NeRSI: Neural implicit representations for 5D seismic data interpolation

ABSTRACT Due to challenging field operations and resource constraints, seismic data acquisition often requires coping with missing traces. Interpolation algorithms are crucial for reconstructing these missing traces to enable improved subsurface analysis and interpretation. Although deep learning has made exciting advances in seismic reconstruction, its focus has predominantly been on 2D and 3D data sets with relatively low rates of missing data. Reconstruction of 5D seismic data entails considering simultaneous sources and receivers deployed in areal arrays to solve the reconstruction problem. The latter offers greater data redundancy, which can be leveraged to enhance interpolation quality. Traditional 5D deep-learning interpolation methods rely heavily on synthetic training pairs, posing challenges when applied to real-world data. This necessitates transfer learning techniques, which can be cumbersome. To address this, we introduce a self-supervised, coordinate-based deep interpolation algorithm that mitigates the need for labeled data. Using a multilayer perceptron (MLP) network can effectively encode the continuous seismic 5D wavefield. Once trained, the MLP can infer missing trace amplitudes from their coordinates. We contribute to boosting the MLP, enabling it to generate seismic profiles rather than single-point predictions. This enhancement significantly strengthens the model’s performance and efficiency. Moreover, we apply nuclear norm regularization to the output profiles, improving the reconstruction quality. The effectiveness of our algorithm is illustrated with synthetic and field data experiments.