RECOVERY OF 2-DIMENSIONAL PERTURBATIONS O F THE VELOCITY OF A VERTICALLY-INHOMOGENEOUS MEDIUM FROM MULTICOVERAGE DATA (LINEARIZED FORMULATION)

Under consideration is a linearized problem of percovery of local two- dimensional perturbations of a vertically-inhomogeneous medium of a gi ven structure by using multicoverage data of an ideal system (with the sources and receivers filling a straight line completely). After a Fo urier transform with regard to time and source coordinates is made, it reduces to a decompasable system of Fredholm integral equations of fi rst kind with a continuous kernel relative to Fourier transform compon ents with regard to the horizontal variable of the function to be soug ht. This paper reports results of numerical SVD analysis of linear fin ite-dimensional operators that appear in the process of discretization of this system for a realistic model for a vertically-inhomogeneous e nclosing medium. It is shown that the concept of <<r>>-solution to thi s system - a solution obtained by truncating SVD of the matrices repre senting these linear finite-dimensional operators in some basis - are meaningful even at small values of parameter <<r>> (r - is a number of singular vectors corresponding to largest singular values and retaine d upon truncating the SVD). Sensitivity of <<r>>-solutions to errors i n specification of a vertically-inhomogeneous enclosing medium is inve stigated numerically. Also they are compared with the ideal multicover age data prestack migration into the enclosing vertically-inhomogeneou s medium.