1. A downhole tool in a borehole for determining properties of a formation, the tool comprising: a nuclear source for irradiating the formation; a plurality of detectors capable of measuring at a plurality of radial depths into the formation; a plurality of antennas capable of measuring at a plurality of radial depths into the formation, wherein the detectors and the antennas are collocated or at least partly overlap; a controller for enabling the antennas and the detectors to perform a resistivity and a sigma measurement for the plurality of radial depths; and a processing apparatus arranged to combine the detector and antenna measurements to determine an invasion profile of the borehole fluid into the formation, based on the resistivity measurements for the plurality of radial depths and on the sigma measurements for the plurality of radial depths and to determine the properties of the formation based on the resistivity measurements for the plurality of radial depths and on the sigma measurements for the plurality of radial depths, wherein the properties comprise water saturation in an invaded zone and in an uninvaded zone of the formation and water salinity in an invaded zone and in an uninvaded zone of the formation.