Magnetic modelling of unexploded ordnance (UXO) is a well documented method used to interpret magnetic anomalies occurring in UXO excavation surveys. By treating UXO as a ferrous spheroidal object, the induced dipole moment can be estimated by approximation of UXO characteristics such as shape, size, and orientation. Inversion of magnetic data with respect to UXO requires one to solve the equation for the induced dipole moment, while also determining the location and orientation of the object. This is a highly non-linear, non-unique problem, where many solutions often are present, which make it difficult for standard inversion methods, such as linearized approaches and maximum likelihood estimators, in assessing uncertainties and correlations in estimated model parameters that often result in an incomplete solution. In this study, we treat the problem concerning magnetic UXO inversion by a probabilistic approach using Markov Chain Monte Carlo (McMC) sampling. To deal with the potential multimodality a combination of two well known McMC sampling methods is employed in a single-chain approach: The extended Metropolis algorithm is used for efficient local sampling, and the Gibbs sampler is used to help exploring the possible multimodal density of the posterior. By adding a Gibbs step we significantly increase the efficiency of the extended Metropolis, making it viable to use as a single-chain sampler for this problem. We refer to the algorithm as the Gibbs-within-Metropolis algorithm. We test and compare the proposed algorithm to a multi-chain McMC parallel tempering setup using the extended Metropolis algorithm. We then present synthetic cases and a real data case, where the algorithm is used. We demonstrate how the probabilistic approach allow full inference of the parameters describing an UXO, while also including the possible presence of remanent magnetization.
Bibliographical noteThis is a pre-copyedited, author-produced PDF of an article accepted for publication in Geophysical Journal International following peer review. The version of record is available online at: https://doi-org.proxy.findit.dtu.dk/10.1093/gji/ggz421
- Inverse theory
- Probability distributions
- Magnetic anomalies: modelling and interpretation