The Effect of Anelasticity on Periods of the Earth's Free Oscillations (Toroidal Modes)

Abstract

It is known that the anelastic properties of the Earth characterized by a ‘Q’ structure will affect the periods of free oscillation. It is generally considered that the effect is negligible compared to the other perturbing effects due to rotation, ellipticity, and lateral inhomogeneities. Nevertheless, it is of some interest to investigate the precise magnitude of this effect for the observed free oscillation modes since it could provide us with another constraint in the determination of the Q structure of the Earth. An application of perturbation theory provides us with a good estimate of the magnitude of the changes in the periods of an elastic model due to inclusion of anelastic effects. Calculations based on currently accepted mean elastic and anelastic models for the Earth show that the shift in period due to anelasticity is at most 0·023 per cent for the toroidal modes from _0T_2 to _0T_(99), the maximum occurring near _0T_(60). For more extreme Q models, which may be locally applicable, period shifts of the order 0·1 per cent occur, with the maximum again near _0T_(60), corresponding to a period of approximately 150 s. Observational accuracy for the toroidal oscillations is around 0·1 per cent so that anelastic shifts in toroidal oscillation periods are at the present limit of observational accuracy. Viewed in terms of propagating surface waves, the dispersion due to anelasticity results in at most 0·005-0·01 km s^(−1) variations in the phase and group velocities. Such shifts are within the observational resolution of surface dispersion measurements using narrow band filtering techniques. Compared to other perturbing effects, anelasticity is significant for the toroidal oscillation only in the 50- to 300-s period range. In this range, lateral variations in structure generally cause larger perturbations. However, when viewed in terms of propagating surface waves in selected homogeneous regions, anelasticity becomes the dominating effect. Further, the frequency shift due to anelasticity is scaled by (1/Q)^2, so that the anelastic effect can be well within observational accuracy and comparable to any perturbing effect for more extreme, yet acceptable, Q models. In particular, when applied to surface waves propagating across a tectonic region with a strong low velocity zone in the upper mantle, the anelasticity induced dispersion on frequency shift can be significant and measurable. In such cases a joint inversion of elastic and anelastic properties is appropriate.