Full Waveform Inversion of Multi-frequency GPR data using a Multiscale Approach based on Deep Learning

Ground penetrating radar (GPR) full waveform inversion (FWI) can make full use of kinematics information and dynamics information to achieve the highest theoretical resolution, serving as a promising tool for reconstructing subsurface structures and the physical properties of the medium. However, conventional FWI is constrained by strong nonlinearity, easily falls into the local minimum, and requires multiple forward simulations coupled with intensive adjoint wavefield calculations, which cannot satisfy the requirements of engineering exploration. To mitigate the nonlinearity of the inversion and improve computational efficiency, this paper designs a FWI framework based on deep learning, featuring a multi-frequency and multiscale fusion strategy. Utilizing a multi-output convolutional neural network (CNN) constructed by the hybrid dilated convolution, the receptive field is expanded without incurring additional computational complexity and memory consumption. The dilated CNN predicts multiple sets of available low-frequency data from its respective higher-frequency components of GPR data and integrates the multi-frequency strategy to guide FWI to converge the global minimum. The sizes of computational models are selected according to distinct electromagnetic wave frequencies, and the very deep super-resolution (VDSR) model facilitates the automatic mapping of grids at different scales which reduces unnecessary calculation and boosts inversion efficiency. The synthetic and field cases prove that the proposed framework significantly enhances the spatial resolution, robustness, and efficiency of FWI. The dilated CNN and VDSR constructed have demonstrated robust generalization and noise tolerance abilities, which are suitable for geophysical tasks.