Deep Direct Current Resistivity Inversion

Climate change threats groundwater resources, requiring sustainable management of this critical asset. Widely applied in hydrogeology, direct current resistivity (DCR) methods have been a preferable tool for imaging groundwater resources due to its potential to efficiently image a relatively large area in a relatively short period. DCR methods use electrodes to inject electrical currents into the subsurface ad measure the resulting potential difference (i.e., voltage).

The quantitative interpretation of these data (i.e., the spatial prediction of the geological subsurface properties) requires solving a challenging geophysical inversion problem. Deterministic DCR inversion methods are common approaches to reach this objective but might be computationally expensive, requiring a large degree of expertise and predicting a single model unable to capture the small-scale details of subsurface geology. The main goal of this work is to overcome these limitations through the development and implementation of a deep DCR inversion workflow.

The proposed methodology follows three main steps: data acquisition, deep neural network (DNN) training and DCR data inversion. For the second step, it is generated a training dataset of electrical resistivity models by geostatistical simulation to represent a variety of possible subsurface scenarios. These models will be the input to train a variational autoencoder (VAE; Kingma & Welling, 2013; Lopez-Alvis et al., 2020). After training, the VAE outputs electrical resistivity simulated models given measured DCR data. The predicted models are then forward modelled (Cockett et al., 2015) to calculate predicted data, which are compared with the recorded data. The misfit between the observed and simulated data is used to iteratively update the DNN weights and parameters.

The proposed method is illustrated with its application to a set of DCR data acquired in the southern region of Portugal comprising an area highly affected by droughts and industrial pressure.

Cockett, R., Kang, S., Heagy, L. J., Pidlisecky, A., & Oldenburg, D. W. (2015). SimPEG: An open-source framework for simulation and gradient-based parameter estimation in geophysical applications. Computers and Geosciences, 85, 142–154. https://doi.org/10.1016/j.cageo.2015.09.015

Kingma, D. P., & Welling, M. (2013). Auto-Encoding Variational Bayes. https://doi.org/10.48550/arXiv.1312.6114

Lopez-Alvis, J., Laloy, E., Nguyen, F., & Hermans, T. (2020). Deep generative models in inversion: a review and development of a new approach based on a variational autoencoder. https://doi.org/10.1016/j.cageo.2021.104762