Quantitative Analysis of Numerical Dispersion with Finite Difference Method

The continued product formula of differential coefficients can be obtained by deriving second-order time, 2Nth-order space difference equation from first order speed-stress elastic wave equation. It is necessary to calculate the difference matrix between the numerical simulation results of from second-order space to tenth-order space in uniform media of half space to get the sum of absolute value by using the defined formula. If we analyze the various reasons that cause numerical dispersion and calculate results of the absolute sum, the numerical dispersion can be effectively reduced if space order is increased in a certain range. However, the effect of limiting the numerical dispersion will decrease when the space order reaches a certain level, now it's time to increase time order. This article aims at providing suggestive advices by analyzing effects in the process that discrete time and space variation of wave equation.