Pulsed-neutron borehole measurements involve a physical process in which a source emits energetic neutrons that lose energy upon collisions with formation nuclei, and are eventually captured by a nucleus to form a heavier, excited state. The excited nucleus decays to its ground state by the emission of gamma rays. Both thermal-neutron and gamma-ray populations decay with time at a rate defined by Sigma, which is a nuclear property that quantifies a material’s ability to capture thermal neutrons. The large contrast in Sigma between hydrocarbon and salty connate water enables calculations of water saturation directly from pulsed-neutron measurements. Sigma logs have proven useful in the assessment of thinly bedded formations because they exhibit a small volume of investigation, and have been deemed superior to resistivity logs in the petrophysical evaluation of carbonate formations. The recognized potential of Sigma logs in formation evaluation initiated the development of multi-detector Logging-While-Drilling (LWD) Sigma measurements. These measurements are acquired using one thermal-neutron and two gamma-ray detectors at different spacings from the source. Such a design is aimed at providing distinct radial depths of investigation to detect filtrate invasion in the near-wellbore zone. Despite their formation-evaluation potential, multi-detector time-decay measurements commonly remain affected by invasion, shoulder-bed, and well-deviation effects. The purpose of this dissertation is to develop a fast-forward simulation method to reproduce multi-detector time decays and combine the method with inversion techniques to improve the petrophysical interpretation of LWD Sigma measurements. First-order perturbation theory and a library of pre-calculated Monte Carlo detector-specific sensitivity functions and time decays are used to numerically simulate borehole Sigma measurements in realistic logging environments. The new simulation method is one hundred thousand times faster than rigorous Monte Carlo calculations and remains within two capture units of disparity. Next, the fast-forward simulation method is embedded within inversion algorithms to estimate layer-by-layer radial length of invasion and formation Sigma corrected for shallow invasion, shoulder-bed, and well-deviation effects. Both fast-forward and inverse modeling algorithms are benchmarked against laboratory and synthetic time decays. The improvement of formation Sigma obtained with inversion-based interpretation leads to an improvement in the estimation of Sigma-derived water saturation. Likewise, the estimated radial length of invasion is combined with neutron and density measurements to correct the latter for invasion effects. Results indicate that the inversion-based interpretation method is well suited for the evaluation of high-porosity formations invaded by salty mud filtrate. Inversion-based interpretation of field LWD time decays enables the estimation of lower values of water saturation when compared to conventional Sigma interpretation or resistivity methods. Estimated values of water saturation are as much as fifty percent lower than predicted by conventional interpretation of Sigma logs in the case of measurements affected by shoulder-bed effects, and as much as one hundred percent lower than predicted by the conventional interpretation method for measurements additionally affected by salty filtrate invasion. The key attributes of the combined petrophysical interpretation of multi-detector Sigma, neutron, and density measurements developed in this dissertation are that it explicitly enforces the physics of all nuclear measurements, honors the pressure and temperature dependency of reservoir fluid nuclear properties, and takes into account a-priori information such as mud-filtrate salinity, connate-water salinity, and bed-boundary locations. / text