EikoNet: Solving the Eikonal equation with Deep Neural Networks, with applications to hypocenter inversion, seismic tomography, and multi-pathing

Abstract:

The recent deep learning revolution has created enormous opportunity to accelerate compute capabilities in the context of physics-based simulations. Here, we propose EikoNet, a deep learning approach to solving the Eikonal equation, which characterizes the first-arrival-time field in heterogeneous 3D velocity structures. Our grid-free approach allows for rapid determination of the travel time between any two points within a continuous 3D domain. The travel time solutions are allowed to violate the differential equation, which casts the problem as one of optimization, with the goal of finding neural network parameters that minimize the degree to which the equation is violated. In doing so, the method exploits the differentiability of neural networks to calculate the spatial gradients analytically, meaning the network can be trained on its own without ever needing solutions from a finite difference algorithm. Training and inference are highly parallelized, making the approach well-suited for GPUs. EikoNet has low memory overhead, and further avoids the need for travel-time lookup tables. The method is rigorously tested on several velocity models and sampling methods to demonstrate robustness and versatility. We outline the application to earthquake hypocenter inversion, ray multi-pathing, and tomographic modelling. We demonstrate several distinct advantages of this method over conventional finite-difference approaches.