Excitation of torsional oscillations of the Earth: Higher modes

Abstract

Spherical models of the earth, with physical properties varying continuously with depth, are considered. The periods and spectral amplitudes of the torsional free oscillations lTn are calculated for several focal depths, for higher modes l = 1, 2, and 3, and values of n up to several hundreds. The displacement caused by a torque source at various depths (the initial motion being a unit step-function in time) is next calculated by means of a series of spherical functions; at least 800 terms in n must be included in it in order to include the spectral range in which the group velocity reaches a maximum associated with Sa waves. Three continental models are considered: the Lehmann and Gutenberg models, both with a low-velocity layer at 150-km depth, and a model without a low-velocity layer in the upper mantle. For all of them the displacement caused by the higher modes is weak relative to that produced by the fundamental mode, if the focus is at the surface. But the higher modes predominate as soon as the depth exceeds 100 km, the fundamental mode being then little excited. Because of the strong discontinuities in the first model, the dispersion curves and resulting seismograms are very complicated. There is no striking difference between the results for the second and third models, but for the Gutenberg model the features of the ‘guided’ group of waves resemble more closely those of the experimental Sa waves. At epicentral distance θ = 45°, on the seismograms obtained by superimposing the displacements for the three first higher modes, there appear, clearly separated from the main group of waves, long-period body waves: S, sS, and SS. Other body waves may be identified inside the main group.