We are engaged in a coordinated research program in inverse problems. Over the present contract period we have made substantial progress in all the areas of proposed research. This progress report described accomplishments in the following areas: (1) treatment of perturbations from non-constant reference speed in one dimensional propagation problems; (2) development and computer coding of a three dimensional inversion algorithm in the constant reference speed case; (3) increase of efficiency of the computer code for velocity inversion which makes the central processing requirements of the code comparable to processing now done in the seismic community; (4) examination of the validity and use of the Kirchhoff approximation in the inverse problem; (5) velocity inverrsion via our methods in the context of the parabolic approximation; and (6) applications of inversion techniques to non-destructive testing.