Open AccessExact and Approximate Generalized Ray Theory in Vertically Inhomogeneous Media
Author(s) -
Chapman C. H.
Publication year - 1976
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1976.tb04154.x
Subject(s) - series (stratigraphy) , simple (philosophy) , motion (physics) , term (time) , mathematics , mathematical analysis , homogeneous , born approximation , exact solutions in general relativity , high frequency approximation , plane (geometry) , geometry , classical mechanics , physics , optics , quantum mechanics , scattering , paleontology , philosophy , epistemology , combinatorics , biology
The generalized ray method in a vertically inhomogeneous model is formulated without any approximation by homogeneous layers. The solution is obtained as an infinite series in multiply ‘reflected’ waves. Each term can be solved using the exact method or the plane‐wave, first‐motion or geometrical approximations. It is shown that the first‐motion approximation of the series converges rapidly, the ratio of successive terms in the infinite series being‐(2 l + 1)(2 l )(6/π) 2 . In addition it is shown that the first‐motion approximation, which reduces to the geometrical approximation when the latter is valid, is a useful alternative to geometrical ray theory, being more generally valid and being almost as simple to compute.