June 2022: Wouter Deleersnyder

The salinization map of the region of Flanders, Belgium shows the depth of the interface between fresh and salt groundwater in the coastal and polder area. It serves as an exploratory tool to examine the potential of groundwater projects that improve freshwater availability in the shallow subsurface. Flanders environment agency published an updated map in 2019, based on airborne time-domain electromagnetic induction data. The result of the inversion is, however, overly smooth, which potentially conceals interesting features.

Via an inverse problem, the electromagnetic induction data can be mapped onto a conductivity profile, which serves as a proxy for salinity via petrophysical laws. The inverse problem is ill-posed and regularization improves the stability of the inversion. Based on Occam’s razor principle, a smoothing constraint is typically used with a very large number of thin layers. However, the salinity profiles in the Belgian coastal plains are sometimes sharp, impeding the correct estimation of the fresh-saltwater interface. In practice, the real underground might be either blocky or smooth, or somewhere in between. Standard constraints are thus not always appropriate.

With our novel wavelet-based inversion scheme, the original time-domain AEM data can be re-interpreted in a flexible fashion, meaning that we can easily generate an ensemble of inversion models with different types of Occam's razor minimum-structure. The flexibility is due to the wavelet basis. In simple terms, a wavelet function can be seen as a building block and a simple model is one that can be built with few building blocks of various sizes. Our proposed inversion scheme adds a regularization term that limits the number of building blocks in the wavelet-domain to make sure only the necessary complexity is retrieved. The scale-dependency makes the use of small blocks more expensive, as it corresponds to adding detail. The scheme is tuned by only one additional parameter (which determines the wavelet basis function) and can recover blocky, intermediate and smooth structures. It is also capable to recover high amplitude anomalies in combination with globally smooth profiles, a common problem for smooth inversion, and an essential feature to accurately predict the salinity.