Deep Learning to Estimate Permeability using Geophysical Data
This work addresses the challenge of subsurface imaging and real-time monitoring in hydrogeophysics, offering a faster and more accurate method for permeability estimation, though it is incremental as it applies deep learning to an existing domain problem.
The paper tackles the problem of estimating 3D permeability fields from time-lapse electrical resistivity tomography data, which traditional methods handle poorly due to ill-posedness and dimensionality issues. It presents a deep learning framework that achieves an average mean squared error below 0.5, an R2-score above 0.75, and computational speed-ups of at least 10,000 times compared to forward models.
Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Subsurface process models based on hydrogeophysics are used to generate this synthetic data for deep learning analyses. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R2-score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(104) times faster than running a forward model. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings (O(105) - O(107)) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of the permeability field.