Geodesic
Bi-Characteristic Curves of Body and Surface Waves and Application in Geophysics
Serdica Mathematical Journal, Tome 41 (2015) no. 4, pp. 513-526.

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In this paper is given a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with Earthquake as a source of the signal and at least three receiver stations on the surface. The wave propagation in such media is described by a system of three strongly coupled hyperbolic equations with piece-wise constant coefficients. The characteristic set and bi-characteristic curves are computed in a homogeneous half-space with free boundary as well as the formulae of reflection and diffraction of the bi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-characteristic curves for the inverse problem in geophysics and Earth modelling are given. 2010 Mathematics Subject Classification: 35L53, 35Q86, 86A15.
Keywords: Strongly coupled linear hyperbolic systems, modelling of multi-layered solid body, applications in Geophysics 
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     author = {Boyadzhiev, Georgi},
     title = {Bi-Characteristic {Curves} of {Body} and {Surface} {Waves} and {Application} in {Geophysics}},
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Boyadzhiev, Georgi. Bi-Characteristic Curves of Body and Surface Waves and Application in Geophysics. Serdica Mathematical Journal, Tome 41 (2015) no. 4, pp. 513-526. http://geodesic.mathdoc.fr/item/SMJ2_2015_41_4_a11/