基于变分模态分解的地震随机噪声压制方法

针对经验模态分解（EMD）方法中递归迭代式筛选过程耗时过长、分解精度不高等问题，提出了基于频率域内全局自适应的变分模态分解（VMD）的地震随机噪声压制方法。与EMD类方法的迭代筛选模式不同，VMD方法的分解过程可转换至变分泛函最优求解过程，以每个带限窄带（BIMF）分量的估计带宽之和最小为约束，通过增广Lagrange目标函数将变分问题由约束性变为非约束性，采用交替方向乘子（ADMM）算法寻求变分泛函的最优解达到信号自适应分解的目的。ADMM中频率中心及带宽交替更新对偶上升，使两者同时达到最优趋势，并生成所有BIMF分量，具有更高的时间效率。同时，各模态分量在频谱上均具有带限特性，可实现信号频带的高分辨率、自适应剖分。实验结果表明，基于VMD的地震随机噪声压制方法具有优异噪声压制、幅值保持性能的同时，还具备较高的计算效率，可满足高维大尺度地震数据的处理要求。

Seismic random noise attenuation based on variational mode decomposition

The empirical mode decomposition (EMD) method usually has heavy computational burdens and low resolution in recursive iterative sifting process.To deal with these problems a globally adaptive variational mode decomposition (VMD) method in the frequency domain is proposed.Different from the EMD recursive iterative sifting mode,the VMD decomposition process can be transformed to solving the optimization problem of the variational functional,which is constrained with the minimum sum of the estimated bandwidth of each band-limited intrinsic mode function (BIMF) component.By introducing an augmented Lagrange function to build the unconstrained term,the alternate direction method of multipliers (ADMM) is used to seek the optimal solution of the variational functional to achieve the signal decomposition.During the iterative process,the center frequency and bandwidth of each component are constantly updated,all BIMF components are obtained at one time with higher time efficiency than EMD.Each modal component has band-limited characteristics in the frequency spectrum to achieve high resolution and adaptive splitting of the signal band.Finally,tests on theoretical model and field data show that the proposed VMD method has not only excellent noise-attenuation and amplitude-preservation performances,but also high computational efficiency,which can meet the processing requirements of high-dimensional and massive seismic data.