Research On The High Precision Forward Of 3D Wave Equations

The study of the propagation of the wave in the underground medium is of great value to the geological exploration.In order to simulate the underground wave field better,it is necessary to develop and perfect the solution to the problem,and the wave equation is acting as an important branch of the forward problem.In many areas,the wave equation has important applications.For example,we can describe the propagation of seismic waves in underground media by using various wave equations in elastic dynamics,and acquire seismic data by forward modeling of wave equation.The formation of seismic data can be used to simulate the forward equation of wave equation.For the problem of volatility equation,it is faced with the difficulties such as the constructive scheme has some restrictions on the step size,the numerical solution is not suitable and so on,and there will be considerable computation and storage in the practical application.Therefore,the research on forward of wave equation has important theoretical significance and extensive application value.The study of the two-dimensional wave equation has laid a theoretical foundation for the study of higher dimensional wave equation.Firstly,the paper introduces the main methods of forward modeling,including finite difference method,finite element method and pseudo-spectral method.The paper gives a brief introduction to the initial boundary value problems of wave equation and three common difference schemes of finite difference method,including classical explicit scheme,classical implicit scheme and VonNeumann scheme.For finite element method,the paper introduces the main six-step process.As to the pseudo-spectral method,the paper introduces the central difference and time derivative,as well as Fourier transform and spatial derivative.Secondly,the two-dimensional wave equations are used as the mathematical model.Then,the finite difference method of explicit and implicit scheme is used to discretize the model,which constructs the eleven-point implicit scheme and the fifteen-point implicit scheme,and adopt different methods to deal with the boundary condition,and the convergence of the algorithm is verified.Followed,the paper uses MATLAB to simulate the explicit difference calculation format of the structure,and analyze the simulation results,which shows that the second and third boundary condition processing is superior to the general boundary condition processing method.Finally,the mathematical model of the three-dimensional wave equation is studied on the basis of the two-dimensional wave equation,where the three-dimensional wave equation is discretized,the fifteen-point implicit scheme and the twenty-one implicit scheme are constructed,different ways are used to solve the boundary condition,and the convergence of the algorithm is verified.To simulate the explicit difference calculation format of the structure and analyze the simulation results,MATLAB is used which shows that the virtual auxiliary boundary layer method is better than other two methods.