5:15 PM - 6:45 PM
[SCG40-P09] Physics-informed neural network for travel time prediction for 3D velocity structure model in Nankai Trough
Keywords:Nankai Trough, Travel time calculation, Physics-informed neural network, Hypocenter determination, 3D seismic velocity structure
In the Nankai Trough region, subduction-zone large earthquakes are known to have occurred repeatedly. The accumulation of seismic observation data in this region has prompted extensive studies of the seismic activities, including both fast and slow earthquakes. Accurate hypocenter determination in this region is important from viewpoints of the hazard assessment and scientific perspectives. The basis of hypocenter determination analysis is the theoretical calculation of travel time from the hypocenter located within the subsurface medium to the seismic observation stations on the Earth's surface. Travel time calculation is performed for a model of subsurface velocity structure. An accurate calculation requires a three-dimensional (3D) travel time calculations based on a 3D velocity structure model that reflects the real structure well. It is generally not easy to set up an appropriate 3D velocity structure model. However, several realistic 3D velocity structure models have been published (e.g., Nakanishi+2018) for the Nankai Trough region owing to accumulated velocity structure data. As for methods for 3D travel time calculations, there are many established tools using ray-tracing and grid-based numerical methods. Nevertheless, calculations based on simple structures such as those of 1D are still widely used in many studies. For travel time calculations and hypocenter determination based on published 3D velocity structure models to be used more widely, constructing and publishing a tool that can easily provide the travel time results can be a solution.
One approach to do so is a surrogate modeling of the nonlinear relationship between the input (the locations of source and receiver) and response output (travel time) using machine learning models such as deep neural networks (NNs). Physics-informed neural networks (PINN, Raissi+2019), which have recently attracted attention as a new solution method for partial differential equations (PDEs), can incorporate physical laws described by a PDE in the loss function defined for training. This allows for construction of a NN that models the nonlinear relationship between the locations of the source-receiver pair and the travel time without the need of training data (Taufik+2023).
In this study, we developed a PINN trained for travel time in a 3D P-wave velocity structure model in the Nankai Trough region, which can perform travel time calculations in a fraction of second. The model of Nakanishi+2018, which has incorporated the results of marine seismic surveys within the region, was used. We introduced a fully connected NN that takes the 3D Cartesian coordinates of the epicenter and observation positions as input and outputs the travel time. Many residual evaluation (collocation) points are randomly distributed in the domain where the travel time function is defined. The sum of squared residuals of the eikonal equation, which are evaluated from the predicted travel time by the NN and the seismic wave velocity in the model, for all the points was used as the loss function. The NN was trained to minimize this loss function (e.g., Smith+2021). By learning the travel times between randomly chosen locations of seismic sources in the 3D domain and arbitrary observation points on the Earth's surface, the NN can rapidly calculate travel times for all source-receiver pairs during inference.
The travel times calculated by this NN were compared with those calculated by the fast-marching method. We generally obtained good agreements except for slightly degraded results in the vicinity of the hypocenter, for which we require further improvements. We found the travel time calculation using this NN takes less than 0.1 second for 5,000 source-receiver pairs, confirming that fast travel time calculations based on the 3D velocity structure model. Because we consider to make this tool publicly available in the future, we look forward to exchanging opinions with potential users during the conference.
One approach to do so is a surrogate modeling of the nonlinear relationship between the input (the locations of source and receiver) and response output (travel time) using machine learning models such as deep neural networks (NNs). Physics-informed neural networks (PINN, Raissi+2019), which have recently attracted attention as a new solution method for partial differential equations (PDEs), can incorporate physical laws described by a PDE in the loss function defined for training. This allows for construction of a NN that models the nonlinear relationship between the locations of the source-receiver pair and the travel time without the need of training data (Taufik+2023).
In this study, we developed a PINN trained for travel time in a 3D P-wave velocity structure model in the Nankai Trough region, which can perform travel time calculations in a fraction of second. The model of Nakanishi+2018, which has incorporated the results of marine seismic surveys within the region, was used. We introduced a fully connected NN that takes the 3D Cartesian coordinates of the epicenter and observation positions as input and outputs the travel time. Many residual evaluation (collocation) points are randomly distributed in the domain where the travel time function is defined. The sum of squared residuals of the eikonal equation, which are evaluated from the predicted travel time by the NN and the seismic wave velocity in the model, for all the points was used as the loss function. The NN was trained to minimize this loss function (e.g., Smith+2021). By learning the travel times between randomly chosen locations of seismic sources in the 3D domain and arbitrary observation points on the Earth's surface, the NN can rapidly calculate travel times for all source-receiver pairs during inference.
The travel times calculated by this NN were compared with those calculated by the fast-marching method. We generally obtained good agreements except for slightly degraded results in the vicinity of the hypocenter, for which we require further improvements. We found the travel time calculation using this NN takes less than 0.1 second for 5,000 source-receiver pairs, confirming that fast travel time calculations based on the 3D velocity structure model. Because we consider to make this tool publicly available in the future, we look forward to exchanging opinions with potential users during the conference.