Anisotropic Ray Theory for Surface Waves

Exact Ray Theory

The path of the surface wave can be determined from the following equations, where the source and receiver have been rotated to the equator. is colatitude, is longitude, is direction of the wavevector measured counterclockwise from east, and is the local phase velocity,
and
.
The surface-wave phase is subsequently determined from
,
where is the angular frequency of the wave. The effects of attenuation, , may be determined from
,
where is the group velocity and is the local attenuation.

Perturbation Theory

where is the source-receiver distance, subscripts s and r represent source and receiver respectively, indicates perturbation from spherical symmetry.




where and