Performances of 3D Frequency-Domain Full-Waveform Inversion Based on Frequency-Domain Direct-Solver and Time-Domain Modeling: Application to 3D OBC Data from the Valhall Field

This study addresses the performances of different approaches to tackle 3D frequency-domain Full Waveform Inversion (FWI). FWI is becoming an appealing method to build high resolution velocity models from wide-azimuth seismic data. Three-dimensional frequency-domain solutions of the wave-equation for frequency-domain FWI can be computed with several methods. In the frequency domain, direct or iterative solvers can be used to solve the linear system resulting from the discretization of the wave equation. Alternatively, frequency responses can be computed by time-domain modeling coupled with discrete Fourier transform or phase-sensitive detection method. For a large number of seismic sources, the computational time of all of the methods scale along similar lines to the size of the problem, although the performances of the direct-solver approach is hampered by the limited scalability and the memory demand of the lower-upper decomposition of the forward-problem operator. We implement the direct-solver and the time-domain modeling approaches in 3D acoustic frequency-domain FWI, which is applied to real 3D wide-azimuth OBC data from the Valhall field, North Sea, at low frequencies (< 5 Hz). We show, for this case study, that even if less flexible for high-performance computing, the direct-solver approach is one order of magnitude more efficient in computing time/resources that the time-domain approach, if the signal-to-noise ratio in the data is sufficiently-high to limit the inversion to few frequencies. We finally discuss the performances, pros and cons of both methods, which depend on the wave physics (acoustic versus visco-acoustic, anisotropy, extension toward elastic or visco-elastic), the acquisition geometry (streamer-like versus fixed-spread acquisitions) and the computing architectures (small versus large amount of memory per computing node).