Seismic Ray Theory

Summary Seismic ray theory is developed ab initio (apart from one or two standard elementary results) with special emphasis on the variables σ and α, where σ= d log σ/ d log r and α= 2/(1‐ σ). Travel‐time‐distance relations are examined for a variety of types of velocity distribution, including the case α constant and cases where α and σ change discontinuously, or rapidly but continuously, with increase of depth. The analysis is designed to provide an improved basis for working out in quantitative detail the effect on travel‐times of the various types of velocity variation likely to be relevant to the Earth. In particular, it is hoped that the analysis will lead to the most effective use of ray theory in the current difficult problems of the structure of the Earth's outer mantle. Advantage has been taken of the opportunity to present a number of previous results involving σ and α in revised form, as part of a wider logical development. Previous work on deriving seismic velocity distributions from travel‐time data is generalized. The aim of the paper has been to set down a terse account of the basic theory, and no numerical applications have been included. References are given, however, to papers containing applications.