Adaptive finite difference method for traveltime and amplitude

Abstract

The eikonal equation with point source is difficultto solve with high order accuracy because of the singularity of the solution at the source. All the formally high order schemes turn out to be firstorder accurate without special treatment of this singularity. Adaptive upwind finite difference methods based on high order ENO (Essentially NonOscillatory) Runge-Kutta difference schemes for the paraxial eikonal equation overcome this difficulty. The method controls error by automatic grid refinementand coarsening based on an a posteriorierror estimation. It achieves prescribed accuracy at far lower cost than fixed grid methods. Reliable auxiliary quantities, such as take-off angle and geometrical spreading factor, are by-products.