Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

Vlastislav Cerveny & Ivan Psencik


Integral superposition of Gaussian beams is a useful generalization of the standard ray theory. It removes some of the deficiencies of the ray theory like its failure to describe properly behaviour of waves in caustic regions. It also leads to a more efficient computation of seismic wavefields since it does not require the time-consuming two-point ray tracing. We present the Gaussian beam integral superposition of Green function for inhomogeneous, isotropic or anisotropic, layered structures based on the dynamic ray tracing (DRT) in Cartesian coordinates. For the evaluation of the superposition formula, it is sufficient to solve the DRT in Cartesian coordinates just for the point-source initial conditions. Moreover, instead of seeking 3 × 3 paraxial matrices, it is sufficient to seek just 3 × 2 parts of these matrices. The presented formulae can be used for the computation of wavefields generated by various types of point sources (explosive, moment-tensor). Receivers may be situated at an arbitrary point of the medium, including the ray-theory shadow regions. Arbitrary direct, multiply reflected/transmitted, unconverted or converted elementary waves, propagating independently, can be considered.


elastodynamic Green function, inhomogeneous anisotropic media, integral superposition of Gaussian beams

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Seismic Waves in Complex 3-D Structures, 26 (2016), 131-153.