Forward Modeling Of Three-dimensional Wave Equation In Frequency Domain

The seismic wave forward modeling is to study the propagation characteristics of seismic waves in the subsurface medium and is the basis of inversion and migration.Among them,the frequency domain finite difference has the advantages of facilitating parallel acceleration and stability constraints,compared with the time domain.However,the shortcomings of frequency domain forward modeling are also quite obvious.When dealing with large model problems,huge memory loss will occur,resulting in low computational efficiency.The reason is that in the frequency domain forward process,a large sparse matrix needs to be constructed and solved.The dimension of the matrix is proportional to the number of grid points.In order to optimize the memory and efficiency issues,a large number of experts and scholars have been working on the grid for decades,making great progress.Therefore,the focus of this paper is on the study of the grid aspect of the frequency domain forward,under the condition of ensuring accuracy,to reduce the required grid points to reduce memory loss and improve efficiency.In this paper,we derive the mixed 25-point finite difference scheme by optimizing the9-point difference format.Through model trial calculation,we can find that the hybrid25-point finite difference scheme is more accurate than the 9-point finite difference grid.It takes up more memory and is less efficient.It is analyzed that the forward algorithm of the rotating coordinate system only applies to the same horizontal and vertical spatial sampling interval.So we add the idea of the average derivative to the 25-point finite difference,and realize the frequency domain forward modeling on the non-uniform grid.Compared with the traditional mixed 25-point finite difference format,it can effectively reduce the accuracy requirement.The memory loss has improved the computational efficiency to some extent.In recent years,underground media faced by seismic exploration have become more and more complex.As the three-dimensional problem is closer to the real situation of the underground medium,it is getting more and more attention from experts and scholars.To this end,we formulate the three-dimensional mixed 27-point finite difference scheme and add the idea of average derivative,so that the three-dimensional frequency domain forward modeling can also be used for non-uniform grids.We regard continuous non-uniform grids as many A collection of non-uniform meshes.By reducing the number of grid points,the memory loss is reduced and the calculation efficiency is improved.At the same time,the three-dimensional frequency domain forward modeling is more practical and flexible.