2-D and 3-D joint inversion of loop–loop electromagnetic and electrical data for resistivity and magnetic susceptibility

Frequency-domain loop–loop electromagnetic (EM) methods are sensitive to the magnetic susceptibility of the Earth as well as its resistivity. Thus, inversion techniques have been used to simultaneously reconstruct both resistivity and susceptibility models from EM data. However, to take full advantage of inversion methods, calibration errors must be assessed and removed because ignoring them can result in misleading models. We present a multidimensional inversion method that jointly inverts EM and direct current (DC) resistivity data to derive offset errors as well as resistivity and susceptibility models, assuming that calibration errors can be represented by in-phase and quadrature offsets at each frequency. Addition of independent data such as DC data is effective for more accurately estimating the offsets, resulting in more reliable subsurface models. Synthetic examples involving small-loop EM data show that simultaneous inversion for resistivity and susceptibility is not stable, because of strong correlations between in-phase offset parameters and background susceptibility, but that the offsets are well determined when the data misfit is reduced rapidly in the early iteration step. Improvements achieved by joint inversion are mainly on the resistivity model. For airborne electromagnetic (AEM) data, the inversion process is stable, because AEM data are acquired using more loop–loop geometries and a wider range of frequencies. As a result, both the resistivity and susceptibility models are significantly improved by joint inversion.