Generalized spherical harmonics are used to simplify the calculation of the perturbation matrix elements (coupling coefficients) for the free oscillations of an anisotropic and laterally heterogeneous earth. In the asymptotic limit of large angular order, the local frequency pertubration which depends on the azimuth and on the location of Earth's surface is defined, and the correspondence to surface waves is established.

Free oscillations of a homogeneous, anisotropic, elastic, rectangular parallelepiped are studied by means of the group theory. Normal modes are classified and selection rules for excitation are obtained.

The correspondence between free oscillations and surface waves of a laterally heterogeneous earth is established. Starting from the Born approximation of Woodhouse, for large angular order, coupling between neighbouring multiplets along the same dispersion branch leads to the apparent distance shift noted by Woodhouse and Dziewonski, which they obtained from a surface wave approach.