Stability is one of the basic problems for solving wave equations numerically. For the stability of the staggered–grid high–order difference method of first–order elastic wave equations in 3–D TI media, a unified stability condition of finite difference equations with different difference accuracy is derived. It is proved that the stability condition is determined by the Courant number of elastic waves along the X, Y, Z directions. It can be seen from some stability criteria of different difference accuracies, that this staggered–grid high–order FD scheme is accurate as well as efficient.

[Abstract] All numerical methods of seismic wave simulation have the aim to improve their computational accuracy and efficiency. Through converting the odd high-order temporal derivatives of velocity(or stress) to spatial derivatives of stress(or velocity), we use the high-order difference method which has any order of the temporal and spatial difference accuracy and the staggered-grid technique in calculations of the first-order elastic wave equations expressed with velocity and stress. The snapshots and the simulated results of a realistic model show that this method is more accurate and less dispersive than conventional FD methods. Mean-while bigger spatial grids and temporal steps can be used to raise computational efficiency.