A deep learning-based surrogate model for seismic data assimilation in fault activation modeling

TL;DR

This work tackles uncertainty quantification in fault activation under subsurface resource exploitation by introducing SurMoDeL, a deep-learning surrogate that replaces expensive forward geomechanical simulations. It couples a data-driven surrogate with physics-informed enhancements: (i) SurMoDeL II adds a fault-opening indicator to the input, and (ii) a two-network variant SurMoDeL 0/1 uses a classifier to split training data by opening behavior and combines predictions probabilistically. The approach achieves accurate predictions of fault metrics $A_a$ and $\delta_S$ with small training sets, enables rapid Monte Carlo sampling, and supports Bayesian inversion using seismic moment data $M_0(t)$ via Metropolis-Hastings MCMC. A global Sobol sensitivity analysis identifies the stress regime parameter $M_2$ as the dominant driver of fault activation and sliding under progressive loading. Overall, SurMoDeL demonstrates substantial potential for fast, physically informed uncertainty quantification in fault activation modeling and seismic-data assimilation, with promising extensions to open-mode dynamics and real data.

Abstract

Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of governing parameters, and data errors challenge the reliability of predictions. In the absence of direct measurements, inverse modeling and stochastic data assimilation methods can offer reliable solutions, but in complex and large-scale settings, the computational expense can become prohibitive. To address these challenges, this paper presents a deep learning-based surrogate model (SurMoDeL) designed for seismic data assimilation in fault activation modeling. The surrogate model leverages neural networks to provide simplified yet accurate representations of complex geophysical systems, enabling faster simulations and analyses essential for uncertainty quantification. The work proposes two different methods to integrate an understanding of fault behavior into the model, thereby enhancing the accuracy of its predictions. The application of the proxy model to integrate seismic data through effective data assimilation techniques efficiently constrains the uncertain parameters, thus bridging the gap between theoretical models and real-world observations.

Figures (13)

• Figure 1: Sketch of a SurMoDeL NN with $L=4$ hidden layers, $n_0=4$, $n_5=2$, and $n_l=6$ for $l=1,\dots,4$.
• Figure 2: (a-b) Model domain and computational grid used in the full forward simulation. The pumping well produces water from a confined aquifer between -1.100m and -1.200 m. (c-d) Pore pressure distribution within the vertical fault plane at $t_5$ and $t_{10}$. (e-f) Distribution of sliding (active) and non-sliding (inactive) triangular elements generated by the triangulation over $\Gamma_f$ with the associated sliding values, $\left\| \mathbf{g}_T \right\|_2$, within the vertical fault at $t_{10}$. These outcomes are obtained by running a full forward simulation with the parameter set $\mathbf{p}=\{0,20,0.4286\}$Zoc_etal19.
• Figure 3: Evolution of the relative loss function during the training of the SurMoDeL.
• Figure 4: SurMoDeL training results. (a) Cumulative distribution functions of $A_a$ (top row) and $\delta_S$ (bottom row) at different time steps ($t_1$, $t_5$, and $t_9$). The blue lines represent results from the geomechanical model using the $N_p=125$ parameter combinations, while the orange lines depict the outcomes from the SurMoDeL using the same inputs. The green lines show the cumulative distributions from $10^5$ SurMoDeL evaluations on MC realizations. (b) Median values (solid lines) and the $2.5\%$ and $97.5\%$ quantiles (dashed lines) for $A_a$ (top) and $\delta_S$ (bottom) obtained using the full forward model (grey) and SurMoDeL (red).
• Figure 5: SurMoDeL validation results on 125 random points from the parameter space $\Psi$. (a) Cumulative distribution functions of $A_a$ (top row) and $\delta_S$ (bottom row) at different time steps ($t_1$, $t_5$, and $t_9$). The blue lines represent results from the geomechanical model using the $N_{MC}=125$ MC validation samples, while the orange lines depict the outcomes from the SurMoDeL using the same inputs. The green lines show the cumulative distributions from $10^5$ SurMoDeL evaluations on MC realizations. The red line shows for the sake of comparison the SurMoDeL outcome on the training points. (b) Median values (solid lines) and the $2.5\%$ and $97.5\%$ quantiles (dashed lines) for $A_a$ (top) and $\delta_S$ (bottom) obtained using the full forward model (grey) and SurMoDeL (red).