Conclusions

I have presented a finite-difference method of traveltime computations, based on the linearized eikonal equation. Preliminary numerical experiments show that the method is as simple and robust as can be expected from the theory. The required assumption is that a reasonable estimate of the traveltime is available prior to linearization. Such an estimate may result from the computation in a different velocity model, with a different method (e.g., ray tracing), or by an analytic evaluation.

In the situations where the underlying assumption is valid, the linearized approach may allow us

• to employ unconditionally stable implicit finite-difference schemes with an easy control of the numerical stability,
• to parallelize the essential parts of the algorithm with minimum effort,
• to compute branches of the multi-valued traveltime other than the first arrival,
• to connect traveltime computations with tomographic velocity estimation,
• to couple traveltime and amplitude computations.

Future research is necessary to confirm these expectations.