Fourier Neural Operator-based surrogate modeling of offshore tsunami propagation and its application to rapid tsunami source inversion

The accurate and rapid estimation of tsunami sources immediately after an earthquake is essential for real-time tsunami forecasting. Recent advances in offshore tsunami observation networks have made it increasingly feasible to estimate tsunami sources from observed waveforms using adjoint-based inversion methods. However, conventional adjoint approaches require repeated forward and adjoint simulations, resulting in substantial computational costs that limit their applicability to real-time systems. To address this challenge, we introduce a surrogate model for tsunami propagation based on a Fourier Neural Operator (FNO). The proposed FNO model learns tsunami propagation governed by linear long-wave equations and efficiently approximates the operator mapping from the initial conditions to future wavefields, enabling extremely fast tsunami simulations. Furthermore, by leveraging automatic differentiation, the model computes the gradients of the objective function efficiently without explicitly deriving the adjoint equations, thereby significantly simplifying the implementation of inversion methods. In this study, we develop an initial height inversion method to estimate the initial sea surface height and a fault parameter inversion framework by integrating an FNO model with a crustal deformation model. The proposed methods were validated using both synthetic data and real tsunami observations from the 2024 Hyuga-nada earthquake (M 7.1) recorded by the N-net system. The results demonstrate that accurate and rapid source estimation can be achieved within a few minutes, indicating the potential of the proposed approach as an efficient inversion framework for future real-time tsunami forecasting systems.