10:00 AM - 10:15 AM
[SCG40-25] Inversion for the spatial distribution of frictional parameters on the Long-term SSE fault with Physics-Informed Neural Networks
Keywords:Physics-Informed Neural Networks (PINNs), Slow Slip Events (SSEs), earthquake cycle simulation, rate and stade dependent friciton law, GNSS
Various modes of fault slip, including earthquake and slow slip events (SSEs), have been observed in many subduction zones. This diversity might reflect the heterogeneous frictional properties on the subducting plate surface. Assessing this possibility thus requires methods to constrain these frictional properties. Data assimilation, a technique to integrate a physics-based model and observations, was employed to estimate frictional properties from GNSS observations of afterslip (Kano et al., 2015; 2020) and a Long-term SSE (L-SSE) (Hirahara and Nishikiori, 2019). A physics-based model, where fault slip is governed by a laboratory-derived rate and state friction law (RSF) (Dieterich, 1979) was employed. The estimation of frictional parameters on an L-SSE fault assumed uniform frictional properties on a prescribed fault geometry (H&N, 2019). The extension of this approach to assess spatial variations of friction is a challenge due to the difficulty of optimizing large dimensional model.
In this study, we use a machine-learning based approach for the estimation of the spatial distribution of friction on an L-SSE fault. We employ Physics-Informed Neural Networks (PINNs), which solve the PDEs representing the physics-based model and determine the controlling parameters from the data (Raissi et al., 2019). The method provides a mesh-free and simple framework to solve PDEs and invert for the model parameters. PINNs have been applied to various problems including travel time calculation (Smith et al., 2021), full-waveform inversion (Rasht-Behesht et al., 2022), seismic tomography (Waheed et al., 2021), and the modeling of crustal deformation (Okazaki et al., 2022). Regarding fault slip simulations, Fukushima et al. (2023) applied PINNs to model SSEs. They assumed a single-degree-of-freedom spring slider system and conducted the fault slip simulations (forward problem) and the estimation of frictional parameters from fault slip observations (inverse problem).
In this study, we extend the PINN-based method to estimate the frictional parameters in a 3D fault slip model. We adopt the Bungo L-SSE model of Hirahara and Nishikiori (2019). This model assumes the rectangular dipping fault with a single L-SSE patch, and the frictional parameters are uniform inside and outside the patch, respectively. Simulation variables are fault slip velocities v and state variables θ, and the governing equations consist of the quasi-dynamic equations of motion (Rice, 1993) and RSF with aging law (Ruina 1983).
For the estimation of the frictional parameters distribution, we construct two neural networks. One neural network represents the solutions of v(t, x, y) and θ(t, x, y), and the other represents the frictional parameter distribution a(x, y), a-b(x, y), and L(x, y). We define the loss function as Ltotal = Lini + Lode + Ldata, where each term represents the residuals of the initial condition, governing equations, and observation data, respectively. We optimize neural network parameters to minimize this loss function, finally obtaining the solutions and the frictional parameter distribution which best satisfy both the physics and the observations.
We conduct numerical experiments to estimate the spatial distribution of frictional parameters. We generate two types of synthetic data; fault slip velocities and surface displacement rates, which are calculated using slip response functions (Okada, 1992). The spatial distribution of frictional parameters is estimated well from the inversion of the fault slip velocity data. In the case of the surface displacement rates data, the method also succeeds in recovering the geometry and friction properties of the velocity-weakening region. These results show that the PINNs-based approach is a promising approach for estimating the spatial distribution of friction from GNSS observations.
In this study, we use a machine-learning based approach for the estimation of the spatial distribution of friction on an L-SSE fault. We employ Physics-Informed Neural Networks (PINNs), which solve the PDEs representing the physics-based model and determine the controlling parameters from the data (Raissi et al., 2019). The method provides a mesh-free and simple framework to solve PDEs and invert for the model parameters. PINNs have been applied to various problems including travel time calculation (Smith et al., 2021), full-waveform inversion (Rasht-Behesht et al., 2022), seismic tomography (Waheed et al., 2021), and the modeling of crustal deformation (Okazaki et al., 2022). Regarding fault slip simulations, Fukushima et al. (2023) applied PINNs to model SSEs. They assumed a single-degree-of-freedom spring slider system and conducted the fault slip simulations (forward problem) and the estimation of frictional parameters from fault slip observations (inverse problem).
In this study, we extend the PINN-based method to estimate the frictional parameters in a 3D fault slip model. We adopt the Bungo L-SSE model of Hirahara and Nishikiori (2019). This model assumes the rectangular dipping fault with a single L-SSE patch, and the frictional parameters are uniform inside and outside the patch, respectively. Simulation variables are fault slip velocities v and state variables θ, and the governing equations consist of the quasi-dynamic equations of motion (Rice, 1993) and RSF with aging law (Ruina 1983).
For the estimation of the frictional parameters distribution, we construct two neural networks. One neural network represents the solutions of v(t, x, y) and θ(t, x, y), and the other represents the frictional parameter distribution a(x, y), a-b(x, y), and L(x, y). We define the loss function as Ltotal = Lini + Lode + Ldata, where each term represents the residuals of the initial condition, governing equations, and observation data, respectively. We optimize neural network parameters to minimize this loss function, finally obtaining the solutions and the frictional parameter distribution which best satisfy both the physics and the observations.
We conduct numerical experiments to estimate the spatial distribution of frictional parameters. We generate two types of synthetic data; fault slip velocities and surface displacement rates, which are calculated using slip response functions (Okada, 1992). The spatial distribution of frictional parameters is estimated well from the inversion of the fault slip velocity data. In the case of the surface displacement rates data, the method also succeeds in recovering the geometry and friction properties of the velocity-weakening region. These results show that the PINNs-based approach is a promising approach for estimating the spatial distribution of friction from GNSS observations.