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Perturbed ray tracing on a heterogeneous sphere
Author(s) -
Virieux Jean
Publication year - 1989
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl016i005p00405
Subject(s) - ray tracing (physics) , spherical harmonics , azimuth , distributed ray tracing , spherical coordinate system , coordinate system , slowness , tracing , adiabatic process , physics , action angle coordinates , hamiltonian (control theory) , mathematical analysis , classical mechanics , computational physics , geometry , generalized coordinates , mathematics , computer science , optics , mathematical optimization , quantum mechanics , operating system
We propose a fast ray tracing method on a laterally heterogeneous Earth. When the square of slowness is expanded into spherical harmonics, an approximate analytical ray tracing can be performed. Using a Hamiltonian formulation, we introduce new coordinates, that have the specific adiabatic invariance of action/angle coordinates. A first‐order solution is constructed in this new coordinate system. Excellent agreement is obtained between numerical and approximate analytical ray tracings, for the global model of Nakanishi and Anderson [1984] with an azimuthal order 6.