, Volume 4, Issue 1, pp 55-65

On the relationship between ray theory and the banana-doughnut formulation

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Abstract

In the conclusion of their seminal paper Dahlen et al.(Geophys. J. Int., 141, 157–174, 2000) state that their results extend ray theory to finite-frequency waves. In view of the importance of that paper, which led to developments in theoretical and computational seismology, we feel that it is important to clarify certain mathematical statements therein. Certain technicalities may have escaped the attention of the authors, and the consequences of these statements may have been misunderstood. We clarify the conclusion about the apparent lack of sensitivity along the ray, which is not a general statement about ray theory, but about the particular formulation of Dahlen et al.(Geophys. J. Int., 141, 157–174, 2000), since their definition used for sensitivity depends directly on whether or not a scatterer is on the ray. In particular, we note that there are mathematical problems in the derivation of some of the results of Dahlen et al.(Geophys. J. Int., 141, 157–174, 2000) and we attempt to provide derivations that avoid these issues. In general, we maintain that their formulation is a contribution to the properties of ray theory, rather than its replacement or extension.