Research On Forward Problem Of Three Dimensional Wave Equations In Hemispherical Regions

In the field of seismic exploration,forward modeling is often used,which plays an important role in seismic data,interpretation and observing system design etc.The steps of forward modeling of wave equation are that the known mathematical model,seismic source,(Such as rock formation density,velocity,etc.),simulate the propagation of seismic waves in various media to form artificial seismic records,and there are two types of wave equations widely studied: one is the acoustic equation and the other is the Elastic wave equation.With the development of science and technology and the deepening of research on seismic geology in underground geology,the simulation dimension of seismic technology has been developed from two-dimensional to three-dimensional,and three-dimensional numerical simulation can study the influence of underground media on seismic wavefield in more detail.Finite Difference,Finite Element and Finite Volume Method are often used methods for solving the forward problem of wave equation.In this paper,firstly,the research background,research significance and progress of wave equation forward modeling are introduced,and then the forward problem of two-dimensional wave equations is studied in semicircular region.According to circular region,two-dimensional wave equation is chosen as a specific mathematical model.By using the polar coordinate method,the equation is transformed to the two-dimensional wave equation in polar coordinates.Finally,the discrete equation is obtained by the finite difference method,and the boundary conditions are given to form the forward difference scheme of two-dimensional wave equation.To verify the feasibility of the algorithm,MATLAB numerical simulation is carried out.Then,based on the research of forward problem of two-dimensional wave equation,a three-dimensional numerical simulation technique of seismic wave was built.The three-dimensional mathematical model in the hemisphere area was established by spherical coordinate transformation method.The finite difference method is used to discretize and obtain the discrete equation,and the boundary conditions are processed to form the forward difference scheme of the three-dimensional wave equation.The solution process is numerically simulated by MATLAB,and then the absolute error of the displacement function is compared.The results fully show that the numerical forward modeling method can effectively deal with the seismic forward modeling problem and overcome the computational difficulties of the wave equation to a certain extent,which not only has theoretical innovation significance but also has strong feasibility and high efficiency.