Abstract: We first review the finite-difference scheme proposed by Qin in 1988 which solves the eikonal equation along expanding wavefronts and analyze its advantages and disadvantages. We also show some problems about its programming implement. Then we show an implement method in the C⁺⁺ programming language, which aims at solving the problems. (1) To ensure the stability of the program, we also consider the refracted and diffracted waves to calculate the traveltimes. The new method improves the local algorithmic stabilities of Qin’s method without losing the precise. (2) To improve the efficiency of the program, we propose a queue storage structure of the wavefront points. (3) We build a convenient and doable program structure for the expanding wavefronts method. We append four boundaries to the original velocity model, which not only makes programming simple but also save the time dealing with the model boundaries.

Key words: traveltime, expanding wavefronts, eikonal equation, queue structure, C⁺⁺