SURFACE-WAVE PROPAGATION ON A ROTATING, ANISOTROPIC EARTH

We present a JWKB theory for the propagation of monochromatic surface waves on a rotating, anisotropic, laterally heterogeneous earth model. The theory allows for slowly varying topography on the earth's surfac e and any internal discontinuity, and incorporates the effect of self- gravitation and anelasticity on the wavefield. The analysis is based u pon slowly varying variational principles and involves a local dispers ion relation and local radial eigenfunctions which depend explicitly o n the direction of the local wavevector as a result of the rotation an d anisotropy of the earth model. The amplitude is determined by a cons ervation law for the surface-wave energy. In addition to the usual dyn amical phase, which is the integral of the local wavevector along a ra y path, there is an additional variation in phase. All rotating earth models, isotropic models included, support such an additional variatio n in phase, which is an analogue of the Berry phase in adiabatic quant um mechanics. The Berry phase vanishes in non-rotating earth models wi th a local radial two-fold axis or a local horizontal mirror plane.