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.

Accuracy and efficiency are most urgent problems in elastic wave simulation. Staggered‐grid is an effective method to improve the accuracy with high efficiency. By the combination of variable grids and locally variable time‐steps, a staggered‐grid high‐order finite‐difference method with oddly arbitrarily variable spatial grids and arbitrarily variable local time‐steps is presented. The numerical results show that the simulation accuracy and efficiency are increased effectively by avoiding oversampling both in space and time domain. Additionally, compared with the traditional method, this modeling method has advantages in seismic wave simulation in the medium with fractures, caves and complicated structures. It can describe such medium in details, and has high accuracy and efficiency.

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