Modelling and inferring fracture curvature from borehole GPR data: A case study from the Bedretto Laboratory, Switzerland

Fracture curvature has been observed from the millimetre to the kilometre scales. Nevertheless, characterizing curvature remains challenging due to data sparsity and geometric ambiguities. As a result, most numerical models often assume planar fractures to ease computations. To address this limitation, we present a novel approach for inferring fracture geometry from travel-time data of electromagnetic or seismic waves. Our model utilizes co-kriging interpolation of control points in a three-dimensional surface mesh to simulate fracture curvature effectively, resulting in an unstructured triangular grid. We then refine the fracture surface into a structured grid with equidistant elements so that both small-scale heterogeneities and large-scale curvature can be modelled. To constrain the fracture geometry, we perform a deterministic travel-time inversion to optimally place these control points. We validate our methodology with synthetic data and address its limitations. Finally, we infer the geometry of a large (more than 200 m) fracture observed in single-hole ground-penetrating radar field data. The fracture surface closely agrees with borehole televiewer observations and is also constrained far from the boreholes. Our modelling approach can be trivially adapted to multi-offset ground-penetrating radar or active seismic data.