Geofyzikální ústav Akademie věd ČR, v.v.i.

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Červený and Pšenčík - 2017 - Elementary Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

Červený and Pšenčík - 2017 - Elementary Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

Ivan Pšenčík, a researcher of the Institute of Geophysics of the CAS, v. v. i., and Vlastislav Červený from the Department of Geophysics, Faculty of Mathematics and Physics, Charles University present an algorithm for calculation of a high-frequency elementary Green function expressed in terms of the integral superposition of Gaussian beams in inhomogeneous, isotropic or anisotropic, layered structures. The algorithm represents a generalization of the standard ray theory, which removes some of the limitations of the ray theory. It, for example, removes the singularity of the ray theory in the caustic region. It also removes necessity to perform the time-consuming two-point ray tracing. The integral superposition of Gaussian beams can be evaluated at any point of the medium, including points in ray-theory shadow regions, with no need to trace rays to these points.

Described calculation of Gaussian beams is based on the dynamic ray tracing in Cartesian coordinates. It is shown that for the evaluation of the integral superposition, it is sufficient to solve the dynamic ray tracing only for the point-source initial conditions, and instead of calculating 3x3 paraxial matrices, it is sufficient to calculate only their 3 × 2 parts. Great advantage of the described approach is that the dynamic ray tracing in Cartesian coordinates is a basic part of the program package ANRAY designed for ray calculations of seismic wavefields in laterally varying, layered isotropic or anisotropic structures. The generalization of the package to calculate Gaussian beams should be the next step in the described research.

Link to the publication.