NATURAL GAMMA-RAY LOG INTERPRETATION - SEMIEMPIRICAL, PRINCIPAL COMPONENTS-ANALYSIS, AND MONTE-CARLO MULTIPLY-SCATTERED COMPONENTS APPROACHES

Three approaches are presented and evaluated for correcting natural ga mma-ray log responses for variations in logging conditions such as bor ehole and tool diameters, tool standoff, borehole fluid type, and form ation type. The data for all approaches was generated by the specific purpose Monte Carlo code McNGR which was developed at the Center for E ngineering Applications of Radioisotopes for natural gamma-ray logs. T he first approach is the Semi-Empirical and features the use of the ra dioisotope concentration correction factor as a function of an effecti ve absorption parameter. This parameter takes into account the average (two-dimensional) distance through the borehole to the tool surface a nd the borehole fluid density and composition. A standard set of loggi ng conditions was used as the reference case. The second is the Princi pal Components Analysis approach. It consists of the generation of a c omplete set of library spectra over a wide borehole and formation para meter range, and the subsequent reduction of this data set by the PCA approach to 10% of its original size while still maintaining essential ly all of the variance of the original set. Only six principal compone nts are needed to reconstruct the original set of 300 library spectra. The spectrum reconstructions are fast since only vector multiplicatio ns and additions are involved. The library spectra for K-40 U, and Th for this approach were generated by the Monte Carlo code McNGR. The th ird is the Monte Carlo Multiply-scattered Components approach. It firs t involves the decomposition of the K-40, U, and Th library spectra (o nly K-40 is demonstrated here) obtained under standard logging conditi ons (the reference case) by Monte Carlo simulation to produce individu al multiply-scattered characteristic components. These, in turn, are u sed as libraries to fit the total spectrum of any sample of interest w ith parameters sufficiently close to those of the reference case. Empi rical expressions for the multiply-scattered component coefficients ar e obtained as a function of formation acid borehole fluid parameters i ncluding density and composition. Spectrum reconstructions for any des ired sample are then carried out using standard multiply-scattered com ponents and their corresponding empirical coefficients. The advantages and disadvantages of the three approaches are discussed.