Open AccessKay theory for pre-stressed media
Author(s) -
E. Boschi,
E. Di Curzio
Publication year - 2010
Publication title -
annals of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 60
eISSN - 2037-416X
pISSN - 1593-5213
DOI - 10.4401/ag-4893
Subject(s) - ordinary differential equation , infinitesimal , amplitude , mathematical analysis , differential equation , equations of motion , vibration , anisotropy , mathematics , elasticity (physics) , linear differential equation , physics , classical mechanics , optics , quantum mechanics , thermodynamics
Because of the similarity between the equations of motion
governing infinitesimal vibration due to a small perturbing force superimposed
on an already existing state of finite stress and the equations of
linear anisotropic elasticity, methods of analysis used in one may be extended
to the second. In particular, in this paper, the technique of ray expansions
is considered. .Methods for calculation of rays and amplitude coefficients
of the ray series are given. A seismic ray is described by a system of ordinary
differential equations of first order which can be solved by standard
numerical techniques. Another system of ordinary differential equations
is introduced to compute amplitude coefficients