Some properties of spheroidal modes of a homogeneous elastic sphere with special reference to radial dependence of displacement

A ray-theoretical approach is attempted to interpret radial eigenfunctions (radial and tangential displacements) of spheroidal modes of a homogeneous elastic sphere. It is shown that surface displacements of the mode solutions agree well with those expected when relevant body waves are incident on the free surface. The possibility of interpreting amplitude dependence on depth in terms of interference phenomenon of up-going and down-going body waves is also demonstrated. The radial eigenfunctions are computed for a variety of spheroidal modes with relatively high radial mode numbers. An interesting feature is found in these functions: The number of node surfaces in the radial distribution of the radial displacement increases systematically for a given radial mode in conformity with a change of surface value of the tangential displacement from negative to positive with increasing colatitudinal order number.