We investigate two automatic ways of estimating the trade-off parameter in the objective function being minimized in minimum-structure-type solutions to the nonlinear inverse problem: the generalized crossvalidation and L-curve criteria. Both criteria enable an appropriate value of the trade-off parameter to be obtained when the noise in the observations is not known. The particular inverse problem we consider here is the simultaneous inversion of electromagnetic loop-loop data for one-dimensional models of both electrical conductivity and magnetic susceptibility. In the great majority of examples tested, both criteria were successful in determining a suitable value of the trade-off parameter.
It is common to pose geophysical inverse problems as an optimization problem in which an objective function comprising a measure of data misfit and a measure of model character is minimized.
