Simulation of the ray path in techniques for imaging of elastic medium

When solving a wide range of tasks of industrial ultrasonic tomography, material science, seismic tomography there is a problem when the model values of physical quantities differ from the real one. Therefore a focus of many studies are computational formulas, are describing the model having known parameters. In this paper, solutions are considered that determine the ray path from a point source to a selected point in an elastic medium. By using formulas to calculate the position of a ray in space when propagating a longitudinal wave in a gradient medium, we derived explicit formulas for calculating the point of maximum descent of the ray when the receiver is at some limited distance from the source, and also for calculating of the angle of incidence at the surface. The results of application to a small sample of data are presented. Formulas are of practical interest for programming ray traces in a layered homogeneous medium that can be approximated by a continuous gradient.