【摘要】 本文叙述了在普遍的介质与入射波情况下Bremmer理论之推广,并给予简要证明。对下列三种具体情况导出了Bremmer级数之表达式: 1.平面分层介质,平面波斜入射; 2.柱状分层介质,直线波源与柱轴重合; 3.球状分层介质,点光源位于球心。最后,对于波动过程可以用射线严格描写的条件之数学形式作了探讨,并指出Bellman和Kalaba的一篇文章中的不严格处。更多还原

【Abstract】 This paper gives a generalized statement of the Bremmer[1] theory in the case that the medium and the incident wave are of general form (it is called the local principle of the process of wave motion) and proves it schematically. The Bremmer serieses of three concrete cases are deduced in a way similar to that used by Bremmer. These are:1) Planely stratified medium, obliquely incident plane wave;2) Cylindrically stratified medium with a line source coincident with the axis of the cylinder;3) Spherically stratified medium with a point source at its centre.Finally the author has attempted to give a mathematical form for the condition that the process of wave propagation can be described rigorously by rays, and points out the unstrictness in a paper of Bellman and Kalaba[5].更多还原