
Smaglichenko T.A., Smaglichenko A.V., Genkin A.L., Sayankina M.K. Simulation of the ray path in techniques for imaging of elastic medium 

Abstract.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. Keywords: computational schemes, tomography, ray path, gradient model PP. 5258. DOI 10.14357/20718632180305 References 1. Look into the metal: now it's easy / V.G. Shevaldykin [et al.] // In the world NK. 2008. № 1 (39). P. 4653. 2. Passive seismic tomography using induced seismicity at a petroleum field in Oman / H. Zhang [et al.] // Geophysics. 2009. Vol. 74(6). WCB57WCB69. DOI: 10.1190/1.3253059 3. An updated numerical model of the Larderello–Travale geothermal system, Italy / P. Romagnoli [et al.] // Geothermics. 2010. Vol. 39. P. 292313. 4. Zhang H., Thurber C.H. Doubledifference tomography: The method and its application to the Hayward fault, California // Bulletin of the Seismological Society of America. 2003. Vol. 93 P. 18751889. 5. Smaglichenko T.A., Shigeki H., Kaori T. A differentiated approach to the seismic tomography problem: method, testing and application to the western Nagano fault area (Japan) // International Journal of Applied Earth Observation and Geoinformation (Elsevier). 2012. Vol. 16. P. 2741. 6. Protasov MI, Serdyukov AS, Cheverda V.A. Optimal parametrization of a transversally isotropic medium for reversing the times of the first arrivals for a system of observations of vertical seismic profiling with remote sources // Technology of seismic prospecting. 2010. № 3. P. 2531. 7. Sonic Logging While Drilling  Shear Answers / J. Alford [et al.] // Oilfield Review Spring. 2012. P. 415. 8. Smaglichenko T.A., Modification of Gaussian elimination for the complex system of seismic observations // Complex systems. 2012. Vol. 20(3). P. 229241. 9. Seismic tomography. With Applications in Global Seismology and Exploration Geophysics / Edited by G. Nolet // Netherlands: Springer, 1987. 386 p. 10. Burmakov Yu.A., Oblogina TI Seismic rays and hodographs in threedimensional inhomogeneous media // Izvestiya AN SSSR. Physics of the Earth. 1971. №1. C.3745. 11. Tsetsokho V.A. , Belonosova A.V., Belonosov A.S. Calculation formulas of linear geometrical spreading at ray tracing in a 3D blockinhomogeneous gradient medium // Siberian J. Num. Math. / Sib. Branch of Russ. Acad. of Sci. –– Novosibirsk, 2009. –– Vol. 12, № 3. –– P. 325–339. 12. Antonova L, Matveeva N.Wave Kinematics in Three Dimensional Block Gradient Medium. In: Questions of Dynamic Theory of Seismic Wave Propagation. Leningrad: Nauka; 1975. p. 78–88. 13. Petrashen G.I. Elements of the Dynamic Theory of Seismic Wave Propagation // Questions of the Dynamic Theory of Seismic Wave Propagation. L. 1959. P.11107. 14. Features of pathing of quasilongitudinal elastic waves through the boundary between isotropic and anisotropic media: theoretical and experimental research. Nikitin [and others] / / Crystallography. 2012.T. 57, No. 4. P. 628637.
