Uncertainty Quantification of the Fresh-Saltwater Interface from Time-Domain Electromagnetic Data
📝 Abstract
Geophysical methods provide a cost-effective way to characterize the subsurface for hydrogeological projects, but they rely on solving an inverse problem. Traditionally, deterministic approaches are used, which face challenges due to non-uniqueness. Stochastic methods offer uncertainty quantification but demand high computational resources. Bayesian Evidential Learning (BEL) bypasses full stochastic inversion by approximating the posterior distribution at lower cost. However, as with Monte Carlo techniques, efficiency depends on the number of inversion parameters. We show that incorporating prior knowledge into parameterization reduces unknowns and computational burden. Using time-domain electromagnetic data, we identify fresh - saltwater interfaces in the Flemish coastal aquifer. Conventional blocky or smooth deterministic inversions often misrepresent this transition zone as too sharp or too gradual. To address this, we parameterize the zone with two variables - depth and thickness - assuming a linear transition. This retains the compactness of parametric inversion while allowing sharp or gradual interfaces like voxel-based methods. To assess reliability, we invert these parameters stochastically using BEL with Thresholding (BEL1D-T). Results indicate this approach effectively captures uncertainty for synthetic and field data. The transition zone remains uncertain due to survey design and inherent non-uniqueness, yet our probabilistic method achieves this without the heavy computational cost of traditional stochastic approaches.
💡 Analysis
Geophysical methods provide a cost-effective way to characterize the subsurface for hydrogeological projects, but they rely on solving an inverse problem. Traditionally, deterministic approaches are used, which face challenges due to non-uniqueness. Stochastic methods offer uncertainty quantification but demand high computational resources. Bayesian Evidential Learning (BEL) bypasses full stochastic inversion by approximating the posterior distribution at lower cost. However, as with Monte Carlo techniques, efficiency depends on the number of inversion parameters. We show that incorporating prior knowledge into parameterization reduces unknowns and computational burden. Using time-domain electromagnetic data, we identify fresh - saltwater interfaces in the Flemish coastal aquifer. Conventional blocky or smooth deterministic inversions often misrepresent this transition zone as too sharp or too gradual. To address this, we parameterize the zone with two variables - depth and thickness - assuming a linear transition. This retains the compactness of parametric inversion while allowing sharp or gradual interfaces like voxel-based methods. To assess reliability, we invert these parameters stochastically using BEL with Thresholding (BEL1D-T). Results indicate this approach effectively captures uncertainty for synthetic and field data. The transition zone remains uncertain due to survey design and inherent non-uniqueness, yet our probabilistic method achieves this without the heavy computational cost of traditional stochastic approaches.
📄 Content
Sustainably managing groundwater resources in coastal areas requires hydrogeologists to determine the position of the fresh-saltwater interface (FSI) and monitor its temporal variations (Kim et al. 2006;Werner et al. 2013;Bear et al. 1999). Knowing the FSI in coastal aquifers is vital to control the accessibility to freshwater and the environmental well-being of coastal ecosystems (Goebel et al. 2021;Carrera et al. 2010).
Complex subsurface features and dynamic subsurface processes make it diPicult to accurately characterize the FSI, which commonly diPers from the wedge shape described in textbooks and only encountered in simpler coastal geologies (Goebel et al. 2021). The position and shape of the FSI in coastal aquifers depend on multiple factors (Kim et al. 2006), including the density diPerence between freshwater and saltwater (Nguyen et al. 2009), freshwater recharge rates, groundwater extraction (Guo and Jiao 2007), the hydrogeological evolution of aquifers related to seawater levels (Dieu et al. 2022), aquifer heterogeneity (Cong-Thi et al. 2024), and structure (Paepen et al. 2025), leading to complex shapes of the FSI (Goebel et al. 2019). The FSI can be a sharp boundary or a diPuse mixing zone where salinity changes gradually through a transition zone (e.g., Kim et al. 2006;Bear et al. 1999). Moreover, some irregular configurations and salinity reversals can be seen in complex multi-aquifer systems (Yechieli et al. 2001) or in subterrain estuaries, (e.g., Paepen et al. 2020). The transition zone between freshwater and saltwater thus becomes quickly untraceable by conventional borehole observations because of its lateral and vertical variability (Carrera et al. 2010).
Geophysical methods oPer a cost-ePective solution to study the subsurface. Multiple studies showed that the time-domain electromagnetic method (TDEM) is ePective for seawater intrusion and FSI mapping in coastal aquifers (Kafri et al. 2007;Goldman et al. 1991;Yechieli et al. 2001;Kafri andGoldman 2005, Goebel et al., 2019;Delsman et al., 2018;King et al., 2018), due to its sensitivity to conductive bodies. The large-scale mapping capability of airborne (e.g., Goebel et al. 2019) or towed systems (Auken et al. 2019) provides valuable insights into the FSI in complex coastal plains.
However, TDEM data must be further processed by solving an inverse problem to provide information on the FSI. The problem is ill-posed, and the solution is non-unique, meaning that multiple possible models can fit the observed data. Deterministic inversion typically requires additional constraints imposed via regularization methods to provide a solution. For example, blocky inversion yields models with distinct boundaries between layers. Alternatively, smoothness-constraint regularization produces inversion models with gradual transitions (Constable et al., 2015). The inversion is ften based on the discretization of the subsurface into a large number of relatively thin layers. The inverted models often then exhibit excessive sharpness or smoothness (Deleersnyder et al. 2021).
While the traditional deterministic methods produce a single solution and have proven robust, they fail to assess the uncertainty. Stochastic inversion methods provide an alternative for exploring the parameter spaces and assessing uncertainty (Sambridge and Mosegaard 2002;Trainor-Guitton and Hoversten 2011;Ball et al. 2020). However, their computational cost quickly grows with the number of parameters, while their results remain dependent on the selection of the prior distribution of model parameters (Ahmed et al. 2024;Aigner et al., 2025).
When one is interested in a specific target, such as a particular interface, it can be advantageous to integrate this interface into the parameterization itself. This can be done through a hierarchical approach, where the interface is first defined as a boundary between diPerent zones, and then variability within each zone is solved separately. De Pasquale et al. (2019) used such an approach to invert for the depth of the bedrock from ERT data, but the interface itself was restricted to a predefined grid. Alternatively, the interface itself can be parameterized so that the inversion focuses on retrieving the parameters that define this interface. For example, Goebel et al. (2021) use a parametric inversion to invert the saltwater wedge from electrical resistivity data. The interface was represented as a 5 th -order polynomial, with fixed resistivity above and below the threshold and was translated into a predefined regular grid. If these approaches can ePectively represent the interface itself, they ignore the gradual transition characteristic of the FSI. Indeed, in coastal areas, the upper or phreatic aquifer salinity levels tend to rise progressively from a shallow freshwater lens with almost constant salinity (Vandenbohede et al., 2015), originating from rainwater infiltration, to a denser saltwater layer of relatively constant salinity. Cons
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