Use of rotationally invariant parameters derived from the magnetotelluric impedance tensor avoids problems with identification of electrical strike. However, quantitative analysis of an invariant must be used with caution. Layered models from inversion of invariant sounding curves accurately estimate the structure, as does one‐dimensional inversion of an invariant parameter, if the site is away from conductive three‐dimensional (3‐D) heterogeneities. Inversions at sites both above and away from a resistive heterogeneity and above a conductive heterogeneity result in errors. The errors are most serious at sites above a finite conductor. A section created by interpolation of layered models derived from invariants should always be modeled with multidimensional programs to verify the section’s accuracy. The above conclusions hold regardless of the type of invariant parameter used. We found no advantage to using the determinant over the arithmetic mean of the impedance tensor, or vice versa.