Simultaneous inversion of induction data for dielectric permittivity and electric conductivity

A method of inverting induction logging data for evaluating the properties of underground formations surrounding a borehole, the data including induction voltage measurements obtained from a tool placed close to the formations of interest, the method includes: (a) defining a relationship relating the induction voltage to wave number, dielectric permittivity and conductivity; defining a cubic polynomial expansion of the relationship; and solving the cubic polynomial relationship using the voltage measurements to obtain values for conductivity that includes skin-effect correction, and apparent dielectric permittivity; and (b) using the obtained values for conductivity and apparent dielectric permittivity to derive a simulated value of induction voltage; determining the difference between the simulated value of the induction voltage and the measured induction voltage; and iteratively updating the values of conductivity and dielectric permittivity used for the derivation of the simulated value of induction voltage to minimize its difference with respect to the measured value.