Reconstruction and denoising of high-dimensional seismic data via Frobenius-nuclear mixed norm constraints

The seismic data acquisition design with ‘two-wide and one-high’ geometry effectively improves the imaging quality of seismic records. However, when data is acquired in the real field, complex near surface conditions and environmental factors can introduce a variety of noises and gaps in seismic data, impacting the accuracy of seismic imaging. Currently, the method of low-rank matrix/tensor completion is commonly employed for data reconstruction after normal moveout (NMO). In complex subsurface medium, CMP (Common Midpoint) data processed with NMO may not satisfy the linear or quasi-linear assumptions within local data windows. Therefore, this paper exploits the inherent low-rank structure of high-dimensional data to propose a high-dimensional tensor completion method under the Frobenius-nuclear mixed norm constraint (FN-TC). This method unfolds the 4D data tensor into the frequency-space domain along its modes-(m, n) and subsequently imposes a non-convex Frobenius-nuclear mixed norm constraint on the unfolded approximate matrices. This approach closely approximates the rank function of the factor matrices, thereby enhancing the accuracy of data modeling. Theoretical and practical studies demonstrate that the novel FN-TC approach can effectively reconstruct high-dimensional seismic data and suppress noise, thereby providing data support for subsequent high-precision seismic imaging.