A Wave Splitting Approach to Time Dependent Inverse Scattering for the Stratified Cylinder

This paper examines the inverse problem for the stratified inhomogeneous cylinder, in which the unknown velocity function is recovered from reflection data. The analysis is based on Weston’s theoretical wave splitting for stratified three-dimensional media [J. Math. Phys., 28 (1987), pp. 1061–1068], [J. Math.Phys., 29 (1988), pp. 36–45]. The forms of the splitting operators are presented, and the inverse problem is solved numerically by means of the r-equation, an integro-differential equation that characterizes the scattering medium independently of the wave field. Although the r-equation is singular at one round-trip time (corresponding to a caustic when a radially incoming cylindrical wave reaches the z-axis), several numerical examples indicate that the velocity function can be reconstructed quite accurately.