Abstract: Method and apparatus for estimating a resistivity property of an earth formation in a borehole with oil-based drilling fluid. The method may include estimating the resistivity property using a sensitivity of a real part of a measured impedance to a reactance of a gap between a resistivity sensor and a borehole wall. The real component and the quadrature component of resistivity measurements made by a two-terminal imaging tool in a borehole having an oil-based mud are affected by the tool standoff. It is shown that the sensitivity of the real part of the resistivity measurement to the reactance of the gap can be estimated from the time derivatives of the two components of the measurements. This makes possible a principal component analysis of the data to give an improved image of the formation resistivity.