Abstract
The level set method due to Osher and Sethian [J. Comput. Phys. 79, 12–49 (1988)] provides a way to obtain fixed grid solutions to the high‐frequency wave equation. Instead of tracing several rays from the source, the level set method embeds the entire wavefront implicitly in the phase space and propagates it according to the velocity field determined by the local ray direction, thus avoiding the complications involved in the spatial reconstruction of the wavefronts from diverging and scattered rays. A level set method has been developed and implemented as a fixed‐grid alternative to ray tracing to solve the high‐frequency equation for the acoustic phase. Furthermore, an efficient ray‐based method that takes advantage of the full knowledge of the wavefronts afforded by the level set solution to the Eikonal equation has been developed to solve for the geometric spreading term in the expansion. Preliminary results are presented with comparisons to ray tracing and full wave equation solutions. [Work supporte...
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