Superpositions of Gaussian beams and column Gaussian packets in heterogeneous anisotropic media

Ludek Klimes


Based on the integral superposition of Gaussian packets, we derive the equations for the integral superposition of Gaussian beams and for the integral superposition of column Gaussian packets in smoothly heterogeneous media. Whereas Gaussian beams extend along their central rays, column Gaussian packets extend along an arbitrary system of lines.

The equations are applicable to both the anisotropic ray theory and the coupling ray theory in anisotropic media, or to the isotropic ray theory in isotropic media. The superpositions corresponding to the coupling ray theory can be applied to various kinds of reference rays. The equations can be used in both Cartesian and curvilinear coordinates.


Summation of Gaussian packets, summation of Gaussian beams, summation of column Gaussian packets, anisotropy, heterogeneous media, wave propagation, travel time, amplitude, Green tensor, S-wave coupling.

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Seismic Waves in Complex 3-D Structures, 25 (2015), 103-108 (ISSN 2336-3827, online at