Inversion of electromagnetic induction data using a novel wavelet-based and scale-dependent regularization term

SUMMARY The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability and smoothing constraint typically used. However, profiles are not always expected be smooth. Here, we develop new scheme in which transform model wavelet space impose sparsity constraint. This constrained will minimize objective function with least-squares misfit measure domain. A domain allows investigate temporal resolution (periodicities at different frequencies) spatial (location peaks) characteristics model, penalizing small-scale coefficients effectively reduces complexity model. novel scale-dependent regularization term can used favour either blocky or smooth structures, as well high-amplitude models globally structures inversion. Depending on profile, suitable basis chosen. supports multiple types same algorithm thus flexible. Finally, apply this frequency sounding set, but could equally any other 1-D geophysical method.