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

For the purpose of effective suppression of the cycle-skipping phenomenon in full waveform inversion (FWI), we developed a Deep Neural Network (DNN) approach to predict the absent low-frequency components by exploiting the implicit relation connecting the low-frequency and high-frequency data through the subsurface geological and geophysical properties. In order to solve this challenging nonlinear regression problem, two novel strategies were proposed to design the DNN architecture and the learning workflow: 1) Dual Data Feed; 2) Progressive Transfer Learning. With the Dual Data Feed structure, both the high-frequency data and the corresponding Beat Tone data are fed into the DNN to relieve the burden of feature extraction, thus reducing the network complexity and the training cost. The second strategy, Progressive Transfer Learning, enables us to unbiasedly train the DNN using a single training dataset. Unlike most established deep learning approaches where the training datasets are fixed, within the framework of the Progressive Transfer Learning, the training dataset evolves in an iterative manner while gradually absorbing the subsurface information retrieved by the physics-based inversion module, progressively enhancing the prediction accuracy of the DNN and propelling the FWI process out of the local minima. The Progressive Transfer Learning, alternatingly updating the training velocity model and the DNN parameters in a complementary fashion toward convergence, saves us from being overwhelmed by the otherwise tremendous amount of training data, and avoids the underfitting and biased sampling issues. The numerical experiments validated that, without any a priori geological information, the low-frequency data predicted by the Progressive Transfer Learning are sufficiently accurate for an FWI engine to produce reliable subsurface velocity models free of cycle-skipping-induced artifacts.