应用快速不动点延续算法的地震数据重建

Seismic data reconstruction based on fast fixed point continuation algorithm

地形条件或采集成本等因素往往导致现场采集到的地震数据呈现不完整分布,从而影响后续地震数据的分析与处理,因此对原始地震数据做高精度重建显得尤为必要。不动点延续算法是一种基于核范数最小化的重建方法,但该算法需进行奇异值分解(SVD,其计算复杂度为O[mnmin(m,n)],m、n为矩阵的维度),且当矩阵维度较高时运算耗时较长;传统方法是直接利用PROPACK加速包,将计算复杂度降低为O(rmn)(r为矩阵的秩),但此加速方法依然耗时较长。为此,提出一种快速不动点延续算法,通过利用块克雷洛夫迭代近似奇异值分解算法和子空间复用技术,将SVD的计算复杂度降低为O[mcmin(m,c)](c?min(m,n),c∈R^+)为复杂度常数。仿真地震数据和实际地震数据重建结果表明,在确保一定信噪比的情况下,文中提出的快速不动点延续算法的计算效率显著高于传统加速型不动点延续算法。

Due to factors such as terrain conditions or acquisition costs,acquired seismic data may be incomplete or irregularly distributed,which affects subsequent seismic data analysis.Therefore,it is important to reconstruct seismic data with high precision before the data processing.The fixed point continuation algorithm is a very effective reconstruction method based on the minimization of nuclear norm.However,it is based on singular value decomposition(the computation complexity of singular value decomposition is O(mn min(m,n)),where m and n are the dimension of the matrix).Therefore,it will take a long time to solve the problem when the dimension of the matrix is high.Using PROPACK is one of conventional acceleration ways,which can reduce the computation complexity to O(rmn),where r means the rank of observed matrix.But this way still takes a long time.To overcome this issue,an improved fast fixed point continuation algorithm is proposed in this paper,which uses the block Krylov iterative approximate singular value decomposition algorithm and subspace multiplexing technique to reduce the computation complexity of singular value decomposition to O(mc min(m,c)),where(cmin(m,n),c∈R+).Experiments on simulating data and field seismic data show that the proposed algorithm provides much better performance than the conventional algorithm in the computation time with a reasonable signal to noise ratio.