Mathematical statement of the inverse kinematic problem of seismics for 3D inhomogeneous medium. I (Q2729318)

The results of the article under review continue the study by \textit{A.~V.~Belonosova} and \textit{A.~S.~Alekseev} in [Some Methods and Algorithms for Interpolation of Geophysical Data, Nauka, Moscow, 137-154 (1967)] wherein the inverse kinematic problem is studied for a 2D inhomogeneous isotropic elastic medium.NEWLINENEWLINE The aim of the article is to extend the methods of the above-mentioned work to the 3D case of the inverse kinematic problem. The three-dimensional problem essentially differs from its two-dimensional statement. The function of two variables is reconstructed using 2D information, in the original problem the function of three variables is reconstructed using 4D information. This can provide a substantially higher stability of the solution to the 3D problem on a computer. The authors discuss how to pose the inverse problem and then to find a solution numerically.