A deterministic ensemble inversion framework to assess the uncertainty of electrical resistivity tomography combined with cone penetration tests

The hydrogeological setting of the Belgian coastal area near De Panne is characterized by the presence of an upper saline plume within the subterranean estuary. This salinity distribution can be imaged using Electrical Resistivity Tomography (ERT), where the saline plume manifests as a zone of low electrical resistivity. However, a similar low-resistivity response may also arise from specific geological formations, such as clay layers. Therefore, lithological investigations are required to distinguish between low resistivity caused by saline groundwater and by geological heterogeneity, which strongly influences groundwater distribution.

Cone penetration tests (CPT), a direct-push method, are employed to characterize subsurface soil properties. In addition, CPT-based resistivity measurements (CPT-R) are used to discriminate between low-resistivity zones associated with lithology and those related to groundwater salinity. To improve ERT inversion results, CPT-R data are incorporated in several ways: as geostatistical constraints (using correlation lengths derived from geostatistical analysis), through joint inversion, and/or as reference models. This study therefore investigates how these different inversion setups influence the ERT inversion results, with a particular focus on the associated uncertainty.

An ensemble deterministic ERT inversion approach is adopted to assess the inversion uncertainty. Key inversion parameters are randomly varied across 100 realizations, which are subsequently combined into a single ensemble. In total, 12 ensembles are generated, representing different inversion strategies and each using the same set of randomly sampled parameters. These parameters include the regularization strategy (constant or optimized), the type of constraint (smoothness or geostatistical), the inversion approach (ERT-only or joint inversion), and the reference model (none, homogeneous, or heterogeneous). Heterogeneous reference models are constructed using sequential Gaussian simulations based on CPT-R data.

By comparing multiple inversion strategies and integrating CPT-R data within an ensemble framework, the uncertainty associated with resistivity models is systematically assessed. This study highlights how choices in ERT inversion setup directly influence model uncertainty, particularly when heterogeneity is neglected, leading to a strong underestimation of uncertainty.