Iterative reconstructions of electrical conductivity from multiexperiment low‐frequency electromagnetic data

We discuss the extensions of the contrast source inversion (CSI) method to incorporate multiexperiment data. The simplest way to use the multiexperiment data is by using the frequency‐hopping method. In this method, we first solve the inverse problem for a particular experiment and then use the results as the initial estimates for the inversion of the next experiment. In this paper, we have first modified the CSI method so that the results of the inversion from one experiment can be used as input for the inversion of the next experiment, where we only have to invert the differences in material properties and fields. A more sophisticated way to incorporate the multiexperiment data is to invert all available data sets simultaneously. To that end, we introduce two cost functionals. The first is the traditional cost functional where the cost functional of each experiment is added and weighted. The second is the multiplicative cost functional, where instead of adding the cost functional of each experiment we take the product of the cost functional of each experiment. The main advantage of the last cost functional is that the weights of different experiments are determined by the iterative process itself. We consider both the inversion from multifrequency induction‐logging data and the joint inversion from induction‐ and electrode‐logging data in three‐dimensional cross‐well and single‐well configurations.