Introduction

Given the eikonal equation, there is an abundance of raytracing methods in literature. Finite-difference travel time schemes are one class of methods which calculate the first arrival of the wave-front from the eikonal equation. The finite-difference scheme introduced by Vidale (1988) has an explicit minimization condition (i.e., the time along a new computation front is calculated using the minimum time along the previous computation front), important for keeping the scheme stable. The Van Trier and Symes (1989; 1990) algorithm has a similar minimization condition which is applied locally to three points of the four point finite-difference stencil. I analyze their first-order upwind finite-difference scheme and show the implicit minimization condition and the errors introduced in favor of greater computational speed. I extend the algorithm to a 3-D medium and show results of traveltime fields for constant and slowly varying velocity media. The 3-D algorithm is much more susceptible to numerical instability when rapid variations in velocity are present.