Fast inversion of approximate resistivity for oil-based mud resistivity imager based on open-short calibration

This paper proposes a new method for mud-effect correction and inversion of approximate apparent resistivity for oil-based mud microresistivity imaging logging. To correct the interference of the mud layer with electrode measurement signals, the Open-Short Calibration method is combined with a three-layer impedance model, and the open- and short-circuit states of the tool are simulated by the finite element method. By treating the electrode and the pad standoff as an integrated system, the method independently computes and explicitly removes the mud impedance, thereby extracting the formation impedance signal. To rapidly estimate formation parameters, a resistivity-consistency iterative inversion method is further proposed. After the formation impedance is extracted, the consistency residual among multifrequency approximate apparent resistivities is taken as the objective function, and nonlinear optimization is used to efficiently solve for formation resistivity, relative permittivity, and pad standoff. Numerical-model validation and field-well application results show that the proposed method can separate mud-signal interference over the full measurement range and enable quantitative characterization of formation apparent resistivity and related parameters.