Multidetector logging-while-drilling (LWD) Sigma was introduced to the oil industry to measure neutron absorption cross section (Sigma) and radial length of invasion in shallow-invaded formations. Sigma quantifies the ability of a material to absorb thermal neutrons and is calculated from the late time portion of the time decay of thermal neutrons or gamma rays generated from thermal-neutron absorption. The assessment of invasion is made possible with the combination of a thermal-neutron detector and two gamma-ray detectors with different source-detector spacings. However, the interpretation of LWD Sigma logs is often affected by several environmental and/or geometric effects that can mask the formation response. A fast numerical simulation method embedded with inversion-based techniques can be used to estimate intrinsic formation Sigma from borehole measurements affected by shoulder-bed, invasion, and/or environmental effects. We developed a fast and accurate method to numerically simulate LWD multidetector thermal-neutron and gamma-ray time decays in realistic borehole environments. The method relies on Monte Carlo precalculated libraries of particle time decays and detector-specific flux sensitivity functions, while accounting for detector-specific borehole and diffusion effects. Simulations are benchmarked against test-pit measurements and Monte Carlo N-particle (MCNP) transport code calculations. Results indicate that multidetector time decays acquired under complex geometrical conditions can be numerically simulated in approximately 1e-5 the time required using MCNP, with average difference within two capture units. The simulation of time decays, rather than Sigma itself enables a direct relationship between actual rock Sigma and multidetector diffusion-affected time decays, thereby removing intermediate correction steps often used to convert apparent into intrinsic formation Sigma.