INVERSE PROBLEMS OF RAY SEISMIC TOMOGRAPH Y

The paper is concerned with study of uniqueness and, to a degree, stab ility of the solutions to problems of cross-borehole and reflection ra y tomography in case of nonuniform reference media. The main feature o f ray seismic tomography (RST) is incomplete angular view. To recogniz e a class of situations where the solution uniqueness is possible, a c oncept of quasicompleteness is introduced; this concept is valid when the area under study may be covered by a system of lines each of which is tangentially illuminated. The system of lines may depend on featur es of the reference medium. The reference media where the velocity is either one-dimensional function or uniform function of any power are c onsidered in detail. Tor transmitted waves the problem may be reduced to the known problem of integral geometry. The solution is reduced to a Volterra-type equation of first kind. If the solution is sought in a limited band of spatial frequencies, it is stable relative to time va riations in class C-1. A similar result can also be obtained for a uni form reference medium. The uniqueness also exists in reflection tomogr aphy ii the geometry of the reflecting boundary in the reference mediu m is concordant with the velocity function geometry. The solution, how ever, is strongly incorrect. The strongly incorrect solution for trans mitted waves may be obtained in wider classes of velocity function and under weaker conditions relative to quasicompleteness of the ray syst em. It has been shown that a weak incorrectness is reached in similar situations in the 3D problem.