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