Error analysis of dual-energy gamma radiation measurements

Dual-energy gamma radiation systems are currently used to simultaneously determine either the dry bulk density of a porous medium and the volumetric content of one fluid, the volumetric fluid contents of two fluids, or the salt concentration and volumetric water content. In this paper an error analysis based on the well-known error propagation formula is presented for all three types of measurements. For each application, formulae are derived that calculate the variance of a measured variable as a function of the observed count rates, attenuation coefficients, and path length. These formulae can be implemented in data acquisition or postprocessing programs. In addition, formulae are presented that relate the variance to the values of the measured variables, measurement counting time, calibration counting time, path lengths, source intensities, and attenuation coefficients. The latter formulae benefit experimental design. The effect of counting and calibration time, attenuation coefficients, source strengths, and path lengths on the probable error are demonstrated. For each type of measurement, experiments are conducted to test the validity of the presented theory. It was shown that, in general, the difference between the measured value and the true value of a variable is less than 1 standard deviation. 14 refs., 5 figs., 3 tabs