基于L1-L1范数稀疏表示的共偏移距道集地震数据重建方法

Seismic data reconstruction based on L1-L1 norm sparse representation in common offset gather

传统地震数据稀疏重建方法面临着:(1)叠前共炮点道集或CMP道集反射波为双曲线型同相轴,地震数据重建会损害有效波;(2)地震信号存在噪声和畸变,要求重建方法具有较好的噪声鲁棒性.针对这两个问题,提出一种基于L1-L1范数稀疏表示的共偏移距道集地震数据重建方法.该方法利用了共偏移距道集中地震波为水平同相轴,无道间时差,满足空间重建要求,和L1-L1范数稀疏表示具有较好的噪声鲁棒性.首先抽取共偏移距道集地震数据,并根据地震采集信息构造复合采样矩阵,然后采用L1-L1范数稀疏表示对数据稀疏重建后,再将数据反变换回共炮点道集或CMP道集,能够同时实现地震信号稀疏重建和随机噪声压制.理论模型和实际数据试算结果验证所提方法具有较好重建精度和噪声鲁棒性.

Traditional seismic data sparse reconstruction methods are faced with:(1) The reflections are hyperbolic events in the pre-stack common shot point gathers or CMP gathers, the seismic data reconstruction will damage the effective waves;(2) Seismic signal which is contaminated by noise and distortion, requires that the reconstruction method has better noise robustness. Aiming at these two problems, a method of seismic data reconstruction based on L1-L1 norm sparse representation in the common offset gather is proposed. The method utilizes the seismic waves are horizontal events in the common offset gathers, without time differences between traces, and the L1-L1 norm sparse representation has better noise robustness,meets the requirement of data reconstruction. Firstly, the common offset gather seismic data is extracted, and the observation matrix is constructed according to the seismic acquisition information. Then, the data is sparsely reconstructed using the L1-L1 norm sparse representation, and then the data is reversed back to the common shot point gather or CMP gather. The theoretical model trial and the actual data application results verify that the proposed method has better reconstruction accuracy and noise robustness.