Low-Frequency Prediction Based on Multiscale and Cross-Scale Deep Networks in Full-Waveform Inversion

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The well-known cycle-skipping problem in full-waveform inversion (FWI) can make the iterative solution fall into local minima and produce an undesired inverted result when reliable low-frequency components in seismic data and a good initial model are not available. The recovery of low-frequency data can effectively solve the cycle-skipping problem. However, hardware limitations have made it difficult to obtain reliable low-frequency components in seismic data. Thus, we adopt a multi-scale and cross-scale convolutional neural network (MCCNN) to build the nonlinear mapping between high-frequency and low-frequency data from synthetic training data sets. The major benefit of MCCNN is that it can fully use the multi-scale and cross-scale information in the high-frequency data to predict the low-frequency data. Several numerical experiments show the effectiveness and benefits of the low-frequency recovery of MCCNN. On the one hand, introducing the in-stage multi-scale and across-stage cross-scale information can accelerate the convergence rate in the training process and improve the low-frequency prediction accuracy. On the other hand, MCCNN has good generalization abilities in predicting the low-frequency data from the Marmousi and Overthrust models, different model sizes, and wavelet types and frequencies. The acoustic FWI results show that the predicted low-frequency data can effectively prevent the inversion from falling into a local minimum and help FWI obtain an accurate velocity model even if we start from a poor initial model.