Differential Semblance Optimization ("DSO") is a variant of data-fitting (least-squares) inversion of reflection seismograms. The misfit functions used in other implementations of least-squares inversion (for example Tarantola 1986, Kolb et al. 1986) exhibit highly nonconvex dependence on velocity trends. Therefore least-squares inversion appears to require the use of relatively costly global optimization algorithms such as Monte-Carlo minimization, simulated annealing, or genetic algorithms (Sen and Stoffa 1991, Scales et al. 1991, Tarantola 1991). Also local sensitivity analysis (eg. singular value decomposition of the Hessian) does not describe the resolution limits inherent in such misfit functions - they are too nonlinear. In contrast, the DSO misfit function is smooth and convex over a wide range of velocity models, and so can be minimized satisfactorily via efficient local (Newton-like) algorithms. Moreover the quadratic model of the DSO misfit function at the optimum is descriptive of its local behaviour, and so may be used for studies of velocity resolution. In previous work (Symes and Carazzone 1991 and references cited there) we have presented DSO inversion for plane-wave data sets and layered media, including application to field data. In this paper, we describe the DSO misfit function for 2D shot gather inversion of laterally heterogeneous models, and an algorithm for minimizing it, and present a simple, preliminary example of shot-gather velocity inversion.