Uncertainty estimation of conductive thin plates parameters through a Bayesian approach

The uranium deposits of the Athabasca basin (Canada) represent one of the world’s highest-grade uranium resources. They are unconformity-related type at the base of relatively flat-lying sequences, where faults acted as circulation paths for hydrothermal fluids. The fault zones often contain graphitic mineralization and hence represent a valuable exploration guide of small lateral extension but detectable by electromagnetic (EM) surveys. Time-domain EM (TEM) is the method of choice for uranium exploration in the Athabasca, and taking into account the frequencies involved we can approximate the graphitization along the fault as a conductive thin plate.

To better determine the geometry of the deposit, it might be crucial to recover the subsurface resistivity and the geometric parameters of the plate (position, dip, depth, azimuth etc.). Moreover, the assessment of the uncertainty associated to the parameters can help to evaluate the reliability of geological models and to guide the subsequent drilling activities.

A quantitative approach consists of employing Bayesian inversion algorithms, which allows to exploit the prior information available. Indeed, Bayesian inversion algorithms aim to solve the inverse problem statistically returning the posterior probability density function (ppdf). In particular, they are based on the Bayes theorem, which relates the prior information (e.g. from geological and petrophysical models) with the likelihood function to assess the posterior probability density function and thus the uncertainty. We implement the Differential Evolution Markov Chain algorithm (DEMC), a multi-chain approach that integrates the Metropolis selection rule with population evolution to sample the ppdf. The chains run in parallel and each current model is updated drawing two other chains and exploiting the models at the previous iteration. After an initial stage of burn-in, the algorithm reaches the stationary regime where the chains start sampling the ppdf resulting at the end in an ensemble of models. From these models the moments of first and second order (mean and variance) are computed obtaining the uncertainty of the inverse problem solution. As forward operator we employ the LEROI forward code developed by CSIRO (AMIRA), which computes the TEM response of one or more conductive 3D thin plates embedded in a horizontally layered earth.

In this work we propose the DEMC inversion of TEM data as a tool to assess thin plates parameters and uncertainty in the context of uranium exploration.