5-D Seismic Data Interpolation by Continuous Representation

How to represent a seismic wavefield? Traditionally, while seismic wavefields are conceptualized continuously, acquisition geometries capture seismic data discretely using 2-D spatial coordinates. Motivated by recent advances in neural radiance fields for 3-D reconstruction through implicit neural representation, we introduce implicit seismic representation (ISR) for 5-D seismic data interpolation. This approach processes seismic data coordinates as inputs and outputs amplitude values at those coordinates with multilayer perceptrons (MLPs). Due to the continuous nature of the coordinates, ISR can achieve representations at any desired resolution and is easily scalable to a 5-D representation. To achieve a continuous representation of seismic data, we employ a self-supervised learning strategy to train the ISR on observed data. The trained network is then capable of interpolating missing seismic traces by querying every coordinate of the missing data. Our approach’s effectiveness is validated through synthetic and field data experiments, showcasing superior reconstruction abilities. Our findings highlight the potential of the implicit neural representation framework to achieve precise parametrization of continuous seismic wavefields, marking a significant advancement in seismic data processing and analysis.