A Physical Classification of the Earth's Spheroidal Modes

Abstract

This paper shows that five different families of spheroidal modes can be isolated, namely; 1) Inner Core and Stoneley modes (“K” modes); 2) “F” (vertical) modes, with mainly vertical displacement; 3) “C” (Colatitudinal) modes, with mainly horizontal displacement; 4) “R” (Rayleigh) modes, in which the horizontal and vertical displacements are totally coupled, and 5) “H” (Hybrid) modes, with intermediate coupling. V and C modes occur at high phase velocities, R modes at low phase velocities, and II modes at intermediate ones. Each of the families of modes has distinctly different properties, including group velocity, Q, and excitation functions. Except for H modes, these families are arranged in “pseudo-overtone” branches, along which physical properties vary smoothly. A theoretical description of the properties of V, C and K modes is given, using the simplified model of a homogeneous, non-gravitating Earth. Two important observations are explained, using this model: i) The solution for C modes at low values of l are identical to the ones for corresponding T (Torsional) modes, and have, therefore, the same eigenperiods are relative excitation functions, and ii) the radial modes nS0are the l = 0 members of the V family, and their apparent scarcity results simply because only that family has modes with l = 0. Furthermore, the group velocity of K, C, V and R modes is shown to be consistent with the physical concept of dispersion along a pseudo-overtone branch. An interpretation of the existence of the different families in terms of an increase in mode-coupling with angular order is presented. A formal classification of the spheroidal modes into 5 families is made, and a new nomenclature is proposed, which is closely related to their physical properties. © 1978, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan. All rights reserved.