⚡ electrical engineering

STFNet3D: A three-dimensional dynamic rupture inversion model based on neural networks

This paper demonstrates the feasibility of using a one-dimensional Convolutional Neural Network to accurately infer key dynamic rupture parameters from source time functions by training on a large-scale synthetic dataset, thereby providing a reproducible benchmark for machine learning applications in seismic inversion.

Original authors: Qianying Li, Zhenguo Zhang, Zhenlong Song, Xiaofei Chen

Published 2026-08-31

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CC BY 4.0

Original authors: Qianying Li, Zhenguo Zhang, Zhenlong Song, Xiaofei Chen

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Earthquakes begin with a sudden, violent slip along a crack deep within the Earth's crust. This rupture does not happen all at once; it is a dynamic process that starts at a single point and races outward, tearing the rock apart as it goes. The speed of this tear, how much the ground slips, and the friction holding the rocks together are governed by a few hidden physical rules. Scientists have long tried to work backward from the shaking they feel on the surface to figure out exactly what happened underground. They look at the seismic waves that travel through the planet, hoping to decode the story of the rupture. However, this is a difficult puzzle because the relationship between the hidden rules and the shaking we feel is incredibly complex and non-linear. Traditional methods to solve this often require massive amounts of computer time, running simulations over and over again to find a match, which slows down the ability to understand these events quickly.

A team of researchers has now tested a new approach that uses artificial intelligence to solve this puzzle much faster. They created a computer program, which they named STFNet3D, designed to look at the "source time function" of an earthquake. This source time function is essentially a graph that shows how much energy the earthquake released over time, acting like a fingerprint of the rupture process. Instead of trying to guess the hidden rules by running slow, repetitive simulations, the researchers trained a neural network—a type of computer system modeled after the human brain—to recognize the patterns in these energy graphs. They fed the system tens of thousands of simulated earthquakes, each created with known, specific values for the friction between rocks and the stress that caused them to break. The goal was to see if the computer could learn to look at the energy graph and instantly tell them what those hidden values were.

The researchers built a massive library of data to teach their system. They used a powerful supercomputer to simulate 35,000 different earthquake scenarios on a flat, vertical crack in the ground. In each simulation, they changed three key ingredients: the initial stress pushing on the fault, the static friction holding the rocks together before they slipped, and the distance the rocks had to slide before the friction started to weaken. For every single simulation, they recorded the resulting source time function. They then trained their neural network on this data, letting it learn the connection between the shape of the energy graph and the three physical ingredients that created it. The system used a five-layer structure to process the information, gradually refining its understanding of the patterns until it could make predictions with high precision.

When they tested the trained system on new, unseen simulations, the results were strikingly accurate. The computer successfully predicted the initial stress with an average error of less than half a percent. It estimated the static friction with an error of about one percent. The slip-weakening distance, which is the most difficult of the three to pin down, still came through with an average error of roughly three percent. In many cases, the predictions were so close that if you took the computer's guessed values and ran a fresh simulation, the resulting energy graph looked almost identical to the one generated by the true values. The researchers found that the system worked best for the stress and friction values, while the slip-weakening distance showed slightly more variation, suggesting that this specific parameter leaves a slightly fuzzier signature in the energy release pattern.

The study also explored whether a more complex computer model would work better. They tested networks with different numbers of layers, from one up to five. While no single design was perfect for every single parameter, the five-layer model provided the most reliable overall performance. This design allowed the system to capture both broad trends and fine details in the data simultaneously. The researchers noted that the system is not yet ready for real-world earthquakes, as it was trained entirely on perfect, simulated data without the noise and complications of actual ground conditions. However, the work proves that a neural network can learn the physics of rupture from source time functions with remarkable speed. Once trained, the system can perform an inversion in less than a tenth of a millisecond, a task that would take traditional methods hours or days.

This research offers a new tool for the field of seismology, providing a reproducible model and a controlled dataset that other scientists can use to test their own methods. It demonstrates that machine learning can bypass the slow, iterative loops of traditional physics-based modeling to deliver rapid estimates of earthquake source parameters. While the current model is limited to simple, flat faults and synthetic data, it lays the groundwork for future systems that could eventually handle the messy, complex reality of natural earthquakes. The findings suggest that with enough training data, artificial intelligence can become a powerful partner in decoding the violent physics of the Earth, turning the complex language of seismic waves into clear, actionable numbers almost instantly.

Technical Summary: STFNet3D – A Three-Dimensional Dynamic Rupture Inversion Model Based on Neural Networks

Problem Statement
Dynamic rupture inversion is a critical yet highly nonlinear challenge in seismology, essential for understanding the physical laws governing earthquake nucleation, propagation, and termination. Traditional inversion methods for determining fault parameters (such as initial stress, frictional strength, and slip-weakening distance) are often computationally expensive, slow, and limited by the complexity of solving coupled elastic dynamics and friction laws. While machine learning has shown promise in other seismic tasks (e.g., phase picking and hypocenter localization), its application to inferring dynamic rupture parameters directly from source time functions (STFs) remains underexplored. This study addresses the need for a rapid, reproducible framework to invert key dynamic rupture parameters from STFs, serving as a controlled proof-of-concept to benchmark machine learning approaches against traditional methods.

Methodology
The authors developed STFNet, a one-dimensional Convolutional Neural Network (CNN) designed to map Source Time Functions (STFs) to three specific dynamic rupture parameters: shear stress ( $\tau$ ), static friction coefficient ( $\mu_s$ ), and slip-weakening distance ( $D_c$ ).

Data Generation (Forward Modeling):
- A large-scale synthetic dataset comprising 35,000 events was generated using a GPU-based three-dimensional Curved-Grid Finite-Difference Method (CGFDM).
- The simulation model features a vertical planar fault (25 km $\times$ 20 km) with a 3 km $\times$ 3 km nucleation zone.
- A linear slip-weakening friction law was employed. While dynamic friction ( $\mu_d = 0.525$ ) and normal stress ( $\sigma_n = 120$ MPa) were fixed, the target parameters ( $\tau$ , $\mu_s$ , $D_c$ ) were randomly sampled within specific ranges ( $\tau$ : 64.08–70.88 MPa; $\mu_s$ : 0.60–0.70; $D_c$ : 0.25–0.45 m).
- STFs were computed by integrating the moment release rate across the fault surface, derived from simulated slip velocities.
Neural Network Architecture:
- STFNet utilizes a five-layer 1D CNN encoder. The architecture progressively downsamples the temporal dimension while increasing feature channels (16, 32, 64, 128, 256).
- The first three layers use larger kernels (size 7) to capture broad temporal features, while the subsequent two layers use smaller kernels (size 4) to refine high-level representations.
- ReLU activation functions are applied after each convolutional layer, followed by a fully connected layer that outputs the three continuous physical parameters.
Training and Validation:
- The dataset was split into training (75%), validation (15%), and test (10%) sets.
- Hyperparameters (learning rate, batch size, data split, and learning rate schedules) were optimized via grid search. The final configuration used a learning rate of 0.01, a batch size of 64, and a fixed learning rate schedule.
- The model was trained using Mean Squared Error (MSE) as the loss function with an early stopping strategy to prevent overfitting.
- Forward Validation: To assess the physical consistency of the inversion, the predicted parameters were fed back into the forward simulation code to reconstruct STFs, which were then compared to the original true STFs.

Key Results

Predictive Accuracy: On the independent test set, the five-layer CNN achieved high predictive accuracy with mean relative errors of:
- Shear Stress ( $\tau$ ): 0.37%
- Static Friction Coefficient ( $\mu_s$ ): 1.10%
- Slip-Weakening Distance ( $D_c$ ): 2.97%
- The coefficient of determination ( $R^2$ ) values were 0.9914 for $\tau$ , 0.9903 for $\mu_s$ , and 0.9785 for $D_c$ .
Parameter Identifiability: The model performed best for $\tau$ and $\mu_s$ . $D_c$ exhibited slightly larger errors and a broader error distribution, suggesting it is less identifiable from STF information alone compared to the other parameters.
Network Depth: A comparison of CNN architectures (1 to 5 layers) revealed that no single depth minimized error for all parameters simultaneously. However, the five-layer architecture achieved the lowest validation loss (0.0038) and provided the most favorable overall performance.
Waveform Reconstruction: Forward modeling using the inverted parameters generally reproduced the main temporal evolution and pulse shapes of the true STFs. However, discrepancies were noted in cases with delayed rupture initiation or incomplete rupture within the recording window, highlighting the non-uniqueness of the inversion (different parameter combinations can yield similar STFs).

Significance and Claims
The authors position this work not as a demonstration of the universal applicability of deep learning to real-world dynamic rupture inversion, but as a controlled proof-of-concept study. The primary contributions are:

Reproducible Framework: The provision of a reproducible CNN-based model (STFNet3D) for inferring dynamic rupture parameters from STFs.
Benchmark Dataset: The creation of a controlled, large-scale synthetic dataset (35,000 events) specifically designed for testing and benchmarking STF-based inversion methods.
Computational Efficiency: The trained model offers extremely low inference costs (<0.1 ms per event), making it suitable for rapid parameter estimation once the upfront cost of synthetic data generation (~1,458 GPU-hours) is incurred.

Limitations and Future Directions
The paper explicitly acknowledges several limitations:

Synthetic Data: The model was trained and tested exclusively on synthetic data under simplified physical conditions (planar vertical fault, uniform parameters). It does not yet account for real-world complexities such as measurement noise, path/site effects, or heterogeneous fault geometries.
Scope: The current framework is restricted to uniformly distributed parameters and does not address complex fault geometries or spatially heterogeneous frictional properties.
Validation: The study does not provide a quantitative comparison with conventional inversion methods or physics-informed neural networks (PINNs) on the same task.

Consequently, the authors state that the results should not be assumed to represent performance on real observational data. Future work is required to incorporate complex fault geometries, heterogeneous parameter distributions, and realistic observational disturbances, followed by validation against observed earthquake data before the method can be applied to real-time source characterization.

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