A robust seismic tomography framework via physics-informed machine learning with hard constrained data

Accurate traveltime modeling and inversion play an important role across geophysics. Specifically, traveltime inversion is used to locate microseismic events and image the Earth’s interior. Considered to be a relatively mature field, most of the conventional algorithms, however, still suffer from the so-called first-order convergence error and face a significant challenge in dealing with irregular computational grids. On the other hand, employing physics-informed neural networks (PINNs) to solve the eikonal equation has shown promising results in addressing these issues. Previous PINNs-based eikonal inversion and modeling schemes, however, suffer from slow convergence. We develop a new formulation for the isotropic eikonal equation by imposing the boundary conditions as hard constraints (HC). We implement the theory of functional connections (TFC) into the eikonal-based tomography, which admits a single loss term for training the PINN model. We demonstrate that this formulation leads to a robust inversion framework. More importantly, its ability to handle uneven acquisition geometry and topography providing an alternative answer towards the call for an energy-efficient acquisition setup.