基于一种三维低冗余曲波变换和压缩感知理论的地震数据重建

Seismic reconstruction with 3D low-redundancy curvelet transform and compressed sensing theory

基于稀疏变换的重建方法是地震数据重建的研究热点,其中稀疏变换的性质对重建的效率和质量起关键作用。曲波变换对波场数据有非常稀疏的表示和可靠的数值效果,然而三维曲波变换的冗余度在24~32之间,须消耗很多的内存和计算时间。提出基于一种低冗余度曲波变换的地震数据重建方法,介绍低冗余曲波变换并且分析其优点,给出一个解基于分析的1范数模型的快速迭代阈值方法。数据实验结果表明:该低冗余变换将三维曲波变换的冗余度降低了60%,能够有效提高数据重建的计算效率;基于低冗余度曲波变换的数据重建的计算效率是基于原始曲波变换重建效率的4倍,对于10%的采样比例仍然能够得到较好的重建和去噪效果。

Sparse transform based seismic data reconstruction is a hot topic in seismic reconstruction,where properties of the sparse transform may influence the results of reconstruction greatly.Curvelet transform is a multi scale,multi directional,and local transform which has nearly the sparsest expression for seismic data.However,this transform is a highly redundant transform with redundancy about24-32for three dimensional data.To improve the efficiency of curvelet based reconstruction,this paper proposed a low redundancy curvelet transform based seismic reconstruction.The new transform was introduced first and its merits for seismic signal processing were analyzed,followed by an iterative thresholding method for analysis based L1norm regularized models.Numerical experiments illustrate that the low redundancy transform can reduce60%redundancy of the original3D curvelet transform,thus improves greatly the computational efficiency.The reconstruction computational efficiency based on the low redundancy transform is4times of the original curvelet based reconstruction,for example,even for10%sampling ratio,this low redundancy curvelet can get acceptable results.