PWD-PINN: slope-assisted seismic interpolation with physics-informed neural networks

Seismic data can be expressed as a superposition of local plane waves. A gather of traces can be described by the local plane wave differential equation (PDE), that allows to predict each of the traces from the previous one, given the knowledge of the local slope of the events. In the approach presented here, we train a neural network in an unsupervised manner to solve seismic interpolation problems using the local plane wave differential equation and the local slope estimated by the mean of plane wave destruction filters (PWD). The physics-informed neural network (PINN) maps the input grid points in time and space to the amplitudes of the wavefield whilst matching the information contained in the available traces. The proposed approach is tested on two seismic interpolation tasks using synthetic data, specifically, interpolation of data with large gaps and those aliased. Whilst the network shows remarkable interpolation capabilities in both experiments, it tends to struggle fitting aliased data with high frequency content. To mitigate this problem, we propose to include locally adaptive activation functions in the architecture. This leads to improved convergence and reconstruction accuracy.