Lamb's inverse axially symmetric problem

The problem of restoring the velocity of transversal waves in an elastic half-space by a known wave field on the boundary of a medium is studied. The problem is reduced to a system of “integral” equations similar to the Volterra one. Theorems on existence in the small and on uniqueness of the solution are proved. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 51–67. Translated by T. N. Surkova.