Open AccessA geometrical approach to time evolving wave fronts
Author(s) -
Madrid Juan A.
Publication year - 2008
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.2007.03699.x
Subject(s) - curvature , radius of curvature , ray tracing (physics) , radius , amplitude , front (military) , tracing , physics , huygens–fresnel principle , geometrical optics , classical mechanics , geometry , geometrical acoustics , mathematical analysis , optics , mathematics , mean curvature , mean curvature flow , meteorology , computer security , computer science , operating system
SUMMARY The parameter that defines the ray tracing equations in the direct geometrical approach is the product of the radius of curvature of the wave front by the velocity on the wave front ( RV ). To show this, we derive motion equations for the centre and the radius of curvature of an expanding wave front. The continuity of RV along rays implies Snell's Law. For constant velocities the equation for the radius of curvature reduces to the original Huygens' Principle. The variable RV can be computed during ray tracing and used to determine the local radius of curvature, which in turn can be used in geometrical spreading, amplitude corrections and structure interpretation.