Forward modeling of spectral gamma-ray (SGR) logging in sedimentary formations

We propose a new approach to improve spectral gamma -ray (SGR) logging forward modeling by considering the radioactive minerals present in the rock as gamma -ray sources. This is based on the radioactive attenuation theory. The assumptions are: 1) minerals with K-40, U-238, and Th-232 content are considered radioactive sources uniformly distributed in the rock; 2) the measured radioactivity is proportional to the concentration of radioactive minerals and inversely proportional to the rock bulk density; 3) the radioactivity is only attenuated by absorption of gamma -rays. The forward modeling was tested using a synthetic case of sandstone with clay minerals and brine -saturated pores to analyze the sensitivity of SGR to changes in illite/smectite-illite/mica ratios and sandstone porosities. Finally, it was further validated with 44 core samples, of which 22 are from two shale gas and 22 from two clastic formations. The Pearson correlation coefficient applied to measure the misfit between the simulated and observed K, U, Th, and SGR data attained values of 0.82, 0.83, 0.61, and 0.57, respectively. A further improvement to 0.87, 0.85, 0.65, and 0.69 was achieved when applying joint inversion for data where illite/smectite and illite/mica ratios were not specified. The correlation between the simulated and observed data supports the viability of the proposed SGR forward modeling approach method.