Ray model of elastic wave trajectory in inhomogeneous medium

At present, there are many theoretical and experimental works in the scientific literature dedicated to the study of the regularities of elastic wave propagation in various inhomogeneous media. Both layerwise inhomogeneous (or discretely inhomogeneous) media and continuously inhomogeneous media are discussed. Layerwise inhomogeneous media represent a multilayer structure in which the layers themselves are homogeneous, and their physical properties change sharply at the boundary between the layers. Continuously inhomogeneous media are media whose physical characteristics are continuous functions of coordinates. Examples of continuously inhomogeneous media are: the Earth's atmosphere with temperature that is not constant in altitude; water in the ocean with different salinity in depth; solid products with different hardness in thickness, etc. The same physical properties are observed for all such media. For all such media, the same peculiarity is observed, consisting in the dependence of the velocity of elastic wave propagation on the coordinates. The presence of this feature leads to curvature of their propagation trajectory. Therefore, when studying the regularities of elastic wave propagation in continuously inhomogeneous media, it is necessary to take into account the dependence of the velocity of these waves on the coordinates.