ERROR ANALYSIS OF DUAL-ENERGY GAMMA-RADIATION MEASUREMENTS

Dual-energy gamma radiation systems are currently used to simultaneous ly determine either the dry bulk density of a porous medium and the vo lumetric content of one fluid, the volumetric fluid contents of two fl uids, or the salt concentration and volumetric mater content. In this paper an error analysis based on the well-known error propagation form ula is presented for all three types of measurements. For each applica tion, formulae are derived that calculate the variance of a measured v ariable as a function of the observed count rates, attenuation coeffic ients, and path length. These formulae can be implemented in data acqu isition or postprocessing programs. In addition, formulae are presente d that relate the variance to the values of the measured variables, me asurement counting time, calibration counting time, path lengths, sour ce intensities, and attenuation coefficients. The latter formulae bene fit experimental design. The effect of counting and calibration time, attenuation coefficients, source strengths, and path lengths on the pr obable error are demonstrated. For each type of measurement, experimen ts 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.