Remarks on the travelling wave decomposition

In elastic wave propagation on a spherically symmetric earth model, a norma l mode sum is converted into a sum of equivalent travelling waves by means of a travelling wave decomposition (TWD). For two decades, seismologists ha ve assumed that each travelling wave in the TWD is associated with only rea l phase velocities, that is, no evanescent waves travel on a spherically sy mmetric earth model. In this paper, this assumption is proven false. By inc luding a countably infinite set of waves travelling as evanescent waves, se veral conceptual difficulties confronting the TWD are resolved.