Optimal Difference Method Research And Application

In the complex medium, elastic wave simulation is important and quite active research direction in mechanics, mathematics, and geophysics. The finite-difference is an effective method in realizing the elastic wave to forward simulation. The conventional finite-difference requires very fine computational grids when accuracy of computation is improved. This problem is avoided when the derivatives are computed by multiplication in the Fourier domain, but this method is restricted to computational environments. Therefore, this thesis has studied the optimal difference method, and applies it in the elastic wave to forward simulation.The optimal-difference is a fast difference. It introduces the optimal difference operator in the finite-difference foundations. The optimal-operator is designed by minimizing the corresponding peak relative error in group velocity.This thesis also discussed the application of this method in the elastic wave to forward simulation. The difference is carried on the displacement-stress elastody-namic equation. The operator half length takes to 4-6 and each wave length takes 3 sampling, then the precise wave field can be obtained.In the process of solution, staggered-mesh technology which is similar with Virieux is used. This technology calculates the different wave field quantity on the different mesh point. However, because the model size is limited, it produces the disturbance wave field. This disturbance uses the Higdon boundary condition to absorb it. This kind of boundary condition is composed of some operator, and simultaneously solves four vertices problems. It is more important that identical formula can apply to different dimension and does not need to make the revision.The optimal-difference is stable to all Poisson ratio, so it does not limited to medium model when this method is used to simulate the propagation of elastic wave and the speed of computation is quicker one magnitude than conventional difference.