Methods were studied for determining the initial travel time and ray paths with stability when an non-linear travel time inversion is performed in an inhomogeneous structure. The travel time calculation was based on Faria and Stoffa`s method. First, the 2-dimension space was sectioned by grids, and `slowness` was assigned to all the lattice points. Starting from the vibration source, travel time at each lattice point is sequentially calculated. This method calculates travel time for any structure without breakup. In this study, an algorithm more sophisticated than the method of Faria, et al., was developed, and the improvement of travel time calculation accuracy led to the accurate determination of the direction of incidence into the lattice points during the initial motion. The calculation of ray paths was effected by tracing back from the receiving points the incidence into the lattice points or by following back the ray paths to the vibration source. This method performs stable calculation for a heavily inhomogeneous structure and, with the algorithm being simple, do the parallel programming as well. 1 ref., 6 figs., 1 tab.