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Interpolation of aliased seismic data constitutes a key step in a seismicprocessing workflow to obtain high quality velocity models and seismic images.Building on the idea of describing seismic wavefields as a superposition oflocal plane waves, we propose to interpolate seismic data by utilizing aphysics informed neural network (PINN). In the proposed framework, twofeed-forward neural networks are jointly trained using the local plane wavedifferential equation as well as the available data as two terms in theobjective function: a primary network assisted by positional encoding is taskedwith reconstructing the seismic data, whilst an auxiliary, smaller networkestimates the associated local slopes. Results on synthetic and field datavalidate the effectiveness of the proposed method in handling aliased (coarselysampled) data and data with large gaps. Our method compares favorably against aclassic least-squares inversion approach regularized by the local plane-waveequation as well as a PINN-based approach with a single network andpre-computed local slopes. We find that introducing a second network toestimate the local slopes whilst at the same time interpolating the aliaseddata enhances the overall reconstruction capabilities and convergence behaviorof the primary network. Moreover, an additional positional encoding layerembedded as the first layer of the wavefield network confers to the network theability to converge faster improving the accuracy of the data term.

PINNslope: seismic data interpolation and local slope estimation with physics informed neural networks