The computer implementation of a two-and-one-half dimensional (2.5-D) constant density prestack inversion formalism with laterally and depth-dependent background propagation speed is a Kirchhoff-type inversion, summing data from a line of receivers over traveltime curves in the depth-dependent background medium with weights determined from Born/Kirchhoff inversion theory. This theory predicts that the output will be a reflector map with peak amplitudes on each reflector being in known proportion to the angularly dependent geometrical optics reflection coefficient. The 2.5-D feature provides for out-of-plane spreading correction consistent with the prescribed background medium. The method is applied to a synthetic data set and to a physically modeled data set generated at the Seismic Acoustic Laboratory. The graphical output demonstrates the validity of the formalism as a Kirchhoff migration. Parameter estimation for the synthetic data confirmed the theory. Parameter estimation for the experimental data was less successful, partially due to problems with amplitude control in the original experiment and partially due to the limited aperture of the common-shot data, thereby suggesting that a common-offset inversion might be more useful for parameter estimation.