4:30 PM - 4:45 PM
[SCG45-11] Bayesian multi-source seismic tomography using active- and passive-source seismic data based on physics-informed neural network
Keywords:Bayesian seismic tomography, Active- and passive-source seismic data, Bayesian multi-source estimation, Phyisics-informed neural network
Estimating the velocity structure of seismogenic zones is crucial for understanding structural factors that influence slow and fast earthquake patterns. A velocity structure model also serves as essential data for seismic wave analysis. The underground velocity structure can be estimated through tomographic analyses using various travel time data. Active seismic exploration data typically estimate shallow subsurface velocities, while natural earthquakes are effective for deeper structures where controlled-source waves do not reach. Integrating these data in a single tomographic analysis is essential for a well-resolved structural model from deep to shallow levels.
Given the aforementioned usages of estimated velocity structures, ensuring the reliability of estimation results is important. Bayesian estimation, which formulates the posterior probability distribution by treating target parameters as stochastic variables, is valuable for this purpose. When using only active-source data, the estimation focuses solely on the velocity structure, as source and receiver positions are known accurately. Conversely, when using arrival times of natural earthquakes with inaccurate prior information on source positions, it is desirable to redetermine these positions from the data. However, incorporating hypocenter positions as estimated variables complicates Bayesian estimation due to the increased dimensionality and varying scales of parameters.
In this study, we propose a multi-source Bayesian tomography method using both active seismic exploration and passive natural earthquake data to address these issues based on the concept of Bayesian multi-model estimation (Agata+2021, 2022). For each natural earthquake hypocenter, multiple random sources are generated based on prior distribution. By considering a likelihood function that integrates over these multi-source models, we account for the variance in hypocenter locations. This approach allows us to focus on the velocity structure without fixing hypocenter positions to initial guesses. For the Bayesian tomography technique, we use a method based on physics-informed neural networks (PINN, Raissi+2019) previously proposed by the authors (Agata+2023,2025). PINN incorporates physical laws described by partial differential equations (PDE) into deep learning. PINN enables a mesh-free framework for inverse problems like tomography by representing both PDE solutions and parameter distributions using neural networks (NN). In Bayesian tomography with PINN, the forward propagation of NN rapidly provides travel times for a given velocity structure, keeping computational costs manageable even with multiple sources introduced.
To validate the effectiveness of this method, we conducted numerical experiments for 3D travel-time tomography using both active and passive data. The base model has a horizontal stratified structure with a velocity bump in the central part of the model domain. For passive natural earthquake data, 20 reference points for hypocenters were randomly placed in the deep portion of the model. In a small cubic region centered around each reference point, 201 random points were generated, with one being the true hypocenter and the other 200 used as multi-sources in the tomography. 138 active sources and 57 receivers were placed at the surface. We obtained the mean model that closely matched the true values and the uncertainty quantified reasonably. When the hypocenters were fixed at the reference points, the mean model showed discrepancies due to the incorrect hypocenter positions. These results suggest the effectiveness of our proposed method in accurately estimating the velocity structure even without precisely identifying the true hypocenter locations. In the future, we plan to apply this method to an actual site such as the Nankai Trough region.
Given the aforementioned usages of estimated velocity structures, ensuring the reliability of estimation results is important. Bayesian estimation, which formulates the posterior probability distribution by treating target parameters as stochastic variables, is valuable for this purpose. When using only active-source data, the estimation focuses solely on the velocity structure, as source and receiver positions are known accurately. Conversely, when using arrival times of natural earthquakes with inaccurate prior information on source positions, it is desirable to redetermine these positions from the data. However, incorporating hypocenter positions as estimated variables complicates Bayesian estimation due to the increased dimensionality and varying scales of parameters.
In this study, we propose a multi-source Bayesian tomography method using both active seismic exploration and passive natural earthquake data to address these issues based on the concept of Bayesian multi-model estimation (Agata+2021, 2022). For each natural earthquake hypocenter, multiple random sources are generated based on prior distribution. By considering a likelihood function that integrates over these multi-source models, we account for the variance in hypocenter locations. This approach allows us to focus on the velocity structure without fixing hypocenter positions to initial guesses. For the Bayesian tomography technique, we use a method based on physics-informed neural networks (PINN, Raissi+2019) previously proposed by the authors (Agata+2023,2025). PINN incorporates physical laws described by partial differential equations (PDE) into deep learning. PINN enables a mesh-free framework for inverse problems like tomography by representing both PDE solutions and parameter distributions using neural networks (NN). In Bayesian tomography with PINN, the forward propagation of NN rapidly provides travel times for a given velocity structure, keeping computational costs manageable even with multiple sources introduced.
To validate the effectiveness of this method, we conducted numerical experiments for 3D travel-time tomography using both active and passive data. The base model has a horizontal stratified structure with a velocity bump in the central part of the model domain. For passive natural earthquake data, 20 reference points for hypocenters were randomly placed in the deep portion of the model. In a small cubic region centered around each reference point, 201 random points were generated, with one being the true hypocenter and the other 200 used as multi-sources in the tomography. 138 active sources and 57 receivers were placed at the surface. We obtained the mean model that closely matched the true values and the uncertainty quantified reasonably. When the hypocenters were fixed at the reference points, the mean model showed discrepancies due to the incorrect hypocenter positions. These results suggest the effectiveness of our proposed method in accurately estimating the velocity structure even without precisely identifying the true hypocenter locations. In the future, we plan to apply this method to an actual site such as the Nankai Trough region.