Title: Deep learning to estimate permeability using geophysical data

Abstract

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. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data.more » The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. 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 once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10⁵) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. 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 permeability field.« less

Authors:

Mudunuru, Maruti K.  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-2158-7723"

Cromwell, Erol L. D.  ^[1];

• Search DOE PAGES for author "Cromwell, Erol L. D."
• Search DOE PAGES for ORCID "0000-0002-9212-4371"

Wang, Hongsheng ^[2]; Chen, Xingyuan ^[1]

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+ Show Author Affiliations

1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Publication Date:

Fri Jul 15 00:00:00 EDT 2022

Research Org.:

Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Biological and Environmental Research (BER). Earth and Environmental Systems Science Division; USDOE

OSTI Identifier:

1883390

Alternate Identifier(s):

OSTI ID: 1960964

Report Number(s):

PNNL-SA-175440
Journal ID: ISSN 0309-1708

Grant/Contract Number:  

AC05-76RL01830; AC02-05CH11231

Resource Type:

Accepted Manuscript

Journal Name:

Advances in Water Resources

Additional Journal Information:

Journal Volume: 167; Journal ID: ISSN 0309-1708

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

58 GEOSCIENCES; Artificial neural networks; Ensemble methods; Deep learning; Hydrogeophysics; Electrical resistivity tomography; Permeability; Multi-physics; Dimensionality reduction; Deep neural networks; Scalable deep learning