INTRODUCTION

The original finite difference traveltime calculations implemented after Van Trier and Symes (1990) did not have an adaptive step determination. As a result, numerical instabilities appeared in unpredictable cases, for example the simple constant gradient velocity model in Figure 2. Such instability does not present a problem for research algorithms because numerical instabilities can be controlled by decreasing the grid spacing. However, for production programs this is impractical as users may not have complete control of each step of the finite difference calculation.