Various resistivity logging tools, systems, and methods are disclosed. At least some system embodiments include a logging tool and at least one processor. The logging tool provides transmitter-receiver coupling measurements that include at least direct coupling along the longitudinal tool axis (Czz), direct coupling along the perpendicular axis (Cxx or Cyy), and cross coupling along the longitudinal and perpendicular axes (Cxz, Cyz, Czx, or Czy). The processor performs a multi-step inversion of said transmitter-receiver coupling measurements to obtain values for model parameters. Based at least in part on the model parameters, the processor determines borehole corrections for the transmitter-receiver coupling measurements and may further provide one or more logs derived from the borehole corrected transmitter-receiver coupling measurements. In at least some embodiments the logging tool assembly further collects borehole size measurements and measurements of borehole fluid resistivity for use in performing the inversion and determining the borehole corrections.