Five-dimensional Seismic Data Reconstruction and Denoising based on A Preconditioned Riemannian Gradient Descent

Abstract Seismic data acquisition routinely suffers from insufficient spatial sampling and noise contamination, both of which degrade imaging quality and interpretation accuracy. Reconstruction methods based on low-rank assumptions can recover missing traces effectively, yet they incur high computational cost from large-scale singular value decomposition (SVD), which limits their practical efficiency. To address this bottleneck, we develop a preconditioned Riemannian gradient descent (PRGD) method based five-dimensional (5D) seismic data reconstruction. Within a Riemannian optimization framework, PRGD weights the gradient by a data-driven preconditioner, thereby reducing sensitivity to step-size selection. Simultaneously, the method exploits the low-rank structure of the tangent space of the manifold of low-rank matrices, avoiding large-scale SVD and considerably lowering computational complexity. Experiments on synthetic and field data demonstrate that, compared with the classical damped rank-reduction (DRR) method, PRGD achieves higher reconstruction accuracy in fewer iterations. It requires approximately one-seventh of the computation time of DRR and maintains superior reconstruction performance under 80% to 90% missing-trace ratios.