Inversion of band-limited reflection seismograms using stacking velocities as constraints

The authors consider the problem of determining the acoustical impedance of a layered medium from reflection seismograms which have small or missing low-frequency components. To regularise this ill-posed inverse problem, the authors incorporated stacking (RMS) velocities, which are available at data pre-possessing stage, as a penalty in an optimisation problem. They show that when this information is included, the problem becomes regularised. In particular, they show that for the linearised problem, the operator mapping the impedances to the data is bounded below, and for the nonlinear problem, they show the optimisation cost functional has a non-degenerate minimum. Various features of the theory are demonstrated in numerical simulations.