Learning Seismic Low-Frequency Extrapolation in a Latent Space Using Limited Data

Low-frequency (LF) information in seismic exploration has long been a subject of great interest because of its association with long-scale subsurface features, which ensures the convergence of seismic inversion toward an accurate solution. However, the absence of LF component in field seismic data is a common occurrence due to restrictions posed by data acquisition equipment and environmental constraints. Thus, the reconstruction of LF information from bandlimited seismic data is a pressing issue. In this letter, we introduce a data-driven deep-learning approach for seismic LF extrapolation within a latent space, which is defined by an autoencoder (AE) in a self-supervised manner. Initially, seismic data undergoes compression into a low-dimensional latent space through the encoder component of AE. Subsequently, LF components are extrapolated within this latent space, which can be later reformulated into the data space using the decoder component of AE. Two training strategies, either synchronous or step-wise, are introduced to train the network by utilizing specific loss designs. In numerical experiments, the mean absolute percentage errors (MAPEs) of the LF extrapolation results for all validation samples, processed via traditional end-to-end strategy without/with an enriched dataset, synchronous, and step-wise training with limited data, register at 52.5%, 20.6%, 13.3%, and 10.6%, respectively. The findings attest to the efficacy of the AE in the mitigation of redundant information, thereby streamlining the computational complexity inherent to frequency extrapolation. Notably, the proposed approaches achieve accurate LF extrapolation performance with a limited amount of data.