Methods of estimating borehole and formation properties using an electromagnetic induction logging tool having random tool decenter positions during data acqu

Described herein is a method including acquiring a set of transimpedance coupling voltages, between different antenna components of different axes of a transmitting station transmitting into a formation and different antenna components of different axes of a receiving station receiving from the formation, using an induction tool undergoing random movement during the acquisition. Fourier coefficients for the set of transimpedance coupling voltages are determined using a least square process. A mean tool eccentering azimuthal angle and an apparent formation azimuthal angle are estimated as a function of the Fourier coefficients. Compensated measurements are computed as a function of the Fourier coefficients. An inversion loop receives as input the compensated measurements, the estimated mean tool eccentering azimuthal angle, and the estimated apparent formation azimuth, and outputs final parameters as a function thereof.