Efficient 3-D frequency-domain mono-parameter full-waveform inversion of ocean-bottom cable data: application to Valhall in the visco-acoustic vertical transverse isotropic approximation

Computationally efficient 3-D frequency-domain full waveform inversion (FWI) is applied to ocean-bottom cable data from the Valhall oil field in the visco-acoustic vertical transverse isotropic (VTI) approximation. Frequency-domain seismic modelling is performed with a parallel sparse direct solver on a limited number of computer nodes. A multiscale imaging is performed by successive inversions of single frequencies in the 3.5-10 Hz frequency band. The vertical wave speed is updated during FWI while density, quality factor Q(P) and anisotropic Thomsen's parameters delta and epsilon are kept fixed to their initial values. The final FWI model shows the resolution improvement that was achieved compared to the initial model that was built by reflection traveltime tomography. This FWI model shows a glacial channel system at 175 m depth, the footprint of drifting icebergs on the palaeo-seafloor at 500 m depth, a detailed view of a gas cloud at 1 km depth and the base cretaceous reflector at 3.5 km depth. The relevance of the FWI model is assessed by frequency-domain and time-domain seismic modelling and source wavelet estimation. The agreement between the modelled and recorded data in the frequency domain is excellent up to 10 Hz although amplitudes of modelled wavefields propagating across the gas cloud are overestimated. This might highlight the footprint of attenuation, whose absorption effects are underestimated by the homogeneous background Q(P) model (Q(P) = 200). The match between recorded and modelled time-domain seismograms suggests that the inversion was not significantly hampered by cycle skipping. However, late arrivals in the synthetic seismograms, computed without attenuation and with a source wavelet estimated from short-offset early arrivals, arrive 40ms earlier than the recorded seismograms. This might result from dispersion effects related to attenuation. The repeatability of the source wavelets inferred from data that are weighted by a linear gain with offset is dramatically improved when they are estimated in the FWI model rather than in the smooth initial model. The two source wavelets, estimated in the FWI model from data with and without offset gain, show a 40ms time-shift, which is consistent with the previous analysis of the time-domain seismograms. The computational efficiency of our frequency-domain approach is assessed against a recent time-domain FWI case study performed in a similar geological environment. This analysis highlights the efficiency of the frequency-domain approach to process a large number of sources and receivers with limited computational resources, thanks to the efficiency of the substitution step performed by the direct solver. This efficiency can be further improved by using a block-low rank version of the multifrontal solver and by exploiting the sparsity of the source vectors during the substitution step. Future work will aim to update attenuation and density at the same time of the vertical wave speed.