Differential semblance optimization (DSO) is an approach to inversion of reflection seismograms which avoids the severe convergence difficulties associated with nonlinear least-squares inversion. The method exploits both moveout and amplitude characteristics of reflections. We have implemented a version appropriate to plane-wave (p-tau) seismograms and layered constant-density acoustic earth models. Theoretical and numerical analyses of this version of DSO indicate that stable and reasonably accurate estimates of both velocity trend and reflectivity can be derived. To test DSO further, we applied it to a marine data set from the Gulf of Mexico, where the method produced results which compare favorably to well-log information. The method can be extended to incorporate laterally heterogeneous velocity models.