Physics-informed deep learning quantifies propagated uncertainty in seismic structure and hypocenter determination

Subsurface seismic velocity structure is essential for earthquake source studies, including hypocenter determination. Conventional hypocenter determination methods ignore the inherent uncertainty in seismic velocity structure models, and the impact of this oversight has not been thoroughly investigated. Here, we address this issue by employing a physics-informed deep learning (PIDL) approach that quantifies uncertainty in two-dimensional seismic velocity structure modeling and its propagation to hypocenter determination by introducing neural network ensembles trained on active seismic survey data, earthquake observation data, and the physical equation of wavefront movement. An analysis of an earthquake in southwest Japan using our method revealed that accounting for such uncertainty propagation significantly reduced the bias and uncertainty underestimation in the hypocenter determination, enabling quantitative evaluation of the focal depth relative to the plate boundary. Our results highlight the potential of PIDL for various geophysical inverse problems, such as investigating earthquake source parameters, which inherently suffer from uncertainty propagation.