Using Uncrewed Aerial vehicles (UAVs) to rapidly scan areas for potential unexploded ordnance (UXO) can provide an efficiency increase while minimizing detonation risks. We present a complete overview of how such mappings can be performed using scalar magnetometers, including initial sensor testing, time stamping validation, data positioning, noise removal, and source model inversion. A test survey was performed across disarmed UXO targets, during which three scalar magnetometers were towed in an airframe (“bird”) 10 m below a small (<25 kg) high speed (∼10 m/s) UAV to avoid magnetic disturbances from the UAV itself. Data were collected across ∼58 min of flight, with each sensor traversing ∼31.7 km to acquire dense data coverage across a 600 m × 100 m area. By using three individual magnetometers in the bird, UXO detection results across single-sensor data and several different multi-sensor configurations can be compared. The data obtained exhibited low apparent noise floors (on the order of tens of picoTesla) and retained a precision that enabled targeted modelling and removal of high-frequency noise with amplitudes of ±5 picoTesla. All of the different gradiometer configurations tested enabled recovery of most targets (including all major targets), although the horizontal configuration performed significantly worse in comparison.

SUMMARY 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 nonlinear, 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 multichain 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 allows full inference of the parameters describing a UXO while also including the possible presence of remanent magnetization.

Summary We investigate if it is theoretically possible to discriminate between unexploded ordnance (UXO) and non-UXO sources by modelling the magnetic dipole moment for ferrous objects of different shapes and sizes. This is carried out by approximating the volumetric demagnetization factors of rectangular prisms, representing shapes similar to a long rod or flat steel plate. By modelling different UXO as prolate spheroids the demagnetization factors can be determined which can be compared with the magnetic response of a prism. The inversion is carried out in a probabilistic framework, where the UXO forward model and the non-UXO forward model are assigned individual prior models in terms of shape, size, orientation and remanent magnetization of the object. 95 independent realizations of the prism prior model are generated to make 95 synthetic anomalies exemplifying non-UXO objects, which are inverted for using the UXO model. It is investigated if an identical magnetic moment can be produced between the two models and how well resolved the magnetic moment is in terms of the measured anomaly. The case study is carried out in two steps where we first have little prior information of expected UXO properties and another where a UXO prior is introduced with expected values of aspect ratio and size of 24 different UXO, that are often encountered in the North Sea. With no prior information of expected UXO, discrimination is at many times implausible, unless elongated rod prism objects are considered, where the magnetic moment often can not be reproduced by a spheroid. Introducing the UXO prior we achieve a much better discrimination rate when using the list of expected UXO properties. By using the UXO prior we can account for a much higher remanent magnetization allowed in the prior, and still achieve high discrimination capabilities in comparison to a case with no UXO prior.

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Summary A test site containing 24 targets of various disarmed unexploded ordnance (UXO) and non-UXO items were placed on a beach on the island of Rømø (Denmark) in a 600 m x 100 m area. Scalar magnetic anomalies were measured at 3-5 m altitude using an uncrewed aerial vehicle (UAV), towing a bird with a three-sensor triangular configuration to achieve a dense coverage with flight lines of 2 m spacing. The triple-sensor dataset is utilized in a probabilistic inversion setup to infer the magnetic moments of the 24 targets. The purpose of the study, is to try and distinguish between different types of ferromagnetic objects (UXO, non-UXO) using magnetic anomaly data. The inversion methodology uses different forward models (prolate spheroids, rectangular prisms) to infer target shape, size and orientation in an attempt to discriminate between UXO and non-UXO items. Stochastic inversions are carried out using different prior assumptions of remanent magnetization strength ($10\%$, $50\%$ and $80\%)$ of the induced dipole moment. Among the three levels of remanent magnetization strength in the prior, only some cases of discrimination seem evident for the lowest strength of remanence. One item is correctly classified as a true-negative (i.e. non-UXO) when assuming low remanent magnetization strength ($10\%)$ of the induced moment). However, at low remanent strength, one false-negative classification emerges, making any discrimination unreliable when assuming such low remanent magnetization. In addition to the discrimination study, different covariance models are utilized to optimize the inversion by addressing correlated errors and noise in the triple-sensor data set. Three covariance models are tested to try and account for spatially correlated noise and potential errors among the three sensors of each overflight. In many cases, the covariance models presented show a potential increase in sampling efficiency and consistency between data and the noise model, suggesting a more robust approach to a noise model in magnetic anomaly inversions. If the noise model is poor, however, it may bias the results by addressing the anomaly signal as noise. The inversions with correlated noise models are compared with inversions using a simple uncorrelated noise model. For several cases of data anomalies, differences between the inversion estimates when using correlated and uncorrelated noise models were evident, indicating that some bias may appear when assuming uncorrelated noise. Due to the general high presence of correlated signals in magnetic survey data, correlated noise models can significantly improve the overall uncertainty estimate of the estimated dipole moment. The study demonstrates, in terms of the 24 targets considered, that discrimination between UXO and non-UXO using magnetics is difficult. However, when using scalar magnetic data of high quality and resolution, the estimated dipole moments are often well resolved and uniquely defined in magnitude and position. This could provide valuable posterior information for future inversion studies by building a library of inferred magnetic moments from targets that have been found and inspected.