A Fast Uncoiled Randomized QR Decomposition Method For High-dimension Seismic Data Reconstruction And Simultaneous Sources Separation

Due to the limitation of acquisition conditions and the influence of field environments,it is difficult to obtain ideal complete regular sampling seismic data.Irregular sampling seismic data not only interfere with the operation of subsequent data processing,but also affect the establishment of the velocity model of subsurface strata and make the fault structures fuzzy.In the end,the purpose of accurate interpretation and description of subsurface geological structure can't be achieved.Therefore,the problem of regular interpolation and reconstruction for seismic data has been extensively studied.Besides,in the traditional seismic acquisition,it usually extends the interval time of adjacent shots or increases the distance between the shot points to avoid the crosstalk interference in the signals generated by the sources.However,this traditional acquisition method will prolong the operation period and increase the cost of exploration.With the concept of blended acquisition technology was proposed,the exploration cost is reduced effectively.But the blended data usually contain several traditional single shot data,because the blended acquisition ignores the interference between the shots.Hence,the separation technology for blended seismic data becomes a key step.In this paper,the problem of high-dimensional seismic data reconstruction is studied.The existed researches show that the well sampled seismic data can be represented by a low rank block Hankel or block Toeplitz matrix.The incomplete data and random noise can destroy the low rank property of the block matrix.Hence,the recovery of missing seismic traces can be treated as a rank reduction problem.This paper presents a fast rank reduction algorithm named uncoiled randomized QR decomposition to interpolate the pre-stack 5D irregular missing seismic traces.The randomized QR decomposition algorithm is used to improve the efficiency of the reduced rank decomposition.Moreover,for the low computational efficient problem of the rank-reduced level-4 block Toeplitz matrix,a fast uncoiled diagonal average strategy is designed.The new diagonal average algorithm can greatly reduce the amount of data storage and decrease the computational cost.Compared with the popular matrix rank reduction algorithms,such as the Singular Value Decomposition(SVD)and the Lanczos bidiagonalization decomposition method,this method has higher computational efficiency and faster reconstruction speed.The problem of separation of seismic data with large blending factor is also studied in this paper.The blended acquisition of multi-source seismic data is regarded as a forward problem,and the separation problem of blended data comes down to an inverse problem.In this paper,an iterative method which combined uncoiled random QR decomposition algorithm and threshold filtering is used to suppress the crosstalk noise,extract effective signals iteratively and realize the separation of blended data.In the end,the validity of the proposed method is verified by the synthetic data experiments and a field data test.