Anisotropic-ray-theory geodesic deviation and two-point ray tracing through a split intersection singularity

Petr Bulant & Ludek Klimes


We demonstrate the principal problems with tracing the anisotropic-ray-theory S-wave rays. While the initial-value rays can safely be traced by solving Hamilton's equations of rays, it is often impossible to determine the coefficients of the equations of geodesic deviation (paraxial ray equations, dynamic ray tracing equations) and to solve them numerically. As the result, we often know neither the matrix of geometrical spreading nor the phase shift due to caustics. We show how surprisingly large is the number of rays which cannot be correctly calculated in the velocity model with a split intersection singularity.


Wave propagation, elastic anisotropy, heterogeneous media, anisotropic ray theory, geodesic deviation, KMAH index, two-point ray tracing, S-wave singularities.

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Seismic Waves in Complex 3-D Structures, 24 (2014), 179-187 (ISSN 2336-3827, online at