Simultaneous 1D inversion of loop–loop electromagnetic data for magnetic susceptibility and electrical conductivity

Abstract Magnetic susceptibility affects electromagnetic (EM) loop–loop observations in ways that cannot be replicated by conductive, nonsusceptible earth models. The most distinctive effects are negative in-phase values at low frequencies. Inverting data contaminated by susceptibility effects for conductivity alone can give misleading models: the observations strongly influenced by susceptibility will be underfit, and those less strongly influenced will be overfit to compensate, leading to artifacts in the model. Simultaneous inversion for both conductivity and susceptibility enables reliable conductivity models to be constructed and can give useful information about the distribution of susceptibility in the earth. Such information complements that obtained from the inversion of static magnetic data because EM measurements are insensitive to remanent magnetization. We present an algorithm that simultaneously inverts susceptibility-affected data for 1D conductivity and susceptibility models. The solution is obtained by minimizing an objective function comprised of a sum-of-squares measure of data misfit and sum-of-squares measures of the amounts of structure in the conductivity and susceptibility models. Positivity of the susceptibilities is enforced by including a logarithmic barrier term in the objective function. The trade-off parameter is automatically estimated using the generalized cross validation (GCV) criterion. This enables an appropriate fit to the observations to be achieved even if good noise estimates are not available. As well as synthetic examples, we show the results of inverting airborne data sets from Australia and Heath Steele Stratmat, New Brunswick.