A Study On The Application Of Compression Sensing In Seismic Data Velocity Modeling

Velocity analysis is the cornerstone of the subsequent processing of seismic data.How to obtain a high-precision velocity model has always been one of the topics that geophysicists have been specializing in.An accurate velocity model can greatly improve the quality of the imaging of underground media structures,making the result of interpretation more reliable.Normal velocity modeling is to pick up the velocity spectrum uniformly,and the unpicked part is determined by linear interpolation with the known.If there are too few velocity spectrum sample points,it will cause a large error in the velocity of the interpolation part.In order to be able to build a complete and accurate velocity model,the velocity spectrum sample points that need to be picked must meet the Nyquist sampling theorem,which has led to a substantial increase in labor.However,the emergence of compressed sensing provides a solution to this problem.Compressed sensing theory proves that when the signal is sparse,the original data can be reconstructed from data that is much smaller than the sampling point specified by the Nyquist sampling theorem.In this paper,we will discuss the application of compressed sensing in velocity modeling with seismic data.Following the theory of compressed sensing,through the study of the nature of the measurement matrix,we calculate the sampling matrix according to the principle of minimizing the maximum cross-correlation value and sample the non-sparse signal makes the perception matrix satisfy the RIP property to meet the use conditions of compressed sensing.Then it is to study the compressed sensing reconstruction algorithm,including convex optimization algorithm,greedy algorithm includes m matching pursuit algorithm(MP)and orthogonal matching pursuit algorithm(OMP),understand the advantages and disadvantages of different algorithms,determine the use of each algorithm.At the same time,we also analyzed the impact of different iteration times on the accuracy of reconstruction results.An earthquake velocity modeling method based on compressed sensing algorithm is formed.By analyzing the nature of seismic data,the transform domain is selected according to the purpose,and the seismic velocity data is sparsely represented,and then calculated the required sampling matrix with the principle of minimizing the maximum cross-correlation value according to the sparse basis.The velocity spectrum is analyzed by velocity scanning to pick up the velocity spectrum of the target sample point.Finally,the reconstruction algorithm is used to establish a complete velocity model in the direction of sparse sampling.The reconstructed velocity model can be compared with known velocity data such as logging to determine the accuracy of the reconstructed results.If the result is good,the reconstructed result can be used for subsequent data processing;If the result error is large,modify the parameters,such as increasing the sampling rate or increasing the number of iterations,so that the reconstruction result reaches a certain accuracy.The paper uses the indoor physical model data of the regressive sand to realize the test based on the compressed sensing velocity modeling algorithm.First convert the seismic data to a sparse representation in the frequency domain,and determine the sparse sampling matrix by sparse basis.Then velocity scan the sampling point to pick up the velocity spectrum.Finally,a complete velocity model is obtained through a reconstruction algorithm,which is used for dynamic correction and stacking to obtain stacked section.By comparison with normal velocity analysis modeling,dynamic correction and stacked section,the results of velocity modeling based on compressed sensing are all acceptable.The reconstructed velocity model has the same velocity distribution as the theoretical velocity model,and the structure of the stacked section is also consistent with the actual physical model.Compared with the conventional velocity modeling,the focus of the velocity modeling method based on compressed sensing falls on the construction of the sampling matrix to determine the sampling point and reconstruction of the complete velocity model through the sampling point.Most of the work in this method is mainly done by computer calculation,which greatly reduces the manual workload and tries to avoid the thinking error caused by subjective factors.