三维高阶快速步进波前重构旅行时计算精度分析

Analysis on computation precision of wavefront-reconstructing traveltime for 3-D high-order rapid stepping algorithm

快速步进算法是波前重构的一种快速无条件稳定算法。本文把二阶和三阶差分格式引入该算法中,详细地研究了影响快速步进算法的误差因素,着重研究了差分阶数、网格尺寸大小和速度变化对算法的影响。通过对非均匀模型和层状介质模型的计算表明,一阶差分格式误差较大,二阶和三阶差分误差明显低于一阶差分的误差;当差分的阶数相同时,网格尺寸减小误差明显减小;网格成倍增大时,误差也成倍增大。二者近似呈线性变化的关系。在实际应用中采用二阶差分格式即可,在用于地震波层析成像时,网格尺寸一般选为10m和20m就能满足计算精度要求。

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.