Discontinuous Galerkin Finite Element Method Seismic Wave-field Forward Modeling

The numerical simulation of seismic wave field is an important means to study the law of seismic wave propagation in underground media.In the past few decades,numerical simulation methods such as finite difference method,finite element method(FEM)and pseudospectral method have appeared successively.These methods have their own advantages and limitations in seismic wave field simulation.In recent years,a new finite element method,Discontinuous Galerkin FEM(DG-FEM),has been gradually applied to seismic wave field simulation.DG-FEM inherits the advantages of traditional FEM and can adapt to the numerical simulation of seismic wave fields under various complex geological structures such as undulating surface.Under the same conditions,DG-FEM has higher precision than other numerical simulation methods.Due to the complete locality of DG-FEM,DG-FEM can better deal with complex geological problems such as contact discontinuity,large gradient and large deformation.Based on these characteristics of DG-FEM,and also to meet the requirements of numerical simulation for complex geological structures,this paper introduces the discontinuous finite element method into the process of solving seismic wave equations.Firstly,the DG-FEM is used to solve the seismic wave equation.The discontinuous finite element governing equation of the acoustic wave equation and the elastic wave equation are derived.Secondly,the algorithm implementation of DG-FEM to solve the wave equation is introduced in detail,and the fourth-order Runge-Kutta time discrete format is applied.Then,Open Mp multi-thread parallel operation is performed on the obtained large matrix equation to improve the operation efficiency.The algorithm is tested on homogeneous medium,layer medium and undulating surface complex model.Numerical experiments show that DG-FEM has high precision and can adapt to the numerical simulation of various geological structures,especially suitable for simulating the propagation of seismic waves in complex medium structures such as undulating surfaces.