Mode-ray duality

Abstract

Earlier results in the theory of terrestrial radio waves are applied to seismology. A partial field of the complete eigen-value solution for a sphere can be interpreted as real rays. Watson's transformation and the WKBJ approximation are employed to establish links between the index trio (l, m, n) of a mode and the corresponding parameters of the ray trajectory associated with this mode. It is shown that Snell's law for rays and Jean's formula are complementary. The condition of constructive interference is expressed as an integral equation for the eigen-frequencies _nω_l.