Observations of Coupled Spheroidal and Toroidal Modes

In low-frequency seismic spectra the Coriolis force theoretically causes quasi-degenerate coupling of spheroidal and toroidal modes whose spherical harmonic degrees differ by unity and whose frequencies are close. It has been found that the coupling causes clearly observable effects on seismic spectra below 3.0 mHz. Many fundamental toroidal modes have a spheroidal component and vice versa. For example, the 0St• modes for If = 8-22 are significantly coupled to the 0Tt• modes for If = 9-23. The mean frequencies of pairs of coupled multiplets are repelled, and the mean attenuations are averaged. The shifting of complex frequencies must be adequately encompassed in the construction of spherically averaged and aspherical models of the density and elastic and anelastic structure of the earth. The coupling also causes variations in multiplet amplitudes which result in spectral peaks at toroidal mode frequencies on vertical and radial components and at spheroidal mode frequencies on transverse components. The variations must be taken into account in constructing Green's functions for the study of low-frequency source mechanisms.