UMRS Data Inversion Using Tempered Hamiltonian Monte Carlo Method and Its Application to Water Detection in the Tunnel

Underground magnetic resonance sounding (UMRS) has the problem of low data quantity and low data quality in tunnel detection, a probabilistic statistical method is needed for data inversion. We used Hamiltonian Monte Carlo (HMC) to obtain UMRS inversion results, and we implemented a "tempered" scheme in HMC, in order to obtain higher efficiency and accuracy of inversion. This is the first time tempered HMC (THMC) has been applied to UMRS inversion and tunnel detection. It adds the neglected temperature term into HMC, effectively improving the escape ability, and improving computational efficiency. First, UMRS and THMC methods are briefly introduced in this article. Then, we investigate the relationship between different temperatures and the ability of THMC to jump out of the local optimal and find the temperature range suitable for UMRS inversion. We designed a series of schemes to test the performance of two methods and demonstrate that UMRS inversion using THMC has clear advantages. The inversion results of synthetic data show that THMC has higher efficiency and accuracy than HMC under extreme conditions, such as weak signal and high noise. Finally, we introduce the general situation of the study site and apply the two methods to the observation data inversion. THMC obtains results that are more consistent with the actual situation, which proves that it has strong practicability. We believe that THMC is more suitable for UMRS data inversion than HMC. THMC is helpful in improving the detection accuracy and efficiency of UMRS, ensuring the safety of tunnel construction, and preventing the delay of the construction period.