Introduction

The fast marching method Sethian (1996) is widely used for solving the eikonal equation in Cartesian coordinates. The method's principal advantages are: stability, computational efficiency, and algorithmic simplicity. Within geophysics, fast marching traveltime calculations Popovici and Sethian (1997) may be used for 3-D depth migration or velocity analysis.

Unfortunately, first-order implementations lead to inaccuracies in computed traveltimes, which may lead to poor image focusing for migration applications. In addition, first-order traveltimes are not accurate enough for reliable amplitude calculations. This has lead to the development of the fast marching method on non-Cartesian Alkhalifah and Fomel (1997); Sun and Fomel (1998), and even unstructured Fomel (1997) grids. These non-Cartesian formulations reduce inaccuracies, while retaining the fast marching method's characteristic stability and efficiency. Unfortunately, the cost is the loss of algorithmic simplicity.

We implement a second-order fast marching eikonal solver, which reduces inaccuracies while retaining stability, efficiency and simplicity.