Remarks on the travelling wave decomposition

In elastic wave propagation on a spherically symmetric earth model, a normal mode sum is converted into a sum of equivalent travelling waves by means of a travelling wave decomposition (TWD). For two decades, seismologists have assumed that each travelling wave in the TWD is associated with only real phase velocities, that is, no evanescent waves travel on a spherically symmetric earth model. In this paper, this assumption is proven false. By including a countably infinite set of waves travelling as evanescent waves, several conceptual difficulties confronting the TWD are resolved.