Whole-space inversion using phase correction method for multi-frequency dielectric array logging tool

Systems, methods, and devices for evaluation of an earth formation intersected by a borehole using a logging tool. Methods include exciting an upper and lower transmitter; receiving signals at a plurality of receivers between the upper and lower transmitter; estimating a phase shift attributable to a volume of interest of the formation adjacent to a section of the carrier corresponding to the plurality of receivers by estimating phase shifts attributable only to portions of the volume of interest adjacent to corresponding portions of the section between each adjacent pair of receivers of the plurality of receivers; wherein each adjacent pair is positioned at a corresponding distance that is no more than half of the shortest wavelength of those wavelengths associated with the received signals. Estimating a phase shift between an adjacent pair of receivers may be carried out using a first relative phase value; and a second relative phase value.