Large-scale Marchenko imaging with distance-aware matrix reordering, tile low-rank compression, and mixed-precision computations

A variety of wave-equation-based seismic processing algorithms rely on the repeated application of the Multi- Dimensional Convolution (MDC) operator. For large-scale 3D seismic surveys, this comes with severe computational challenges due to the sheer size of high-density, full-azimuth seismic datasets required by such algorithms. We present a three-fold solution that greatly alleviates the memory footprint and computational cost of 3D MDC by leveraging a combination of i) distance-aware matrix reordering, ii) Tile Low-Rank (TLR) matrix compression, and iii) computations in mixed floating-point precision. By applying our strategy to a 3D synthetic dataset, we show that the size of kernel matrices used in the Marchenko redatuming and Multi-Dimensional Deconvolution equations can be reduced by a factor of 34 and 6, respectively. We also introduce a TLR Matrix-Vector Multiplication (TLR-MVM) algorithm that, as a direct consequence of such compression capabilities, is consistently faster than its dense counterpart by a factor of 4.8 to 36.1 (depending on the selected hardware). As a result, the associated inverse problems can be solved at a fraction of cost in comparison to state-of- the-art implementations that require a pass through the entire data at each MDC operation. This is achieved with minimal impact on the quality of the processing outcome.