Fast 3D frequency-domain full waveform inversion with a parallel Block Low-Rank multifrontal direct solver: application to OBC data from the North Sea

Description

Wide-azimuth long-offset OBC/OBN surveys provide a suitable framework to perform computationally-efficient frequency-domain full waveform inversion (FWI) with a few discrete frequencies. Frequency-domain seismic modeling is performed efficiently with moderate computational resources for a large number of sources with a sparse multifrontal direct solver (Gauss-elimination techniques for sparse matrices). Approximate solutions of the time-harmonic wave equation are computed using a Block Low-Rank (BLR) approximation, leading to a significant reduction in the operation count and in the volume of communication during the LU factorization as well as offering a great potential for reduction in the memory demand. Moreover, the sparsity of the seismic source vectors is exploited to speed up the forward elimination step during the computation of the monochromatic wavefields. The relevance and the computational efficiency of the frequency-domain FWI performed in the visco-acoustic VTI approximation is shown with a real 3D OBC case study from the North Sea. The FWI subsurface models show a dramatic resolution improvement relative to the initial model built by reflection traveltime tomography. The amplitude errors introduced in the modeled wavefields by the BLR approximation for different low-rank thresholds have a negligible footprint in the FWI results. With respect to a standard multifrontal sparse direct factorization, and without compromise on the accuracy of the imaging, the BLR approximation can bring a reduction of the LU factor size by a factor up to three. This reduction is not yet exploited to reduce the effective memory usage (ongoing work). The flop reduction can be larger than a factor of 10 and can bring a factor of time reduction of around three. Moreover, this reduction factor tends to increase with frequency, namely with the matrix size. Frequency-domain visco-acoustic VTI FWI can be viewed as an efficient tool to build an initial model for elastic FWI of 4-C OBC data.

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