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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.




2013-03-03