We perform a numerical-sensitivity study of various physical phenomena of interest for borehole resistivity logging applications in steel-cased wells. Specifically, we analyze the sensitivity of through-casing measurements for detecting water invasion, shale-laminated sands, and electrical anisotropy in the formation. In addition, we study the influence of the frequency of operation on through-casing resistivity measurements. The sensitivity analysis is performed using a highly accurate and reliable numerical method based on a 2D self-adaptive, goal-oriented, high-order, finite-element method (FEM). This method can be applied to simulate all types of resistivity logging measurements, including normal/laterolog, induction, and through-casing resistivity measurements. Results quantify the effects of several physical phenomena that can be sensed through casing and that can be measured with accurate sensors. We find that water invasion and shale-laminated sands behind casing can be detected and accurately quantified at frequencies below [Formula: see text]. On the other hand, measurements are almost insensitive to electrical anisotropy behind casing, but otherwise highly sensitive to frequency variations. Our simulations indicate that a frequency in the range of [Formula: see text] is the most adequate for maximizing the sensitivity of through-casing measurements with respect to spatial variations of electrical conductivity within the formation.