A Monte Carlo-based adaptive weighted reduced order model for gamma density measurement

In practice of nuclear well logging, it is necessary to obtain detector responses in different downhole environ-ments (such as casing, cement and formation). Monte Carlo is a common way to obtain such responses through simulation. However, this could be computationally expensive and time-consuming. To address this issue, a novel reduced order model (denoted as ROM) is proposed to quickly calculated the detector responses under various environmental parameters. Based on the mathematical derivation, the ROM is constructed, and the simulation data is used to derive the coefficients. During this process, the model assigns an adaptive weight factor to each environmental parameter through the residual and optimization method to improve the prediction ac-curacy. The performance of the ROM is evaluated through comparison with the Monte Carlo modeling and its effectiveness and feasibility are verified by the good agreement with Monte Carlo results.