Constructing piecewise-constant conductivity models for the McArthur River, Canada, uranium mine audio-magnetotelluric data-set

   The McArthur River uranium mine located in the Athabasca Basin, Saskatchewan, Canada, is one of the largest high-grade uranium mines in the world. The EXTECH-IV project, managed by the federal and provincial governments and by industrial partners, investigated the unconformity-type uranium deposits in the Athabasca Basin, and methods to find them. The audio-magnetotelluric (AMT) data-set was one of the geophysical data-sets acquired in this region during this project. This data-set has subsequently been inverted using a range of 2D and 3D minimum-structure inversion codes — sum-of-squares measures — to model the basement graphitic fault zone associated with the uranium deposit. The constructed conductivity models are in good agreement with each other and show the approximate location and shape of the graphitic fault zone, the "P2" fault, however, they are smeared-out and fuzzy: there is a smooth transition between the conductive anomaly and the background. Hence, we implemented non-L₂ measures, in particular the L₁ and L₀, and the fuzzy c-mean (FCM) clustering approach to invert this data-set for piecewise-constant models with sharp and distinct interfaces. We also compared the capabilities of these three approaches in constructing piecewise-constant models, the sensitivity of the inversion results to a priori information, and the computational cost of the inversion process. These methods that are extensions of the minimum-structure approach retain the capability, robustness, and efficiency of this approach.

   To invert the data, we discretized the subsurface using an unstructured tetrahedral mesh and included the topography of the study area into the model, unlike the previous studies for which the subsurface was parameterized using rectilinear meshes and the observation points were placed in a flat surface. Instead of rotating the data to align with the trend of the graphitic fault zone, which is in the NE-SW direction, the strike orientation information of the P2 fault was included into the inversion framework. The diagonal and off-diagonal elements of the impedance tensors for a relatively high range of eight frequencies were inverted. 

   The steeply dipping conductive graphitic fault zone in the basement constructed using non-L₂ measures and the FCM clustering approach is more piecewise constant and has sharper interfaces compared to the L₂ inversion results. The model constructed model using the FCM clustering approach is more localized and distinct compared to the non-L₂ inversion results. However, the inversion results using this approach are more sensitive to a priori information provided by the user such as the number of clusters and the cluster center values. Also, this approach introduces more non-linearity into the inverse problem compared to the non-L₂ measures, which can make the inversion process computationally expensive. The dependency of the L₁ measure on a priori information is less than the L₀ measure whereas the obtained models are very similar to each other. Hence, adopting and using one of these three approaches depends on the problem and user preferences. Each of these methods can construct models with sharp, localized, distinct interfaces, which can be more appropriate in many situations than models constructed using the L₂ norm.

Keywords: Audio-magnetotelluric(AMT), inversion, McArthur uranium mine, piecewise-constant models