Extrapolation of Low Wavenumbers in FWI Gradients by a Deep Convolutional Neural Network

Seismic full-waveform inversion (FWI) as a non-linear, iterative optimization benefits from low-frequency data to constrain low-wavenumber model updates and to improve model convergence. However, low-frequency data is often limited in active seismic acquisitions. Using a model-domain approach, we attempt to generate low-wavenumber model updates from existing gradients at higher frequencies within a deep learning framework. Namely, we train a convolutional neural network (CNN) to provide missing FWI model updates associated with low-frequency data from higher frequency updates. We test this technique on the Marmousi II model and quantify the goodness of fit of the inversion result using an R2 score model misfit. We observe that predicted low-wavenumber updates differ significantly from model updates using actual low-frequency data. However, comparing the final models of the corresponding multi-scale strategy FWIs we find that resulting differences are negligible.