Methods and apparatus are disclosed for determining gas saturation, liquid saturation, porosity and density of earth formations penetrated by a well borehole. Determinations are made from measures of fast neutron and inelastic scatter gamma radiation induced by a pulsed, fast neutron source. The system preferably uses two detectors axially spaced from the neutron source. One detector is preferably a scintillation detector responsive to gamma radiation, and a second detector is preferably an organic scintillator responsive to both neutron and gamma radiation. The system can be operated in cased boreholes which are filled with either gas or liquid. Techniques for correcting all measurements for borehole conditions are disclosed.