On high-frequency spheroidal modes and the structure of the upper mantle

Abstract

Summary. The asymptotic properties of spheroidal mode dispersion at high frequency for fixed phase velocity are related to the intercept times T~@), T&) for P and S waves. If the mode eigenfrequency and the ratio of horizontal to vertical displacement at the surface for the mode are known T~@) and T&) may be separately estimated. If discontinuities exist in the velocity model then ‘solotone’ effects occur, in frequency at fixed slowness, and in ~~(p), TO@) estimated from the mode dispersion as a function of slowness. The coupling of P and S waves in the spheroidal modes means that the interaction of P waves with upper-mantle discontinuities affects also the estimates of the S wave TO($) values for which the corresponding turning points lie in the lower mantle. The asymptotic formalism also shows that sharp pulses formed by superposition of spheroidal modes correspond to multiple PS reflections. A study of ~~(p), TO@) estimates derived from spheroidal modes with periods from 45-50 s, calculated for model 1066B, shows that even in the presence of strong upper-mantle discontinuities the errors in intercept time are only about one-tenth of a period. The asymptotic properties may therefor provide a useful means of estimating intercept times from modes with a few seconds period as a supplement to travel-time methods.