Crustal permeability generated through microearthquakes is constrained by seismic moment

We link changes in crustal permeability to informative features of microearthquakes (MEQs) using two field hydraulic stimulation experiments where both MEQs and permeability evolution are recorded simultaneously. The Bidirectional Long Short-Term Memory (Bi-LSTM) model effectively predicts permeability evolution and ultimate permeability increase. Our findings confirm the form of key features linking the MEQs to permeability, offering mechanistically consistent interpretations of this association. Transfer learning correctly predicts permeability evolution of one experiment from a model trained on an alternate dataset and locale, which further reinforces the innate interdependency of permeability-to-seismicity. Models representing permeability evolution on reactivated fractures in both shear and tension suggest scaling relationships in which changes in permeability (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta k$$\end{document}Δk) are linearly related to the seismic moment (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M$$\end{document}M) of individual MEQs as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta k\propto M$$\end{document}Δk∝M. This scaling relation rationalizes our observation of the permeability-to-seismicity linkage, contributes to its predictive robustness and accentuates its potential in characterizing crustal permeability evolution using MEQs.


7.
is the wellbore radius,   is the radius to the external flow boundary and ℎ is the length of the borehole/cylindrical-zone. 9. Figure S9: Magnitude frequency distribution and Gutenberg-Richter fit with uncertainty analysis for EGS Collab (a) and Utah FORGE (b) datasets, respectively.10.Table S1: Comparison of various standalone machine learning and deep learning models trained on Utah FORGE.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.11.Table S2: Comparison of various standalone machine learning and deep learning models trained on EGS Collab.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.12. Table S3: Zero-shot performance for models trained on EGS Collab and tested on Utah FORGE.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.13.Table S4: Zero-shot performance for models trained on Utah FORGE and tested on EGS Collab.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.14.where r is the distance from the borehole wall, h is the length of the borehole section, k is permeability and  is dynamic viscosity of the fluid.After variable separation and integration, we obtain: with average permeability could be expressed as: where   is the downhole injection pressure.  is the far-field pressure at the external radial boundary -defined by the location of the most distant MEQs.The injectivity ( ) is the ratio between injection rate and pressure differential (Δ =   −   ) as  = /Δ, Eq.(S-3) and may be further expressed as: Similarly, for the spherical steady flow shown in Fig. S8(b), the appropriate expression is: After variable separation and integration, Eq.(S-4) this becomes: Thus the average permeability for spherical flow may be expressed as: And substituting injectivity () into Eq.(S-6)yields:  The -value is calculated by the maximum likelihood method (Aki, 1965).We also completed uncertainty analysis for the  -value by calculating the standard error associated with the maximum likelihood method (Shi & Bolt, 1982).
We obtained   = −4.32 and −1.52 for EGS Collab and Utah FORGE earthquake catalogs, respectively.Both values are quite small, consistent with the capability of the seismic networks to capture even small MEQs.Also, based on the linear proportionality relationship between permeability change and seismic moment (see Discussion and Eqs.17-18), the effect of these extremely small magnitude events on permeability changes will be small -and missing these events is unlikely to impact our analysis or conclusions.The -value for the EGS Collab and Utah FORGE are  = 0.90 ± 0.03 ,  = 1.06 ± 0.02 respectively.Based on the Gutenberg-Richter relation, a -value near 1.0 implies a typical distribution of earthquakes, with smaller events being more common than larger ones.

Table S11: Text
We are dealing with a stateful problem, which requires access to autoregressive connections.We selected two widely used RNNs, the Gated Recurrent Unit (GRU) and the Long-term Memory (LSTM) model.We observed that LSTM outperforms GRU in the majority of scenarios.Both unidirectional LSTM and bi-directional LSTM can efficiently model sequential data; however, a bimodel is advantageous when the output depends on the entire predictor sequence as it captures both backward and forward dependencies through time (Goodfellow et al., 2016, Stogin et al., 2020, Mali et al., 2023).In addition, the uni-directional model takes significantly more time to converge and is less stable compared to bi-directional.We compare an average number of epochs required by both models to converge on the EGS collab dataset (Table S11); as evident from the result, the bi-directional model converges much faster and is more stable with smaller standard deviation of  2 than the uni-directional model.

Figure S7 :
Comparison between raw permeability data (ground truth) and predictions on test set (S3) for Utah FORGE for different  values.With increasing  , the prediction curve on the test set monotonically increases. = 150 is used in this study shown in Fig.6B of manuscript.8. Figure S8: Conceptual flow diagram for radial (a) and spherical (b) steady flow.Here

Figure S1 :
Figure S1: Boxplots of seismicity rate and cumulative log seismic moment features of EGS Collab and Utah FORGE datasets.The first column shows the different seismicity rate (A1), and cumulative log seismic moment (A2) distribution among EP3, EP4, and EP5 of EGS collab.The second column shows the different seismicity rate (B1), and cumulative log seismic moment (B2) among Stage 1, Stage 2, and Stage 3 of Utah FORGE dataset.

Figure S4 :
Figure S4: Seismicity rate changes over time under different Δ  for EGS Collab dataset.With increases of Δ  , the seismicity rate changes become much smoother for three episodes.

Figure S5 :
Figure S5: Seismicity rate changes over time under different Δ  for Utah FORGE dataset.With increases of Δ  , the seismicity rate changes become much smoother for three stages.

Figure S6 :
Figure S6: Comparison between raw permeability data (ground truth) and predictions on test set (Ep5) for EGS-Collab for different  values.With increasing , the prediction curve on the test set monotonically increases. = 1000 is used in this study shown in Fig. 6A of the manuscript.

Figure S7 :
Figure S7: Comparison between raw permeability data (ground truth) and predictions on test set (S3) for Utah FORGE for different  values.With increasing , the prediction curve on the test set monotonically increases. = 150 is used in this study shown in Fig. 6B of the manuscript.

Figure S8 :
Figure S8: Conceptual flow diagram of radial (a) and spherical (b) steady flow.Here   is the wellbore radius,   is the radius to the external flow boundary and ℎ is the length of the borehole/cylindrical-zone.

Figure S8 text
Figure S8 text Fig. S8(a) illustrates the conceptual steady radial flow regime for constant injection rate,  at differential pressure,  as:  2ℎ =

Figure S9 :
Figure S9: Magnitude frequency distribution and Gutenberg-Richter fit with uncertainty analysis for EGS Collab (a) and Utah FORGE (b) datasets, respectively.

Figure S9 text
Figure S9 text High resolution seismic monitoring networks were deployed for the EGS Collab and Utah FORGE stimulations.For detailed information regarding the monitoring system, processing, quality control and quality evaluation of the seismic catalogs and statistical parameters, please refer to Schoenball et al. (2020) and Rutledge et al. (2021).We analysed the magnitude of completeness (  ) and values for the EGS Collab and Utah FORGE MEQ catalogs, as shown in Fig.S9.The maximum curvature method(Wiemer & Wyss, 2002) was used to calculate   , which is the maximum value of the first derivative of the frequency magnitude curve.The -value is calculated by the maximum likelihood method(Aki, 1965).We also completed uncertainty analysis for the  -value by calculating the standard error associated with the maximum likelihood method(Shi & Bolt, 1982).

Table S5 :
Transfer learning performance for model trained on Utah FORGE and knowledge is transferred on EGS Collab.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.15.

Table S6 :
Transfer learning performance for models trained on EGS Collab and knowledge is transferred on Utah FORGE.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.16.

Table S7 :
Model performance comparison between models using proposed physics inspired loss and standard MSE loss ( = 0) for standalone models trained on Utah FORGE dataset.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.17.

Table S8 :
Model performance comparison between models using proposed physics inspired loss with standard MSE loss  = 0) for standalone models trained on EGS Collab dataset.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.18.

Table S9 :
Comparison of Bi-LSTM models using different values of trained on EGS Collab.All models were trained across 10 trials, with average  2 scores and variances reported across data splits.19.

Table S10 :
Comparison of Bi-LSTM models using different values of Δ  trained on Utah FORGE.All models were trained across 10 trials, with average  2 scores and variances reported across data splits.20.

Table S11 :
Comparison of LSTM and Bi-LSTM models trained on EGS collab.All models were trained across 10 trials, with average  2 scores and variances reported on test set.

Table S1 :
Comparison of various standalone machine learning and deep learning models trained on Utah FORGE.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.

Table S2 :
Comparison of various standalone machine learning and deep learning models trained on EGS Collab.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.

Table S3 :
Zero-shot performance for models trained on EGS Collab and tested on Utah FORGE.

Table S4 :
Zero-shot performance for models trained on Utah FORGE and tested on EGS Collab.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.

Table S3 -S4 text: Model zero-shot performance
We test the zero-shot capability of our model(Chang et al., 2008)across the two datasets.In this setup, the trained model is tested on a new distribution to see how efficiently it can generalize to the unseen distribution, thus testing its true generalization and continual learning capabilities.Assuming an independent and identical distribution (i.i.d) across data the model is trained using a monotonically decreasing activation function that is Lipschitz continuous in Euclidean space.We show that our model successfully captures this phenomenon and achieves a respectable  2 score; specifically in Supp.TableS3, we report the performance of the model trained on EGS Collab and tested on all 3 Stages of Utah Forge, achieving  2 scores of 0.95, 0.80, and 0.93 respectively.Similarly, Supp.TableS4reports the zero-shot performance of the model trained on Utah FORGE and tested on all 3 episodes of EGS Collab.

Table S5 :
Transfer learning performance for model trained on Utah FORGE and knowledge is transferred on EGS Collab.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.Models (Utah FORGE EGS Collab) Train (EP3)  2 Validation (EP4)  2 Test (EP5)  2

Table S6 :
Transfer learning performance for models trained on EGS Collab and knowledge is transferred on Utah FORGE.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.

Table S7 :
Model performance comparison between models using proposed physics inspired loss and standard MSE loss ( = 0) for standalone models trained on Utah FORGE dataset.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.

Table S8 :
Model performance comparison between models using proposed physics inspired loss with standard MSE loss  = 0) for standalone models trained on EGS Collab dataset.All deep learning models were trained across 10 trials, with average  2 scores and variances reported across data splits.

Table S9
Comparison of Bi-LSTM models using different values of Δ  trained on EGS Collab.All models are trained across 10 trials, with average  2 scores and variances reported across data splits.

Table S10
Comparison of Bi-LSTM models using different values of Δ  trained on Utah FORGE.All models are trained across 10 trials, with average  2 scores and variances reported across data splits.