Global-Feature-Fusion and Multiscale Network for Low-Frequency Extrapolation

Full waveform inversion (FWI) is currently the most accurate technique for obtaining the properties of subsurface media. The absence of low frequencies in the observed data caused cycle-skipping phenomenon and poor initial model which affect the convergence of FWI. We propose a global-feature-fusion and multi-scale network (GM-Net) in a way of supervised learning to compensate for the absent low frequency components in the observed data trace by trace. The difficulty of extrapolating frequency is to achieve smoothness and continuity when changing from high frequency signals to low frequency signals, which is visually shown in the reduction and movement of the sidelobes in high-frequency signals and the overall oscillation of the signals is slowed down. For achieving better extrapolation, the encoder-decoder architecture with multi-scale feature extraction is designed as the backbone of the network. For avoiding the loss of information, we propose to perform 1/2 down-sampling on the original input signal separately based on the odd and even time samples, and then concatenate them along the channel dimension. Since 1-dimensional (1D) seismic data is a type of time-series signal and the wavelengths of low frequencies are long, we pay more attention to the relevance of contextual information. Thus, dilated convolution layers, gridding convolution blocks and non-local attention blocks are used to enlarger the receptive field both in time and channel dimensions to extract and fuse global features. Numerical tests both on synthetic data and different types of field marine data demonstrate the feasibility and generalization of our method.