Abstract：Rapid stepping algorithm is a rapid, condition-free and stable algorithm for wavefront reconstruction. The paper introduced the second-order and third-order difference format into the algorithm, analyzed in detail the error factors affecting rapid stepping algorithm and especially studied the influence of difference orders, grid sizes and velocity variation on algorithm. It is shown by computation of heterogeneous model and layered medium model that first-order difference format has larger error, and the errors of second and third order difference are significantly smaller than that of first-order difference; the error is greatly reduced when the grid size is reduced in a condition of same order of difference; the error has doubled and redoubled when the grid has doubled and redoubled and both of them approximately appear linear relationship. It is ok by using second-order difference format in practical application, and grid sizes are generally chosen as 10m or 20m that can meet the need of computation precision when the algorithm is used for seismic tomographic imaging.
