The SOLA method for the inversion of induced polarization data

SUMMARY Inversion of a given geophysical data set cannot be complete without assessing the resolution and uncertainties associated with the model obtained. However, model appraisal may still be a challenging task from both a theoretical and a computational point of view. To tackle the problems of model estimation and appraisal, we introduce the subtractive optimally localized averages (SOLA) method to the geophysical electromagnetic community, through the example of linear inversion of induced polarization (IP) data. SOLA is a variant of the Backus-Gilbert method: it is computationally more efficient but also allows one to specify directly the target local averages of the Earth’s properties to be estimated, including their uncertainties. SOLA offers great flexibility in the construction of averaging kernels, via the design of target kernels, and direct control over the propagation of data errors into the local-average estimates. With SOLA we obtain a collection of (i) local averages of the ‘true’ Earth model, accompanied with their (ii) averaging kernels and (iii) uncertainties. We investigated the performance of SOLA for the 2-D tomographic inversion of a field IP data set. The obtained chargeability model compares well with previous studies, and, most importantly, its resolution (the spatial extent of the averaging kernels) and uncertainties can be interrogated. We conclude that SOLA is a promising approach for geophysical-electromagnetic linear(ized) tomographies. In the case of IP inversion, to construct chargeability models and evaluate their robustness.