FMM home page FMM Method Examples in continuous media Examples in layered media FMM movies

Nick Rawlinson and Malcolm Sambridge

The Fast Marching Method (FMM) is a grid based numerical scheme for tracking the evolution of monotonically advancing interfaces via finite difference solution of the Eikonal equation. To date, it has been applied to a wide variety of problems including seismic wave propagation, photolithographic development, geodesics, deposition of sediments, medical imaging and optimal path planning (see Like many other grid based techniques used for tracking seismic wavefronts, the FMM is only capable of finding the first-arrival in continuous media; however, it distinguishes itself by combining both unconditional stability and rapid computation, making it a truly practical scheme for velocity media of arbitrary complexity.

In the following web pages, we investigate the potential of the FMM to track a range of later arriving phases in layered media. In particular, we focus on reflections and refractions generated by smooth sub-horizontal interfaces that separate regions of continuous velocity variation. The method we develop can, in principle, track phases composed of any number of reflection and refraction events. Below are a series of links to various aspects of our work on the FMM.


The FMM scheme for continuous and layered media.

FMM examples in smooth media

FMM examples in layered media

Movies of propagating wavefronts

FMM software

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since February 21 2003.

For more information about this page or the FMM, please email