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The paper considers the problem of the transformation of the fronts of weak shock waves in inhomogeneous elastic media with an almost layered structure. The research object is nonstationary wave with strong discontinuity generated in in inhomogeneous transversely isotropic elastic media The aim of this work is to study the effects of bifurcations of discontinuous waves, in particular, on the tasks of propagation in inhomogeneous rocks of seismic waves provoked by explosions, as well as mountain shocks. The research method is the zeroth approximation of the ray method. The paper considers the issue of restructuring of ray systems and fronts of weak shock waves of elastic media. The heterogeneity of which is caused by the variable characteristics of the medium for the regularity of a continuous function, selected in such a way as to ensure that the medium has acquired the properties of a layered structure, but the properties are described by continuous differentiated functions. The work results can be inculcated in research and projection institutes for design of construction of structures, transport and mine destination with the aim of their seismic protection and their screening from action of discontinuous waves generated by different technical failures. KEYWORDS: SHIELDING, DISCONTINUOUS WAVES, ANISOTROPIC LAYERED MEDIA, ELASTIC MEDIUM, RAY METHOD.

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