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Deep Learning to Estimate Permeability using Geophysical Data
Geophysics · Submitted 8 Oct 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. | background 1.00 | 0.06 | 0.03 | asserted 1.00 |
| s1 | Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. | background 1.00 | 0.06 | 0.02 | asserted 1.00 |
| s2 | Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. | gap 0.64 | 0.07 | 0.02 | asserted 1.00 |
| s3 | Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. | background 0.95 | 0.05 | 0.03 | asserted 0.99 |
| s4 | This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. | contribution 1.00 | 0.86 | 0.11 | asserted 0.99 |
| s5 | To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. | method 0.95 | 0.93 | 0.03 | asserted 0.99 |
| s6 | Subsurface process models based on hydrogeophysics are used to generate this synthetic data for deep learning analyses. | method 1.00 | 0.67 | 0.02 | asserted 1.00 |
| s7 | Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. | result 0.99 | 0.93 | 0.28 | asserted 1.00 |
| s8 | 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. | result 1.00 | 0.95 | 0.14 | asserted 1.00 |
| s9 | The R2-score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. | result 1.00 | 0.94 | 0.13 | asserted 1.00 |
| s10 | 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. | result 0.99 | 0.88 | 0.13 | asserted 1.00 |
| s11 | Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. | background 0.59 | 0.10 | 0.03 | hedged possibility 0.82 |
| s12 | 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. | interpretation 0.95 | 0.71 | 0.40 | asserted 0.91 |
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The paper
Original 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. 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.
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Mixup-based data augmentation [ref] is a simple strategy, which effectively produces weakly labeled data from high-quality samples to improve the predictive capability of DL models.
mixup: Beyond Empirical Risk Minimization · INTRODUCTION · 0.96
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Mixup-based data augmentation [ref] is a simple strategy, which effectively produces weakly labeled data from high-quality samples to improve the predictive capability of DL models.
On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks · INTRODUCTION · 0.96
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Mixup-based data augmentation [ref] is a simple strategy, which effectively produces weakly labeled data from high-quality samples to improve the predictive capability of DL models.
How Does Mixup Help With Robustness and Generalization? · INTRODUCTION · 0.96
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