A differential semblance criterion for inversion of multioffset seismic reflection data

Mean square error leading to least squares inversion of multioffset reflection seismograms is insensitive to velocity trend information except in the immediate vicinity of a kinematically correct model. In contrast, differential semblance retains sensitivity to velocity trend changes over a wide range of models. The differential semblance criterion combines mean square error with the mean square differences of inverted models from data sets at neighboring shot positions (or offsets, or slownesses, …). Differential semblance compares model estimates at nearby acquisition parameters which are similar even when the model velocity trends are incorrect. Because the method inverts the data, so that the estimated model amplitudes are meaningful, simple differences between the (unstacked) model estimates give a reliable measure of velocity error. A mathematical investigation indicates that the differential semblance criterion is smooth and convex over a large range of velocity models. Numerical simulation using synthetic data sets verifies this contention.