Generalized focusing of time-lapse changes with applications to direct current and time-domain induced polarization inversions

Often in geophysical monitoring experiments time-lapse inversion models vary too smoothly with time, owing to the strong imprint of regularization. Several methods have been proposed for focusing the spatiotemporal changes of the model parameters. In this study, we present two generalizations of the minimum support norm, which favour compact time-lapse changes and can be adapted to the specific problem requirements. Inversion results from synthetic direct current resistivity models that mimic developing plumes show that the focusing scheme significantly improves size, shape and magnitude estimates of the time-lapse changes. Inversions of the synthetic data also illustrate that the focused inversion gives robust results and that the focusing settings are easily chosen. Inversions of full-decay time-domain induced polarization (IP) field data from a CO₂ monitoring injection experiment show that the focusing scheme performs well for field data and inversions for all four Cole-Cole polarization parameters. Our tests show that the generalized minimum support norms react in an intuitive and predictable way to the norm settings, implying that they can be used in time-lapse experiments for obtaining reliable and robust results.