Deep generative inversion of ERT data for electrical resistivity

Electrical resistivity tomography (ERT) is a geophysical method used to imaging the subsurface and widely used in hydrogeological studies due to its sensitivity to electrical resistivity, which is directly related to rock type, porosity, ionic strength of the pore fluids, and surface conductivity of geologic materials. The prediction of subsurface properties from the recorded data at the surface requires solving a challenging geophysical inversion problem. For near-surface characterization studies, this is often accomplished with deterministic electrical resistivity inversion methods. Deterministic geophysical inversion approaches linearize the problem around an initial solution, resulting in a single smooth representation of the subsurface. Deterministic models are unable to capture the natural variability of the subsurface. Moreover, a single solution does not yield enough information for accurate uncertainty assessment. Contrary to deterministic approaches, stochastic inversion methods predict multiple model realizations that fit similarly the recorded geophysical data and allow assessing uncertainties. Lately, deep learning algorithms based on deep generative models have been used to re-parametrize model and data spaces into low-dimensional domains and solve geophysical inverse problems in a more efficient way.

We propose an ERT inversion methodology in which a deep convolutional variational autoencoder (VAE) network is trained with a set of electrical resistivity models generated using geostatistical simulation. After training the VAE, the latent space is perturbed and updated iteratively with adaptive stochastic sampling to generate electrical resistivity models by inputting the optimized latent vectors to the decoder part of the VAE. From the set of decoded models, we use a finite volume approximation of Poisson’s equation to compute synthetic apparent resistivity models. The misfit between predicted and observed apparent resistivity data is used to drive the convergence of the iterative procedure and condition the optimization of new models in the subsequent iterations.

The proposed methodology is illustrated by applying it to both a two-dimensional synthetic case and to a two-dimensional profile obtained from an ERT survey carried out in an area located in the Southern region of Portugal. In both application examples, the predicted models generate synthetic geophysical data that match the observed one. We show the ability of the model to assess spatial uncertainty and compare the results obtained in the real data set against commercial deterministic ERT inversion methodology.

The work presented herein is supported by the PRIMA programme under grant agreement No. 1923, project Innovative and Sustainable Groundwater Management in the Mediterranean (InTheMED). The PRIMA programme is supported by the European Union.