Abstract
With the aim of imaging subsurface discontinuities, seismic data recorded at the surface of the Earth must be numerically re-positioned inside the subsurface where reflections have originated, a process referred to as redatuming. The recently developed Marchenko method is able to handle full-wavefield data including multiple arrivals. A downside of this approach is that a multi-dimensional convolution operator must be repeatedly evaluated to solve an expensive inverse problem. As such an operator applies multiple dense matrix-vector multiplications (MVM), we identify and leverage the data sparsity structure for each frequency matrix and propose to accelerate the MVM step using tile low-rank (TLR) matrix approximations. We study the TLR impact on time-to-solution for the MVM using different accuracy thresholds whilst at the same time assessing the quality of the resulting subsurface seismic wavefields and show that TLR leads to a minimal degradation in terms of signal-to-noise ratio on a 3D synthetic dataset. We mitigate the load imbalance overhead and provide performance evaluation on two distributed-memory systems. Our MPI+OpenMP TLR-MVM implementation reaches up to 3X performance speedup against the dense MVM counterpart from NEC scientific library on 128 NEC SX-Aurora TSUBASA cards. Thanks to the second generation of high bandwidth memory technology, it further attains up to 67X performance speedup compared to the dense MVM from Intel MKL when running on 128 dual-socket 20-core Intel Cascade Lake nodes with DDR4 memory. This corresponds to 110 TB/s of aggregated sustained bandwidth for our TLR-MVM implementation, without suffering deterioration in the quality of the reconstructed seismic wavefields.
Highlights
Exploration geophysics is an applied branch of geophysics that uses several physical measurements at the surface of the Earth to estimate the physical properties of the first few kilometers of the subsurface
tile low-rank (TLR)-matrix-vector multiplications (MVM) on NEC Vector Engines (VE) outperforms its counterpart on Intel CSL by up to a factor 4, which is aligned with results on synthetic datasets from Section 7.2
Another opportunity lies in the fact that the inverse problem we wish to solve can be slightly modified to include more than one spatial coordinates xB at the time [30]; in other words, our batched tile low-rank matrix-vector multiplication (TLR-MVM) can be replaced by a batched tile low-rank matrix-matrix multiplication (TLR-MMM) where each column of the input matrix represents the wavefield originated from a different virtual source
Summary
Exploration geophysics is an applied branch of geophysics that uses several physical measurements at the surface of the Earth (e.g., seismic, gravity, electromagnetic) to estimate the physical properties of the first few kilometers of the subsurface. Instead of operating the MVM on the original dense data structure, our numerical technique consists in (1) splitting it into tiles with elements contiguously stored in memory, (2) compressing the tile matrix using TLR approximations (e.g., using randomized SVD [22]) up to an application-dependent accuracy threshold, and (3) performing the MVM directly on the compressed TLR data storage. This translates into a reduction of the number of floating-point operations, while further saving memory footprint.
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