Extended modified ray theory field in bounded and unbounded inhomogeneous media

Abstract

Use of the generalized WKB procedure in place of the WKB procedure to obtain solutions to the separated wave equation leads to modified ray theory. The quantitative consequences of this frequency−dependent theory are investigated and compared with ordinary ray theory and normal−mode theory for both bounded and unbounded media under conditions for the formation of a shadow region in ordinary ray theory. The behavior of the modified ray theory field, which always contains a caustic in the types of problems which are examined, depends on whether the ray theory shadow boundary is a limiting ray or a caustic. In the former case the modified ray theory field, suitably extended to take the caustic into account, approaches the normal−mode field far into the shadow region. In the latter case the modified ray theory field in the shadow region agrees with the ordinary ray theory field, also suitably extended. Subject Classification: 30.20.