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 surface and any internal discontinuity, and incorporates the effect of self-gravitation and anelasticity on the wavefield. the analysis is based upon slowly varying variational principles and involves a local dispersion relation and local radial eigenfunctions which depend explicitly on the direction of the local wavevector as a result of the rotation and anisotropy of the earth model. the amplitude is determined by a conservation law for the surface-wave energy. In addition to the usual dynamical phase, which is the integral of the local wavevector along a ray path, there is an additional variation in phase. All rotating earth models, isotropic models included, support such an additional variation in phase, which is an analogue of the Berry phase in adiabatic quantum mechanics. the Berry phase vanishes in non-rotating earth models with a local radial two-fold axis or a local horizontal mirror plane.