基于压缩感知技术的Shearlet变换重建地震数据  

Seismic data reconstruction with Shearlet transform based on compressed sensing technology

作　　者：张良[1] 韩立国[1] 许德鑫 李宇[1] 李慧[1] 

机构地区：[1]吉林大学地球探测科学与技术学院,吉林长春130026 [2]中水东北勘测设计研究有限责任公司,吉林长春130021

出　　处：《石油地球物理勘探》2017年第2期220-225,共6页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目(41674124);国家"863"项目(2014AA06A605)资助

摘　　要：基于预测滤波方法进行地震数据重建的误差偏大,基于波动方程进行地震数据重建的计算量较大,基于某种变换的地震数据重建精度偏低。为此,利用基于压缩感知技术的Shearlet变换重建地震数据。基于信号的稀疏性,在欠采样的情况下,首先根据地震数据的缺失情况设计采样矩阵,然后使用Shearlet变换将地震数据稀疏化,再采用正交匹配追踪算法在Shearlet域中完成对稀疏系数的重建,最后通过Shearlet反变换实现地震数据重建。实验结果表明,基于压缩感知技术的Shearlet变换能够很好地重建地震数据,且重建精度高于基于压缩感知技术的Fourier变换、离散余弦变换、小波变换和Curvelet变换。Seismic data reconstruction based on the prediction filtering usually has huge error; seismic data reconstruction based on the wave equation needs large calculation time; and seismic data reconstruction based on some transform methods suffers low accuracy. Therefore, we propose seismic data reconstruction with Shearlet transform based on compressed sensing. Based on the signal sparsity, the sampling matrix is designed according to seismic data loss, and seismic data get sparse with Shearlet transform. Then, the orthogonal matching pursuit algorithm is used to reconstruct the sparsity coefficients in the Shearlet domain. Finally, seismic data reconstruction is realized by inverse Shearlet transform. Experimental results show that the Shearlet transform based on compressed sensing can well reconstruct seismic data. Moreover, the proposed approach has higher reconstruction accuracy than the Fourier transform, discrete cosine transform, Wavelet transform, and Curvelet transform. © 2017, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.

关 键 词：压缩感知 SHEARLET变换 采样矩阵 地震数据重建 正交匹配追踪 

分 类 号：P631[天文地球—地质矿产勘探]