Shaping regularization in geophysical-estimation problems

Regularizationisarequiredcomponentofgeophysical-es- timation problems that operate with insufficient data. The goal of regularization is to impose additional constraints on the estimated model. I introduce shaping regularization, a generalmethodforimposingconstraintsbyexplicitmapping of the estimated model to the space of admissible models. Shaping regularization is integrated in a conjugate-gradient algorithm for iterative least-squares estimation. It provides the advantage of better control on the estimated model in comparison with traditional regularization methods and, in some cases, leads to a faster iterative convergence. Simple data interpolation and seismic-velocity estimation examples illustratetheconcept.