Iterative Reconstructions of Electrical Conductivity from Multi-Experiment Low-Frequency Electromagnetic Data.

摘要

The authors discuss the extensions of the contrast source inversion (CSI) method to incorporate multi-experiment data. The simplest way to use the multi-experiment data is by using the frequency-hopping method. In this method, the authors 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 the paper, the authors have first modified the CSI method so that the results of the inversion from on experiment can be used as input for the inversion of the next experiment, where they only have to invert the differences in material properties and fields. A more sophisticated way to incorporate the multi-experiment data is to invert all available data sets simultaneously. To that end, they 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, they 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. The authors consider both the inversion from multi-frequency induction logging data and the joint inversion from induction and electrode logging data in three-dimensional cross- and single-well configurations.