The influence of upper mantle discontinuities on the toroidal free oscillations of the Earth

Summary In the simplest approximation the high‐frequency toroidal mode dispersion is simply related to the intercept time τ β (p) as a function of slowness p derived from SH‐wave travel times. Velocity and density gradients in the Earth introduce perturbations to this simple relation. More pronounced effects arise when the mantle contains discontinuities in elastic properties and these disrupt the regular spacing of eigenfrequencies with radial order at fixed slowness p , a 'solotone’effect. A simple iterative approach is introduced which enables the solotone effect to be calculated for an earth model with multiple discontinuities. At futed frequency the discontinuities give rise to a distinctive pattern with varying slowness, particularly in the group velocity behaviour. The perturbations due to the discontinuities depend on the reflection coefficients at these interfaces and so are large for modes with slownesses corresponding to turning points near the discontinuities. For mode phase velocities greater than 9 km/s the details of the solotone perturbation are dominated by beating between the effects of different discontinuities. The theoretical results are illustrated by computations for model 1066B, both directly and using the asymptotic approach. This allows an assessment of the influence of velocity gradients and upper mantle discontinuities on the dispersion. Also the sources of systematic error in Brune's approach to determining toroidal mode dispersion are discussed and bounds on the errors estimated from the calculations.