Transfer learning for low frequency extrapolation from shot gathers for FWI applications

Low-frequency data proved to be crucial for robust full-waveform inversion (FWI) applications. However, acquiring those data in the field is a challenging and costly task. Deep neural networks can be trained to extrapolate missing low frequencies, but no optimal network configuration exists. Therefore, the search for an acceptable network architecture is a tedious empirical task whose outcome heavily affects the performance of the application. Here, we propose and utilize transfer learning to reduce the computational efforts otherwise spent on an optimal architecture search and an initial network training. We re-train the light-weight MobileNet convolutional network to infer low-frequency data from a frequency-domain representation of the individual shot-gathers, which leads to an efficient, yet accurate inference of low frequencies according to wavenumber theory. In particular, we show that the extrapolated 0.25 - 1 Hz from 2-4.5 Hz data are accurate enough for acoustic FWI on part of the original BP 2004 model and the Marmousi II model of double scale. We bridge the gap between the 1 Hz predicted and the 2 Hz modeled data by the application of a Sobolev space norm regularization.