。本文在前人的工作基础上,通过对Curvelet变换及其稀疏性和阈值迭代法的分析、研究和总结,将Curvelet变换与阈值迭代法结合起来,并在此基础上,把地震数据随机噪声衰减和地震缺失道插值问题描述为一个l1模最优化问题。其求解方法即为阈值迭代法。其中在去噪问题中,通过与传统的中值滤波法、FX反褶积法和近些年发展起来的小波阈值法去噪相对比,理论模型和实际资料的计算结果表明,Curvelet阈值迭代法去噪不仅得到了更高的信噪比,而且对有效信号的损失更少;另外,对Curvelet阈值迭代法去噪结果进行方向控制,进一步提高了信噪比。在缺失道插值问题中,对均匀缺失和随机缺失的地震道数据实现了较为精确的插值,取得了较高的信噪比,验证了随机缺失道插值效果好于均匀缺失道插值效果。更多还原

【Abstract】 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.更多还原