We described an implementation of differential semblance velocity analysis based on shot-profile migration, and illustrated its ability to estimate complex, strongly refracting velocity fields. The differential semblance approach to velocity analysis uses waveform data directly: it does not require any sort of traveltime picking. The objective function minimized by the differential semblance algorithm can measure either focusing of the image in offset or flatness of the image in (scattering) angle. We showed that the offset variant of differential semblance yields somewhat more reliable migration velocity estimates than does the scattering angle variant, and we explain why this is so. We observed that inconsistency with the underlying model (Born scattering about a transparent background) can lead to degraded velocity estimates from differential semblance, and we showed how to augment the objective function with stack power to enhance ultimate accuracy. A 2D marine survey over a target obscured by the lensing effects of a gas chimney provides an opportunity for direct comparison of differential semblance with reflection tomography. The differential semblance estimate yields a more data-consistent model (flatter angle gathers) than does reflection tomography in this application, resulting in a more interpretable image below the gas cloud.