Dispersion analysis for the finite element algorithm in acoustic wave equation numerical simulation

This paper focuses on the dispersion problems of finite element algorithm in numerical simulation of seismic wave, and the dispersion function of two-dimensional acoustic wave equation is derived by employing lumped mass matrix and bilinear interpolation finite element algorithm. And, we compared quantitatively the effect of incident direction with the variable ratio of vertical to horizontal grid, spatial sampling interval, seismic wave frequency, and formation velocity on numerical dispersion. The numerical examples and the forward modeling indicate, if we want to suppress the numerical dispersion effectively, it should not be less than 20 samples within the wavelength corresponding to peak frequency of source wavelet; reducing the ratio of vertical to horizontal grid can suppress the numerical dispersion with small incident angle (the angle between the direction of wave propagation and the z axis) remarkably; the slower the propagation velocity of the seismic wave with higher frequency, the more serious its dispersion is; when the ratio of phase velocity to the corresponding frequency is less than twice of spatial sampling interval, not only the numerical dispersion becomes very serious, but also the aliasing phenomenon will happen.