Progressive transfer learning for low frequency data prediction in full waveform inversion

To effectively overcome the cycle-skipping issue in full-waveform inversion (FWI), we have developed a deep neural network (DNN) approach to predict the absent low-frequency (LF) components by exploiting the hidden physical relation connecting the LF and high-frequency (HF) data. To efficiently solve this challenging nonlinear regression problem, two novel strategies are proposed to design the DNN architecture and to optimize the learning process: (1) the dual data feed structure and (2) progressive transfer learning. With the dual data feed structure, not only the HF data, but also the corresponding beat tone data, are fed into the DNN to relieve the burden of feature extraction. The second strategy, progressive transfer learning, enables us to train the DNN using a single evolving training data set. Within the framework of progressive transfer learning, the training data set continuously evolves in an iterative manner by gradually retrieving the subsurface information through the physics-based inversion module, progressively enhancing the prediction accuracy of the DNN and propelling the inversion process out of the local minima. The synthetic numerical experiments suggest that, without any a priori geologic information, the LF data predicted by the progressive transfer learning are sufficiently accurate for an FWI engine to produce reliable subsurface velocity models free of cycle-skipping artifacts.