Comparison of six different methods for calculating traveltimes

We study six different methods for the calculation of seismic traveltimes. All methods yield traveltimes at all points of a regular grid. The methods examined comprise three different variants of finite-difference (FD) eikonal solvers, the graph method, wavefront construction and a combined FD and Runge-Kutta method. The main points of investigation are computational time, accuracy and memory requirements. We took measures to obtain a high level of both general validity and clear understanding of the results. We used a profiling program to be able to measure the time that the actual core algorithm needs, thus avoiding any overhead of highly system-dependent in-/output operations. The comparison shows that no single method is the most appropriate but that the choice depends on the task to be fulfilled. The FD eikonal solver that uses expanding squares proves to be best suited for models which are not too complicated because it offers the best compromise between speed and accuracy, whereas wavefront construction should be applied to complex media because of its superior reliability which then justifies the much higher computational times.