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 http://math.berkeley.edu/~sethian).
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.
CONTENTS
The FMM scheme for continuous and layered media.
Movies of propagating wavefronts
For more information about this page or the FMM, please email