Differential semblance velocity analysis via shot profile migration

Shot profile migration provides a convenient framework for implementation of a differential semblance algorithm for estimation of complex, strongly refracting velocity fields. The objective function minimized in this algorithm may measure either focussing of the image in offset or flatness of the image in (scattering) angle. The gradient of this objective is a by-product of a depth marching scheme, an requires a few extra computations beyond those necessary to produce the prestack data volume. A strongly refracting 2D synthetic data example illustrates the excellent image quality obtainable from model-consistent data. Offset and angle variants behave differently, with more rapid convergence for the offset variant, underlining the importance of a mathematically well posed formulation: in 2D, the angle variant is much less well-conditioned than the offset variant.