Certain logging method and system embodiments obtain multi-component signal measurements from an electromagnetic logging tool conveyed along a borehole through a formation, and invert the measurements for a single frequency using an anisotropic formation model having at least dip, horizontal and vertical resistivity, and horizontal and vertical permittivity, as parameters. A resulting log is provided to represent a position dependence of at least one of said parameters or a formation property derived from at least one of said parameters. Illustrative formation properties include water saturation, rock type, and presence of pyrite or other such materials having anisotropic polarization. Inversions may be performed on measurements acquired at other frequencies to determine a representative dispersion curve for further characterization of the formation.