Simultaneous wavespeed and attenuation reconstruction by complex-valued optimization with adaptive BM3D regularization

International audienceAccurate subsurface imaging by full-waveform inversion (FWI) often requires to account for attenuation. Attenuation can be implemented in frequency-domain FWI with complexvalued velocities. FWI is however traditionally performed in the real domain to update separately real-valued phase velocities and attenuation factor. One reason is that the complexvalued velocity depends on frequency when dispersion effects are taken into account. A drawback of the real-domain inversion is to require a prior mathematical attenuation model, such as the Kolsky-Futterman model, which may introduce some bias in the results. To overcome this issue, we solve the inversion directly in the complex domain. To mitigate non-linearity and account for dispersion, the inversion proceeds over small frequency batches. For each frequency batch, a complex velocity model with an average dispersion term is estimated and is used as initial model for the next frequency-batch inversion. A complex-valued adaptive BM3D denoiser, which does not require any priors about the shape of the targeted medium, is used to mitigate the ill-posedness of the inversion. Numerical results on two synthetic examples show that the regularized inversion manages to reconstruct structures of different shapes, without significant cross-talks between the real velocity and the attenuation factor