Research On Seismic Data Reconstruction Method Based On Weighted L1 Norm

In the process of seismic data acquisition,due to the limitation of complex terrain in the field or the restriction of economic cost,it often leads to irregular missing of seismic traces,which will seriously affect the later data interpretation and judgment results.Therefore,it is necessary to reconstruct the missing seismic data.At present,most seismic data reconstruction methods are based on L1 norm,which does not take into account the continuity between data bodies and reduces the reconstruction accuracy.Therefore,this paper proposes a seismic data reconstruction method based on weighted L1 norm algorithm.This method uses multiscale and multidirectional curvelet transform as sparse basis,and combines it with compressed sensing theory and spectral projection gradient algorithm.The weighted L1 norm algorithm fully considers the continuity characteristics of the effective wave of seismic data,and uses the correlation of the adjacent slice curvelet coefficients as the prior information to promote the sparse coefficient recovery.The weight distribution formula is determined by analyzing the performance of the weighted L1 norm algorithm,and the optimal weighted parameter values are determined by numerical simulation experiments within the value range.In this paper,the two-dimensional seismic data are arranged into three-dimensional seismic data volume along the shot point,detection point and time sequence,and 50%one-dimensional random undersampling is carried out along the shot point direction.The weighted L1 norm algorithm and the standard L1 norm algorithm are used to reconstruct the missing data.The experimental results show that the weighted L1 norm algorithm has better reconstruction effect,but the one-dimensional random undersampling only uses one spatial direction information to restore the missing data,and the reconstruction effect is limited.For this reason,50% two-dimensional random undersampling is performed on the three-dimensional seismic data volume along the direction of the shot point and the detection point.The experimental results show that adding one direction information to restore the missing data can effectively improve the reconstruction accuracy.At the same time,in order to improve the computational efficiency and save the time cost,this paper also proposes the idea of directly processing the frequency slice.Because the frequency sample points have symmetry characteristics,only half of the sample points need to be processed,and the other half is directly obtained by conjugate.The reconstruction method can save about half of the time compared with the time domain reconstruction.Moreover,the transformation of data volume from time domain to frequency domain can further improve the sparsity of seismic signals and effectively improve the reconstruction accuracy.By reconstructing one-dimensional and two-dimensional undersampling theoretical models,noisy data and measured seismic data in time domain and frequency domain,the results show that the method proposed in this paper has high reconstruction accuracy,fast operation speed,strong anti-noise ability,and both effectiveness and practicability.