Efficient progressive transfer learning for full waveform inversion with extrapolated low-frequency reflection seismic data

The low-frequency seismic data provides crucial information for guiding the full-waveform inversion (FWI), especially when strong reflectors exist in the velocity model. However, hardware limitations make it difficult to acquire low-frequency data. To overcome the non-linearity and ill-posedness caused by the absence of the low-frequency data, we develop an efficient progressive transfer learning algorithm for low-frequency extrapolation. The proposed method combines the FWI, the sparsity-promoted bandwidth extension (BWE) algorithm, and the physics-guided data-driven deep learning approach. Compared with pure data-driven learning-based methods and the original progressive transfer learning method without BWE, our proposed algorithm shows better generalization ability. By integrating the physics constraints and the BWE algorithm, the performance of our method is less dependent on the quality of the initial training velocity model and the corresponding training set. We propose a logarithmic transformation to re-balance the loss function to overcome the challenge of predicting the weak reflection low-frequency data. To accelerate the algorithm, we propose a learning-based BWE method for initializing the training set and a truncated FWI method to reduce the iterative workflow’s computational cost. Experimental results show that our method achieves both high efficiency and high accuracy. The subsurface structures below the strong reflectors are successfully reconstructed with our extrapolated low-frequency data.