Can tile low-rank compression live up to expectations? An application to 3D multi-dimensional deconvolution

Wave-equation-based seismic processing algorithms have been developed over the years with the aim of handling the 3D, full-wavefield nature of seismic waves. Multi-Dimensional Deconvolution (MDD) is one of such algorithms, commonly used to remove overburden-related effects from up/down separated wavefields (e.g., removal of free-surface multiples from ocean-bottom data). However, MDD comes with several computational challenges; this is especially the case for its time-domain implementation, which requires repeated access to Terabyte-scale seismic datasets. In this work, we present a novel algorithmic solution that leverages the inherent data sparsity of seismic data in the frequency domain by means of tile low-rank data compression. We further rely on so-called Hilbert reordering to achieve a boost in the compressibility of the dataset under study. Tile Low-Rank Matrix Vector Multiplication (TLR-MVM) is then introduced to speed up the Multi-Dimensional Convolution (MDC) operator that lies at the core of the MDD algorithm. The presented solution is tested on a realistic 3D seismic dataset modelled from the SEG/EAGE Overthrust model, and the impact of two key parameters in tile low-rank compression algorithm, namely tile size and error accuracy, is thoroughly investigated. Inversion is finally performed using the LSQR solver with all MDC operations performed onto GPUs. On a 4 A100 cluster, successful deconvolution for single virtual source is accomplished within 2 minutes (including I/O). To conclude, the proposed algorithm is deployed onto several mainstream hardware the associated roofline performance model is presented.