Natural gamma-ray log interpretation: Semi-empirical, principal components analysis, and monte carlo multiply-scattered components approaches

Three approaches arc presented and evaluated for correcting natural γ-ray log responses for variations in logging conditions such as borehole and tool diameters, tool standoff, borehole fluid type, and formation type. The data for all approaches was generated by the specific purpose Monte Carlo code McNGR which was developed at the Center for Engineering Applications of Radioisotopes for natural γ-ray logs. The first approach is the Semi-Empirical and features the use of the radioisotope concentration correction factor as a function of an effective absorption parameter. This parameter takes into account the average (two-dimensional) distance through the borchole to the tool surface and the borehole fluid density and composition. A standard set of logging conditions was used as the reference case. The second is the Principal Components Analysis approach. It consists of the generation of a complete set of library spectra over a wide borehole and formation parameter range, and the subsequent reduction of this data set by the PCA approach to 10% of its original size while still maintaining essentially all of the variance of the original set. Only six principal components are needed to reconstruct the original set of 300 library spectra. The spectrum reconstructions are fast since only vector multiplications and additions are involved. The library spectra for ⁴⁰K. U. and Th for this approach were generated by the Monte Carlo code McNGR. The third is the Monte Carlo Multiply-scattered Components approach. It first involves the decomposition of the ⁴⁰K, U, and Th library spectra (only ⁴⁰K is demonstrated here) obtained under standard logging conditions (the reference case) by Monte Carlo simulation to produce individual multiply-scattered characteristic components. These, in turn, are used as libraries to fit the total spectrum of any sample of interest with parameters sufficiently close to those of the reference case. Empirical expressions for the multiply-scattered component coefficients are obtained as a function of formation and borehole fluid parameters including density and composition. Spectrum reconstructions for any desired sample are then carried out using standard multiply-scattered components and their corresponding empirical coefficients. The advantages and disadvantages of the three approaches are discussed.