Fourier-ResPINN: a new solution for solving the travel time of first arrival

The accuracy and efficiency of the travel time calculation of seismic wave first arrivals have a profound impact on the performance of seismic data processing techniques. Traditional methods of calculating travel times based on the eikonal equation are accurate, but time-consuming when dealing with large models. Thus, we propose a Fourier-ResPINN model for travel time calculation in order to balance the accuracy and efficiency of such calculation and to improve the network degradation and spectral bias of the vanilla physics-informed neural network (PINN). We use the residual connections instead of the fully connected neural network of PINN and performs Fourier mapping operations on the inputs to the network, to solve the factored eikonal equation. Our numerical experimental results show that Fourier-ResPINN improves the accuracy by about an order of magnitude over ordinary PINN, and is more computationally efficient for complex models than the traditional fast scan method.