High Frequency Wave Propagation

CSIC Building (#406), Seminar Room 4122.
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Escape Equation Methods for Multiple Arrivals

James Sethian

Department of Mathematics at University of California, Berkeley

Abstract: We describe joint work with S. Fomel on how to construct single-pass methods for computing the solutions to multiple arrivals for static Hamilton-Jacobi equations. Our approach computes all possible arrivals from all possible sources simultaneously, and is unconditionally stable in that there is no time step, and hence no CFL condition. The fundamental idea behind these techniques is to transform the Liouville equations into a boundary value partial differential equation representing the exit time and location for all possible trajectories, starting from all interior points, initialized in all directions; extraction of particular boundary conditions comes as post-processing. These 'Escape Equations' can be solved very quickly through a Dijkstra-like algorithm which systematically solves the boundary value PDE by space marching away from the known boundary conditions; the approach is motivated by our work on Fast Marching Methods. We use the techniques to compute multiple arrivals in seismic imaging, and consider possible new applications of these techniques.