Up-to-date assessment of 3D frequency-domain full waveform inversion based on the sparse multifrontal solver MUMPS

Abstract

Summary Efficient frequency-domain Full Waveform Inversion (FWI) can be applied on long-offset/wide-azimuth stationary-recording seabed acquisitions carried out with ocean-bottom cables (OBC) and ocean bottom nodes (OBN) since the wide angular illumination provided by these surveys allows for limiting the inversion to a few discrete frequencies. In the frequency domain, the forward problem is a boundary value problem requiring the solution of large and sparse linear systems with multiple right-hand sides. In this study, we revisit the potential of the massively-parallel sparse multifrontal solver MUMPS to perform efficiently the multi-source forward problem of 3D visco-acoustic FWI. The execution time and memory consumption of the solver are further improved by exploiting the low rank properties of the sub-blocks of the dense frontal matrices, the sparsity of the right-hand sides (seismic sources) and the work in progress on the use of mixed precision arithmetic. We revisit a 3D OBC case study from the North Sea in the 3.5~Hz-13~Hz frequency band using between 10 and 70 nodes of the Jean-Zay supercomputer of IDRIS and show that, even without exploiting low rank properties, problems involving 50 millions of unknowns and probably more can be tackled today with this technology.