A full-waveform inversion (FWI) of ground-penetrating radar (GPR) data can be used to effectively obtain the parameters of a shallow subsurface. Introducing the Markov chain Monte Carlo (MCMC) algorithm into the FWI can reduce the dependence on the initial model and obtain the global optimal solution, but it requires a large number of computations. In order to better detect underground targets based on ground-penetrating radar data, this paper proposes a joint scheme of an improved ResNet and an MCMC full-waveform inversion. This scheme combines the Bayesian MCMC algorithm and an improved ResNet to accurately invert the target dielectric permittivity. The introduction of deep learning networks into the forward calculation part of the MCMC inversion algorithm replaced the complex forward simulation process, greatly improving the inversion speed. It is worth noting that the neural network model was an approximation of complex forward modeling, and, therefore, it contained modeling errors. The MCMC method could quantify and explain modeling errors during the inversion process, reducing the impact of modeling errors on the inversion results. Finally, a simulation dataset was constructed for training and testing, and the errors were statistically analyzed. The results showed that this method can accurately reconstruct underground medium targets, and it has strong robustness and efficiency.

This research introduces a new method for performing the full waveform inversion on cross-hole ground-penetrating radar (GPR) data. This method relies on a Markov chain Monte Carlo (MCMC) technique that integrates a CNN-LSTM network. The cross-hole GPR technique is widely used in geophysical prospecting for its ability to obtain high-resolution subsurface information. However, traditional full waveform inversion methods for GPR data often face challenges such as high computational cost and being trapped in local minima. The CNN-LSTM network is capable of capturing spatial and temporal features, which helps to boost the inversion process’s effectiveness. By integrating the CNN-LSTM network into the MCMC method, this proposed approach aims to overcome these limitations. The CNN part of the network can effectively extract spatial features from GPR data, while the LSTM part can capture the temporal dependencies, providing a more in-depth comprehension of the data characteristics. This understanding is then utilized by the MCMC method to sample more efficiently from the model parameters’ posterior distribution. Numerical experiments demonstrate that compared with traditional methods, the CNN-LSTM network has smaller root mean square errors and can effectively perform the full waveform inversion. This study highlights the effectiveness of combining CNN-LSTM networks with MCMC methods for complex data inversion tasks.

Monte Carlo-based sampling methods (MCMC) can be used to solve inverse problems affecting ground penetrating radar (GPR) data. However, due to their high computational complexity, they have not been widely used in practical applications. This article uses neural network methods to replace the computationally complex forward problem of Monte Carlo methods. However, the neural network method is an approximation of the accurate formula method, and this may introduce model errors. In order to reduce the impact of model errors, in this study, we incorporate the Squeeze-and-Excitation (SE) attention mechanism into Convolutional Neural Networks (CNN) to further improve the accuracy of the network. Moreover, with the statistical advantages of the MCMC method, model errors can be explained during the inversion process, further reducing their impact. We apply the proposed method to solve the inversion problem of crosshole ground-penetrating radar travel time data. Compared with commonly used approximate forward models, the method proposed in this paper has better accuracy. The results of data experiments indicate that this method can effectively invert the velocity of underground media.

The traditional hyperbolic Radon transform suffers from the major problem of how to both obtain a high resolution and preserve the amplitude variation with offset (AVO). In the Radon domain, high resolution (sparseness) is a valid criterion. However, if a sparse model is obtained in the Radon domain due to averaging along the offset direction, then it is not possible to preserve the AVO in the inversion data. In addition, hyperbolic Radon transform has a time-variant kernel based on a traditional iterative algorithm, the conjugate gradient (CG), which requires significant computation time. To solve these problems, we propose a Radon transform based on waveform that contains both cycle and amplitude characteristics of seismic waves. The new transform entails creating an upper envelope for the seismic data and computing a preliminary forward Radon transform in the time domain. The forward Radon transform incorporates a priori information by measuring the energy of each slowness (p) trace to obtain the high-resolution result of the Radon domain. For AVO preserving, the proposed method uses polynomials to describe the AVO characteristics in the inverse Radon transform based on the least-squares inversion. Besides amplitude preserving and high resolution, the proposed method avoids using CG and greatly reduces the cost of computing hyperbolic Radon transform in the time domain. In applications to both synthetic and field data, waveform Radon transform (WRT) has a better performance than the conjugate gradient Radon transform (CGRT).