An apparatus and a method for recording the magnetic induction tensor induced in an earth formation are provided. The apparatus includes a magnetic induction device having at least three mutually orthogonal transmitter dipoles and at least three mutually orthogonal receiver dipoles that are direct-coupled, and at least three mutually orthogonal receiver dipoles that are cross-coupled. The method includes using the apparatus to sample the magnetic induction tensor components at a point. Further, samples may be taken at regularly spaced intervals using the magnetic induction device, moving the triaxial logging unit so that each transmitter and each receiver sequentially occupy the same point, repeating these steps until each transmitter and receiver array have sequentially occupied all desired points, and combining the magnetic induction tensor components to form the magnetic induction tensor. These components are useful in inferring water saturation and estimating hydrocarbon volumes in petroleum reservoirs.