Improving airborne time-domain electromagnetic imaging & characterisation of salt water intrusion

We all have a shared interest in having a solid knowledge of the Earth's interior. A comprehensive understanding of the subsurface structures and processes serves scientific curiosity, next to commercial and public interests. In geophysics, the laws of physics are used to mathematically create models of the earth from measured data.

In this dissertation, we focus on airborne electromagnetic data. Using the principle of electromagnetic induction, we sense the electrical conductivity distribution of the subsurface. Mounting such instruments on airborne vehicles allows efficient large-scale mappings, for example, to image the fresh saltwater interface in the Belgian coastal plain. Knowing the distribution between fresh and saline groundwater is imperative for a sustainable and integrated management of water resources in coastal areas. However, the state-of-the-art data interpretation techniques have some limitations. Firstly, they rely on a one-dimensional assumption, where the electrical conductivity distribution can locally only vary with depth. That assumption reduces the computational burden related to large-scale mappings, but the effect of this approximation on the interpretation has been under-investigated so far. Secondly, the interpretation is often overly smooth, while the fresh-to-saltwater transition is often relatively sharp, hindering an accurate estimation of the iso-salinity interface. In this doctoral thesis, we develop tools and methods that facilitate more reliable airborne electromagnetic interpretations with applications to groundwater salinity mapping. 

Firstly, we propose an appraisal tool that indicates zones in the inversion model that potentially suffer from relying on that one-dimensional assumption. Those zones are thus potentially not in agreement with the multidimensional character of the observed data and should not be interpreted quantitatively. If required by the specific application, a re-interpretation with a full 3D model  should be performed (only locally). 

Secondly, those full 3D inversions require tremendous computational resources, only readily available to some. To overcome those time-consuming simulations, we have constructed a surrogate model, more precisely, a data-driven statistical model, which can replace the 3D simulations. It is trained on 3D simulation data and predicts the approximate output much faster. Given the computational cost related to the simulations, there are limitations in the number of training samples that can be generated. Therefore, the research is limited to two-layered models. The results are encouraging even with few training samples, but obtaining a high accuracy is difficult with relatively simple data fit models.

Thirdly, we propose an alternative regularization term. Regularization methods ease the data-interpretation process (or the inverse problem) by introducing some a priori characteristics for the solution, such as smoothness or sharpness. We propose a multidimensional scale-dependent wavelet-based L1-regularization term to cure the non-uniqueness of the inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used. Finally, we show preliminary results on choosing the optimal wavelet basis function based on high-resolution ground-based geophysical data.