Arsalan Ahmed

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 related to non-uniqueness of the solution. In contrast, stochastic methods offer uncertainty quantification but generally require higher computational resources. Bayesian Evidential Learning (BEL) has been proven as a reliable alternative to solve the inverse problem stochastically. BEL bypasses full stochastic inversion by learning a direct relationship between data and model parameters, allowing to approximate the posterior distribution at a lower computational cost. However, as with most Monte Carlo techniques, BEL efficiency depends on the number of inversion parameters.In this contribution, we show that incorporating prior physical knowledge about the imaged processes into the parameterization of model parameters efficiently reduces the number of unknowns, and subsequently the computational burden of BEL. Using time-domain electromagnetic data (TEM), we characterize the fresh - saltwater transition zone in the Flemish coastal aquifer. This transition can be sharp, gradual or very smooth depending on the local hydrogeological context. Conventional blocky or smooth deterministic inversions then often misrepresent this transition zone as too sharp or too gradual. To address this, we explicitly incorporate the transition zone in the parameterization, with two variables: its depth and its thickness, assuming a linear increase of conductivity within this thickness. The transition zone is underlying a freshwater zone with constant conductivity and overlying a saline zone, also with constant conductivity. This retains the compactness of blocky or layered inversion while allowing sharp or gradual interfaces like voxel-based methods.To assess the reliability and robustness of the method, 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 largely uncertain due to the limited sensitivity of the TEM set-up to the relatively shallow transition observed in the Belgian coastal area. Yet, our probabilistic method achieves this without the heavy computational cost of traditional stochastic approaches. The result also shows that the uncertainty can be efficiently reduced when prior information on the presence of confining layer (e.g., clay layer) is further introduced in the parameterization.Keywords: time-domain electromagnetics, inverse problem, uncertainty quantification, fresh-saltwater interface (FSI)

Understanding the subsurface is of prime importance for many geological and hydro-geological applications. Geophysical methods offer an economical alternative for in-vestigating the subsurface compared to costly borehole investigation methods, but geophysical results are commonly obtained through an inversion whose solution is non-unique. Deterministic inversions providing a unique solution are computationally efficient while stochastic inversions investigating the full uncertainty range are more expensive. In this research, we investigate the robustness of the recently introduced Bayesian evidential learning in one dimension (BEL1D) to stochastically invert time domain electromagnetic data (TDEM). In particular, we analyse the performance and accuracy of BEL1D when using the coarser discretization used for the computation of the forward solution using SimPEG. We demonstrate that it is possible to speed-up BEL1D by introducing a threshold rejection method on the data misfit to by-pass itera-tions. In addition, we discuss the impact of the prior model space on the results. Fi-nally, we apply the algorithm on field data collected in the Luy river catchment (Vi-etnam) to delineate saltwater intrusions. Our results show that the proper selection of timesteps and space discretization is essential to limit the computational cost while maintaining the accuracy of the posterior estimation. The selection of the prior distri-bution has a direct impact on fitting the observed data and is crucial to a realistic un-certainty quantification. The application of BEL1D for stochastic TDEM inversion is an efficient approach as it allows us to estimate the uncertainty at a limited cost.

Understanding the subsurface is of prime importance for many geological and hydrogeological applications. Geophysical methods offer an economical alternative for investigating the subsurface compared to costly borehole investigations. However, geophysical results are commonly obtained through deterministic inversion of data whose solution is non-unique. Alternatively, stochastic inversions investigate the full uncertainty range of the obtained models, yet are computationally more expensive. In this research, we investigate the robustness of the recently introduced Bayesian evidential learning in one dimension (BEL1D) for the stochastic inversion of time-domain electromagnetic data (TDEM). First, we analyse the impact of the accuracy of the numerical forward solver on the posterior distribution, and derive a compromise between accuracy and computational time. We also introduce a threshold-rejection method based on the data misfit after the first iteration, circumventing the need for further BEL1D iterations. Moreover, we analyse the impact of the prior-model space on the results. We apply the new BEL1D with a threshold approach on field data collected in the Luy River catchment (Vietnam) to delineate saltwater intrusions. Our results show that the proper selection of time and space discretization is essential for limiting the computational cost while maintaining the accuracy of the posterior estimation. The selection of the prior distribution has a direct impact on fitting the observed data and is crucial for a realistic uncertainty quantification. The application of BEL1D for stochastic TDEM inversion is an efficient approach, as it allows us to estimate the uncertainty at a limited cost.