HypoNet Nankai PS: rapid hypocenter determination for the Nankai Trough using physics-informed neural networks with three-dimensional P- and S-wave velocity models
Organizations: Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Japan · Earth Sciences New Zealand, New Zealand · Faculty of Sciences, Kyushu University, Japan
Rapid and accurate hypocenter determination based on three-dimensional (3D) seismic velocity models is essential for seismic monitoring in subduction zones, yet it remains computationally demanding. HypoNet Nankai, a hypocenter determination package that uses physics-informed neural network (PINN) travel-time inference for a realistic 3D P-wave velocity model of the Nankai Trough subduction zone, was designed to address this problem, but supported only P-wave arrival times. Here, we present HypoNet Nankai PS, which extends the framework to both P- and S-wave travel times. We first constructed an S-wave velocity model from the existing P-wave model using empirical conversion relations for marine sediments and the crust. Because the resulting S-wave velocity structure has lower velocities and therefore considerably steeper travel-time gradients, the original PINN training procedure designed for the P-wave velocity structure was insufficient. We therefore revised the training procedure by reconsidering the distribution of collocation points, the NN architecture, and the optimizer. Benchmark comparisons with the fast marching method showed that the revised approach substantially reduced the root-mean-square deviations for both P- and S-waves compared with the original algorithm. Recovery tests using synthetic earthquakes were also performed. When applied to 223 earthquakes recorded by DONET stations off the Kii Peninsula, the system yielded hypocenters generally consistent with the JMA catalog beneath the network, suggesting that the 3D velocity model captures travel-time variations accommodated by JMA's 1D model and station corrections. Farther seaward, the estimated hypocenters were substantially shallower than those in the JMA catalog and were located in the oceanic crust and uppermost mantle, consistent with previous relocations that used DONET data and 3D velocity models.
Figures & tables
Setting
A2026
HypoNet Nankai PS
Collocation sampling
Full 3-D domain
Full 3-D domain
Source sampling
Earth’s surface (2D manifold)
Full 3-D domain
Random-distance sampling
No
Yes
Optimizer
Adam
SOAP
NN architecture
Fully connected with RFF
Deeper-PINN with RFF
Domain decomposition
Yes
No
Table 1: Comparison of training algorithm settings between A2026 and HypoNet Nankai PS (this study).
Figure 1: (a) Map of the study region showing the PINN modeling domain and target regions for hypocenter determination. Lines labeled (b) and (c) indicate the locations of the velocity cross sections. (b, c) Cross sections of the N2018 P-wave velocity model (left) and the S-wave velocity model derived by empirical conversion (right) along the profiles marked in (a).
Figure 2: (a) Schematic of PINN-based travel-time learning. (b) Deeper-PINN architecture used in this study, which employs a random Fourier feature embedding.
Figure 3: Comparison of S-wave travel-time fields on the Earth’s surface inferred by the PINN and computed by FMM for five randomly selected sources. (a) Results obtained with the training algorithm used in this study. (b) Results obtained with the training algorithm of A2026 without domain decomposition. The epicenter location, source depth, and RMSD between the PINN and FMM results are indicated in each panel.
Figure 4: Comparison of P-wave travel-time fields on the Earth’s surface inferred by the PINN trained with the algorithm used in this study and computed by FMM for five randomly selected sources. The epicenter location, source depth, and RMSD between the PINN and FMM results are indicated in each panel.
Figure 5: Histograms of the travel-time difference (PINN minus FMM) at surface grid points for the five sources shown in Figures 3 and 4 . (a) P-wave results. (b) S-wave results.
Figure 6: Results of synthetic hypocenter determination using P- and S-wave arrival times at virtual DONET and N-net stations. Map views of MAP-estimated hypocenters are compared with the true locations for true ellipsoidal heights of (a) −50 km, (b) −40 km, (c) −30 km, (d) −20 km, and (e) −10 km. Colors indicate the residual in ellipsoidal height ( hMAP−htrue ). Red crosses mark the true epicenters of events whose recovered locations fell outside the modeling domain. In (a), the locations of cross sections presented in Fig. 7 are indicated.
Figure 7: Cross sections of the synthetic hypocenter determination results shown in Fig. 6 , presented in the y – h plane at (a) x=100 km, (b) x=280 km, (c) x=460 km, (d) x=640 km, and (e) x=820 km. True and MAP-estimated locations are compared. Crosses indicate 2σ confidence intervals for the estimated hypocenter locations. Covariance components are omitted for clarity. NW and SE below the y –axis in (e) denote northwest and southeast, respectively.
Figure 8: Location errors and posterior uncertainties in the synthetic test plotted against the distance to the nearest station (left column) and the azimuthal gap (right column). The distance is the epicentral (horizontal) distance from the true hypocenter to the nearest DONET or N-net station. The azimuthal gap is the largest angle between the azimuths from the true epicenter to two adjacent stations. (a) Absolute horizontal error ∣Δxy∣ between the MAP and true hypocenters. (b) Absolute error in ellipsoidal height ∣Δh∣ . (c) Horizontal 1σ uncertainty σxy obtained from the Laplace approximation of the posterior PDF (in the model Cartesian frame). (d) Corresponding 1σ uncertainty in ellipsoidal height σh . Symbols are colored by the true ellipsoidal height h .
Figure 9: Hypocenter relocation using P- and S-wave arrival times at DONET stations. (a) Map view of MAP-estimated hypocenters compared with the original JMA catalog locations. Colors indicate hypocenter depth. Lines A–C mark the locations of the cross sections. (b) Same map view as (a), but showing estimation uncertainties. (c) Cross sections along A–C showing the changes in hypocenter locations from the JMA catalog. (d) Same cross sections as (c), but showing estimation uncertainties. NW and SE in the cross sections denote northwest and southeast, respectively. The plate boundary (PB) of Nakanishi et al. (2018) and a reference horizon for the Moho, placed 6.5 km below PB as a visual guide, are indicated in the cross sections. Crosses in (b) and (d) indicate 2σ confidence intervals. Covariance components are omitted for clarity. In all the panels, the dashed line indicates a distance of -20 km along the cross sections, which separates the landward group (distances larger than -20 km) from the seaward group (distances smaller than -20 km) in Figure 10 .
Figure 10: Comparison of hypocenter depths estimated by HypoNet Nankai PS with those in the JMA catalog for the events shown in Fig. 9 . The events are divided into two groups at a distance of -20 km along the cross sections (dashed lines in Fig. 9 (a)(b)). (a) Landward group (distances larger than -20 km). (b) Seaward group (distances smaller than -20 km). The diagonal line indicates equal depths. The bias, defined as the mean of our depths minus the JMA depths, and the RMSD of the depth differences are shown for each group.
Accurate 3D seismic velocity modeling through seismic travel-time tomography using both active- and passive-source data provides critical underpinning models for seismicity monitoring and hazard assessment. Because travel-time tomography is an inherently ill-posed inverse problem, UQ of the estimated models using Bayesian methods is also important for reliable downstream interpretations and analyses. However, Bayesian inference for 3D tomography based on conventional grid-based representations faces the ``curse of dimensionality'' and severe computational bottlenecks. Consequently, rigorous Bayesian UQ for margin-wide 3D travel-time tomography has remained largely unexplored. In this study, we propose a meshless 3D Bayesian travel-time tomography method that combines PINNs with a neural representation of the velocity structure, enabling tractable and data-efficient Bayesian inference through function-space particle-based variational inference. To efficiently integrate passive-source data into the Bayesian estimation of the velocity structure, we conduct analytical marginalization treating uncertain source parameters as nuisance parameters, with passive-source relocation carried out in post-processing. We validated the capability of our approach for 3D problems through synthetic experiments. Furthermore, we applied the method to a real-world dataset from marine active-source surveys and natural earthquakes off the Kii Peninsula, Nankai Trough. Our probabilistic 3D ensemble successfully resolves key geological features and provides data-consistent uncertainty maps. The posterior mean hypocenters shifted mainly in the vertical direction by 10-15 km, consistent with a previous relocation result. Finally, the neural representation drastically reduces storage requirements for the entire ensemble velocity model, highlighting the scalability and data efficiency of the proposed framework.
Ryoichiro Agata, Kazuya Shiraishi, Gou Fujie +1
Japan Agency for Marine-Earth Science and Technology · Earth Science New Zealand
Numerous studies have shown that the machine-learning picker PhaseNet produces accurate P and S picks on local earthquake signals, but its performance can degrade sharply on teleseismic signals. To address this limitation, we present a reproducible MsPASS workflow that (i) enables scalable data preparation and management for large seismic archives and (ii) supports standardized PhaseNet training and inference. We assembled a control dataset of 1.6 million waveforms linked to teleseismic P-wave picks made by analysts at the USArray Array Network Facility (ANF). The control dataset confirms that the PhaseNet model trained on regional signals performs poorly on these data. We then trained PhaseNet from scratch on the training split of the ANF control dataset and evaluated it on a non-overlapping held-out test split, increasing P-pick recall by 741.5% and yielding 683.9% more picks within a 0.1s residual window. We also evaluated PhaseNet across different model sizes on both CPUs and GPUs. Increasing the model size by about 120 times improved precision and recall by 15.6% and 23.2%, respectively. However, the scaled model reduced inference throughput by 87.2% on an NVIDIA A100 GPU and by 97.3% on a 128-core high-performance CPU node. These results indicate that scaling PhaseNet is more practical on GPUs than on CPUs, and that simply enlarging the model is not an efficient way to achieve large accuracy gains.
Jinxin Ma, Yinzhi Wang, Gary L. Pavlis +1
Texas Advanced Computing Center, The University of Texas at Austin · Department of Earth and Atmospheric Sciences, Indiana University, Bloomington, IN 47405
Mineral prospectivity modelling (MPM) underpins exploration economics, yet most operational pipelines reduce to data-driven classifiers trained on shallow surface proxies. Such models are blind to the subsurface physics that actually localises ore: heat advection, fluid flow, and lithology-dependent precipitation. We present Korzhinskii-Net, a 2-D radial physics-informed neural network (PINN) that couples Darcy flow, advective-diffusive heat transport, and a softplus-saturated reaction rate into a single differentiable forward model, weakly supervised by surface and remote-sensing proxies. The network is named after Dmitri S. Korzhinskii (1899-1985), whose theory of infiltration metasomatism provides the physical scaffold. We evaluate Korzhinskii-Net on six ore provinces spanning three commodity classes - Udokan (sandstone-hosted Cu), Sukhoi Log, Olimpiada, and Berezovskoye (orogenic Au), Vorontsovskoye (Carlin-type Au), and Dalnegorsk (skarn polymetallic) - under a fair, leakage-controlled 5-fold cross-validation protocol with hard ring-shaped negatives and baseline proxy features disabled. Korzhinskii-Net attains a mean PR-AUC of 0.708 versus 0.235 for the strongest classical baseline (support vector machine), and a mean fractional rank of 0.036 versus 0.475. The improvement is consistent across all six provinces and three commodity systems, suggesting that physics-informed differentiable simulators, even when constrained only by global open-data proxies, can recover localisation patterns that pure feature-based learners systematically miss. We release the full pipeline and evaluation harness as open source.
Boris Kriuk
The Hong Kong University of Science and Technology, Hong Kong SAR