Ray-mode duality for SH waves in earth models with crust and mantle discontinuities—II. The case of N discontinuities

Summary. In examining the effect of discontinuities in the Earth's interior on free oscillations, McNabb, Anderssen & Lapwood derived an equation for the asymptotic behaviour of torsional overtone eigenfrequencies of a discontinuous earth model, the constants in their equation being explicitly determined only for the case of one internal discontinuity. Since Brune's phase correlation method for the evaluation of eigenfrequencies from body-wave data implies a ray-mode duality only for continuous earth models, it is desirable to justify the McNabb et al. formulation from the point of view of ray theory.
By a novel method of ray analysis, Wang, Cleary & Anderssen showed that, for earth models with a single discontinuity between the Earth's surface and the core—mantle boundary, the McNabb et al. formulation can be derived from an adaptation of Brune's method to multiply reflected SH body waves recorded at small epicentral distances. In this paper, the technique of Wang et al. is extended to derive the McNabb et al. formulation (with constants explicitly determined) for the general case of earth models with N discontinuities. This establishes a basis for a ray-mode duality for discontinuous earth models.