A Convolutional Neural Network approach to Electric Resistivity Tomography

Electric resistivity tomography (ERT) is an ill-posed inverse problem commonly solved through deterministic gradient-based methods. Markov Chain Monte Carlo algorithms can be employed to cast this problem into a solid probabilistic Bayesian framework, but they remain a formidable computational task due to the expensive forward model evaluation. Here we explore the potential of convolutional neural networks (CNN) for ERT inversion. A large dataset is used to train the network to learn the relation between the observed data and the subsurface resistivity model, whereas a Discrete Cosine Transform reparameterization allows for a compression of the parameter space, thus reducing the ill-conditioning of the inverse problem. Once trained the network can be used to predict the subsurface model from the observed data in near real-time. We also implement a Monte Carlo inversion framework that propagates onto the estimated model the uncertainties related to both noise contamination and network approximation (the so-called modeling error). To draw general conclusions about the feasibility of the proposed approach, we focus the attention on synthetic inversion experiments. Our preliminary results confirm the feasibility of the CNN-ERT inversion, opening the possibility to estimate the subsurface resistivity distribution and the associated uncertainties in real-time.