5:15 PM - 7:15 PM
[SCG60-P08] Neural Operators for Earthquake Cycle Simulation and Long-Period Ground Motion Forecast
Deep learning based on Neural Networks (NNs) has rapidly advanced owing to big data and the development of computing resources and extended its influence on natural sciences. On the other hand, physical laws such as partial differential equations and their numerical analyses have played a crucial role in the description and prediction of natural phenomena. Since the late 2010s, Scientific Machine Learning (SciML), which integrates physical theory, scientific computing, and machine learning, has emerged as a major research trend. Representative methods such as Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs) have begun to be introduced into seismology. In this study, we examined the potential of NOs, especially the Fourier Neural Operator (FNO), focusing on the following two topics in seismology:
1. Earthquake Cycle Simulation
In earthquake cycle calculations, it is standard practice to evaluate quasi-static change in fault stress by convolving the elastostatic stress Green's function with fault slip rates. This is an application of the boundary integral equation method (BIEM), implemented as the product of a Green's function matrix and a slip rate vector. The elastostatic BIEM requires computation time and memory of O(N2) for the number of subdivided elements N, so ingenuity is required for large-scale applications. This research topic attempted to construct an FNO that achieves this convolution with a low computational order (hopefully, O(N log N) or less).
The training data consist of input slip-rate distributions randomly generated by a Gaussian process and output stress, which is the product of the input slip-rates and the Green's function matrix. We incorporated our trained FNO with a quasi-dynamic earthquake cycle simulation using rate-and-state friction (Dieterich, 1979) to test whether the FNO reproduces the simulated slow slip event in Hirahara & Nishikiori (2019). Results in good agreement with the original BIEM were then obtained. It is remarkable that our FNO, which learned a random basis rather than the slip distribution during the earthquake cycle, was able to calculate the earthquake cycle, because it suggests that the FNO was able to discover the linearity of Green's function. In the presentation, we will also introduce the details of computational performance and accuracy.
2. Long-Period Ground Motion Forecast
Large earthquakes can generate long-period ground motions in distant sedimentary basins, potentially causing damage to high-rise buildings. With early warning in mind, we developed an FNO to predict seismic waveforms at a target observation point using waveform records near the earthquake sources. Following Furumura and Oishi (2023), we focused on earthquakes that occurred off the Pacific coast of the Tohoku region, Japan and estimated seismic waveforms at Kanagawa Prefecture (YFTH) from those at Fukushima Prefecture (HROF). We treated two horizontal components (EW and NS) independently and evaluated the predictive performance of velocity waveform and pseudo spectral velocity. We utilized observational records from the Hi-net and F-net networks operated by the National Research Institute for Earth Science and Disaster Resilience.
Examining the basic architecture of the FNO model, we identified two critical requirements: normalizing the amplitude for individual waveforms and setting the maximum wavenumber, one of the FNO parameters, to several hundred or more, rather than the typical range of a few dozen. We will also report the results for treating the two components jointly and incorporating multiple input stations.
1. Earthquake Cycle Simulation
In earthquake cycle calculations, it is standard practice to evaluate quasi-static change in fault stress by convolving the elastostatic stress Green's function with fault slip rates. This is an application of the boundary integral equation method (BIEM), implemented as the product of a Green's function matrix and a slip rate vector. The elastostatic BIEM requires computation time and memory of O(N2) for the number of subdivided elements N, so ingenuity is required for large-scale applications. This research topic attempted to construct an FNO that achieves this convolution with a low computational order (hopefully, O(N log N) or less).
The training data consist of input slip-rate distributions randomly generated by a Gaussian process and output stress, which is the product of the input slip-rates and the Green's function matrix. We incorporated our trained FNO with a quasi-dynamic earthquake cycle simulation using rate-and-state friction (Dieterich, 1979) to test whether the FNO reproduces the simulated slow slip event in Hirahara & Nishikiori (2019). Results in good agreement with the original BIEM were then obtained. It is remarkable that our FNO, which learned a random basis rather than the slip distribution during the earthquake cycle, was able to calculate the earthquake cycle, because it suggests that the FNO was able to discover the linearity of Green's function. In the presentation, we will also introduce the details of computational performance and accuracy.
2. Long-Period Ground Motion Forecast
Large earthquakes can generate long-period ground motions in distant sedimentary basins, potentially causing damage to high-rise buildings. With early warning in mind, we developed an FNO to predict seismic waveforms at a target observation point using waveform records near the earthquake sources. Following Furumura and Oishi (2023), we focused on earthquakes that occurred off the Pacific coast of the Tohoku region, Japan and estimated seismic waveforms at Kanagawa Prefecture (YFTH) from those at Fukushima Prefecture (HROF). We treated two horizontal components (EW and NS) independently and evaluated the predictive performance of velocity waveform and pseudo spectral velocity. We utilized observational records from the Hi-net and F-net networks operated by the National Research Institute for Earth Science and Disaster Resilience.
Examining the basic architecture of the FNO model, we identified two critical requirements: normalizing the amplitude for individual waveforms and setting the maximum wavenumber, one of the FNO parameters, to several hundred or more, rather than the typical range of a few dozen. We will also report the results for treating the two components jointly and incorporating multiple input stations.