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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 article designs an FWI framework based on deep learning, featuring a multifrequency and multiscale fusion strategy. Utilizing a multioutput convolutional neural network (CNN) constructed by the hybrid dilated convolution (HDC), 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 multifrequency 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.

In audio-magnetotellurics (AMT) inversion, the resistivity model derived from data is crucial for understanding geological properties. Current AMT inversion methods such as Gaussian–Newton (GN) and nonlinear conjugate gradient (NLCG) have limitations, including sensitivity to data errors and reliance on initial models, leading to nonuniqueness and slow convergence. To address these issues, we propose an AMT inversion framework incorporating borehole data and geological constraints. By leveraging borehole information and considering geological patterns, we develop three machine learning data construction methods that enhance the stability and speed of the inversion process. However, borehole data acquisition is costly and limited, and it represents geological properties discretely within a narrow range. Relying solely on it or unconstrained inversion can compromise accuracy. Our approach integrates borehole data into the supervised descent method (SDM) inversion, resolving data gaps and model variations. SDM results are then used as initial models for GN inversion. Synthetic and field data examples demonstrate the efficiency and feasibility of our framework, showing rapid convergence and high-quality results. This approach accelerates AMT inversion by effectively using borehole information, providing a practical solution for improving the process.