EFFECTS OF SLIGHT ANISOTROPY ON SURFACE-WAVES

We present a complete ray theory for the calculation of surface-wave o bservables from anisotropic phase-velocity maps, Starting with the sur face-wave dispersion relation in an anisotropic earth model, we derive practical dynamical ray-tracing equations. These equations allow calc ulation of the observables phase, arrival angle and amplitude in a rag theoretical framework. Using perturbation theory, rye also obtain app roximate expressions for these observables. We assess the accuracy of the first-order approximations by using both theories to make predicti ons on a sample anisotropic phase-velocity map. A comparison of the tw o methods illustrates the size and type of errors which are introduced by perturbation theory. Perturbation theory phase and arrival-angle p redictions agree well with the exact calculation, but amplitude predic tions are poor. Many previous studies have modelled surface-wave propa gation using only isotropic structure, not allowing for anisotropy, We present hypothetical examples to simulate isotropic modelling of surf ace waves which pass through anisotropic material. Synthetic data sets of phase and arrival angle are produced by ray tracing with exact ray theory an anisotropic phase-velocity maps, The isotropic models obtai ned by inverting synthetic anisotropic phase data sets produce decepti vely high variance reductions because the effects of anisotropy are ma pped into short-wavelength isotropic structure, Inversion of synthetic arrival-angle data sets for isotropic models results in poor variance reductions and poor recovery of the isotropic part of the anisotropic input map. Therefore, successful anisotropic phase-velocity inversion s of real data require the inclusion of both phase and arrival-angle m easurements.