Traveltime solution for the two dimensional Eikonal equation in an arbitrarily complex slowness field via first or second order conservative upwind difference formulations
Vestal, Eric William
Symes, William W.
Master of Science
The determination of first-arrival seismic traveltimes radiating outward from a point-source in an arbitrary slowness field plays an important role in methods which require knowledge of curved wavefronts in a complex domain. Adaptations of the 1st order upwind finite difference Godunov and 2nd MUSCL schemes are presented which model the two dimensional Eikonal equation. These formulations prove to be a numerically straightforward and computationally efficient alternative to ray tracing and other finite difference methods. Initial results demonstrate convergence of the methods. Other examples are introduced and analyzed to demonstrate the effectiveness of the method in regions of velocity contrast. Specifically, we show that head waves and crossing rays are modeled correctly to produce a true first-arrival traveltime field. These examples demonstrate that the method is well suited for many structural velocity models, though success is not guaranteed if the family of computational fronts can not expand in the direction of increasing time.
Mathematics; Geophysics; Computer science