Phase shift of a general wavefield due to caustics in anisotropic media

Ludek Klimes


Equations are presented to determine the phase shift of the amplitude of an elastic wavefield due to both simple (line) and point caustics in heterogeneous anisotropic media. The phase-shift rules for a general ray-theory wavefield are expressed in terms of the paraxial matrices calculated by the Hamiltonian equations of geodesic deviation (paraxial ray equations, dynamic ray tracing equations). The phase-shift rules are derived both for 2×2 paraxial matrices in ray-centred coordinates and for 3×3 paraxial matrices in general coordinates.


Anisotropy, heterogeneity, elastic wavefield, ray theory, caustics, KMAH index, paraxial rays.

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Seismic Waves in Complex 3-D Structures, 24 (2014), 95-109 (ISSN 2336-3827, online at