Variational principles for surface wave propagation on a laterally heterogeneous Earth--I. Time-domain JWKB theory

We present a JWKB theory that describes the propagation of well-dispersed Love and Rayleigh wavegroups on a smooth, laterally heterogeneous Earth model. The analysis is based upon an averaged Lagrangian which yields local Love and Rayleigh eigenfunctions, local dispersion relations, and conservation laws for the surface wave energy. The local dispersion relations determine the surface wave trajectories, and the energy equations determine the surface wave amplitudes. The amplitude of a surface wavegroup varies in time as a result of both dispersion and geometrical spreading. The theory allows for smooth topography on the Earth's surface and any internal discontinuities, and incorporates the effect of self-gravitation.