A Novel Nonlinear Quadratic Spectral Decomposition Method for Neutron-induced Gamma Analysis

Abstract: Under complex well conditions, neutron-induced gamma spectra often suffer from drift and resolution degradation, leading to weakened characteristic peaks and increased peak overlap. These nonlinear degradations limit the accuracy of conventional linear spectral decomposition methods used in pulsed neutron logging. To address this issue, we propose a nonlinear quadratic spectral decomposition (NQSD) method. The method incorporates spectral drift and resolution degradation as parameters in a nonlinear model. These parameters are then solved iteratively using a two-step nonlinear weighted least squares approach. To improve computational efficiency in practical applications, a neural-network-based classifier is developed to determine whether the NQSD method should be activated during field data processing. Monte Carlo simulations demonstrate that the proposed NQSD method reduces the overall mean absolute error (MAE) of elemental content by 86.8% compared with the conventional weighted least squares (WLS) method. A classifier with 90% overall accuracy is used to select the appropriate decomposition method. Finally, the proposed method is validated on a coal-bearing interval in Shanxi. The results show that compared with WLS, NQSD reduces the overall MAE of elemental content by 59.8%, with the MAE of calcium, silicon, and total organic carbon (TOC) decreasing by 91.9%, 82.4%, and 27.3%, respectively. These results indicate that the proposed method provides reliable spectral analysis for pulsed neutron logging under complex well conditions, supporting more accurate formation evaluation.