Probabilistic inversion method for 3D geomagnetic data: A new approach to determine the geometry and depth of subsurface sources

Geomagnetic prospecting is traditionally carried out in two dimensions (2D) on the surface of the ground to search for archaeological remains, unexploded ordnance (UXO) or industrial waste. Despite the efficacy of the method in identifying the target, it does not facilitate the precise determination of the depth and geometry of the sources. To reduce this uncertainty, additional data is requisite. One approach is to integrate the vertical variation of the geomagnetic field to provide a more accurate understanding of the depth and geometry of the sources. To this end, we propose an inversion algorithm designed for 3D geomagnetic prospecting data. This algorithm is based on simulated annealing (SA) and extended by a hierarchical refinement strategy.

The SA was chosen for its ability to explore complex, multi-dimensional solution spaces, minimizing the likelihood of hitting the local optimum trap by probabilistically accepting sub-optimal solutions in the early stages of the process, thus allowing a more extensive search before converging on the optimum. A hierarchical refinement strategy has been incorporated into the SA algorithm, which subdivides the model into smaller regions as the inversion stabilizes. This allows the algorithm to continually adjust each subpart until the stop condition is met. This generational approach improves the accuracy of the inversion results and provides a more detailed insight into the geometry of irregular or complex subsurface structures, which is more representative of reality than traditional parametric inversion methods, which rely on predefined geometries and may result in local details being overlooked. In accordance with the refinement strategy, subcomponents self-adjust their boundaries, contingent on their neighborhood, while searching for optimal solutions. This approach enables the model to maintain depth and spatial consistency over successive iterations.

In order to assess the effectiveness of the algorithm, 3D geomagnetic data were collected from two case studies within the ANR's GEOPRAS project. These cases are shipwrecks located on the beaches of Sables-d'Or-les-Pins (Fréhel, Côtes-d'Armor) and Trez Rouz (Camaret-sur-Mer, Finistère) in France. The inversion program provides two subsurface models of shipwrecks as its results. These models contain the information on the magnetization, location and geometry of the shipwrecks. Subsequent excavations showed that the predicted models differed by a few decimeters from the actual finds. Considering the size of the shipwrecks, this demonstrates the robustness and accuracy of the algorithm in reconstructing subsurface shapes and locations.

By reducing uncertainties in depth and geometry, this three-dimensional inversion technique provides a scalable solution for subsurface investigations. While the current focus is on archaeological shipwrecks, the approach is adaptable to broader applications ranging from small-scale cultural heritage studies to large-scale geological exploration. This versatility makes it a powerful tool for advancing geomagnetic prospection across disciplines.