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We present the Eulerian Gaussian beam method in anisotropic media. We derivekinematic and dynamic ray tracing equations based on the level set theory andEulerian theory using the anisotropic eikonal equation. Compared with thetraditional anisotropic Gaussian beam method using ray-centered coordinates,the anisotropic Eulerian Gaussian beam method derived in this work has thefollowing three advantages: (1) it can handle the problem of calculating thedistance from the imaging point to the beam point more easily; (2) it allowsthe travel time and amplitude to be distributed uniformly within the actualcomputational domain without interpolation; (3) it can handle late arrivals,both theoretically and in calculations, due entirely to ray tracing in thephase space.

Eulerian Gaussian beams for high frequency wave propagation in inhomogeneous media of arbitrary anisotropy