Seismic model low wavenumber extrapolation by a deep convolutional neural network

Conventional seismic data are naturally mainly sensitive to the very smooth velocity variations that alter transmission traveltimes (low-model wavenumbers) and very abrupt discontinuities that cause reflections (high-model wavenumbers). Full-waveform inversion (FWI) of seismic data inherits this lack of middle model wavenumber illumination, which results into ringy artifacts in the gradients. Multiple methods have been suggested to overcome this issue. Here we tackle the problem of missing wavenumbers with a deep-learning approach. Namely, we filter out the wavenumbers that are expected to be missing from the acquisition design and then train a deep convolutional neural network to provide the missing wavenumbers trace-by-trace. We test several network configurations and several training sets derived from the Marmousi II model. The neural network shows limited capabilities in generalizing from the input data sets. We also report a tradeoff between the generalization abilities and accuracy on the training data set.