Behavior of Modified Ray Theory

摘要

Both modified ray theory and ordinary ray theory can be obtained from the method of stationary phase. Use of a WKB approximation leads to two points of stationary phase and the result is ray theory. Use of a generalized WKB approximation leads to an infinite number of stationary phase points and the result of using the first two is modified ray theory. The degree to which modified ray theory accurately includes frequency dependent diffraction effects depends on the treatment of caustics and inflection points which arise in the modified ray theory field. In sound propagation problems where there is a shadow region the ray theory field may or may not contain a caustic, whereas the modified ray theory field always contains a caustic and in some cases a cusped or higher order caustic. For ranges much less than the shadow boundary range the modified ray theory field approaches the ray theory field. (Author)