Open AccessA study of the applicability and divergence of the ray series using a modified transport equation
Author(s) -
Buske Stefan,
Kravtsov Yury A.
Publication year - 2005
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2004.02498.x
Subject(s) - series (stratigraphy) , divergence (linguistics) , term (time) , mathematical analysis , extension (predicate logic) , mathematics , boundary (topology) , boundary value problem , order (exchange) , physics , computer science , geology , paleontology , philosophy , linguistics , finance , quantum mechanics , economics , programming language
SUMMARY In this paper, we study an extension of the standard ray‐theoretical transport equation. We include a higher‐order term of the ray series and obtain a modified frequency‐dependent transport equation. This equation is solved analytically and numerically for an elastic 1‐D model. The analysis of the results documents that the ray series diverges just at the boundary of applicability of the underlying high‐frequency approximation. This implies that taking into account higher‐order terms in the ray series neither improves accuracy nor allows a shift of the boundary of its applicability towards lower frequencies.