A method for well logging includes emitting a plurality of bursts of high energy neutrons into a wellbore and formations surrounding the wellbore. During and for a selected duration after at least one of the plurality of bursts, gamma rays are detected at at least one location spaced apart from the emitting and characterizing an energy of the detected gamma rays. After the last burst, gamma rays are detected and energy spectrum and rates of detection with respect to time thereof are determined. The foregoing is repeated for a selected number of times. After the selected number of times background gamma rays are measured. At least one of the numbers of detected gamma rays during a selected time interval and an energy spectrum of the detected gamma rays during the selected time interval is used to determine selected formation properties.