Using a contraction mapping method to determine complex permittivity from electromagnetic propagation measurements

In typical logging while drilling propagation-resistivity tools, formation properties are measured at different operating frequencies. The conductivity and permittivity of the formation are obtained from the inversion of the measured amplitude attenuation and phase shift between a pair of receiver antennas. This paper describes a simple method for computing formation resistivity and permittivity from electromagnetic propagation measurements. It starts with a closed-form solution for a generic propagation tool in homogeneous and isotropic media and uses a contraction mapping method for inverting conductivity and permittivity.