GPR Full-Waveform Inversion through Adaptive Filtering of Model Parameters and Gradients Using CNN

TL;DR

A novel FWI framework is introduced that incorporates an embedded convolutional neural network to adaptively filter model parameters and gradients and leverages the auto-grad tool of the deep learning library, allowing model values to pass through the CNN module during forward computation and model gradients to pass through the CNN module during backpropagation.

Abstract

GPR full-waveform inversion optimizes the subsurface property model iteratively to match the entire waveform information. However, the model gradients derived from wavefield continuation often contain errors, such as ghost values and excessively large values at transmitter and receiver points. Furthermore, models updated based on these gradients frequently exhibit unclear characterization of anomalous bodies or false anomalies, making it challenging to obtain accurate inversion results. To address these issues, we introduced a novel full-waveform inversion (FWI) framework that incorporates an embedded convolutional neural network (CNN) to adaptively filter model parameters and gradients. Specifically, we embedded the CNN module before the forward modeling process and ensured the entire FWI process remains differentiable. This design leverages the auto-grad tool of the deep learning library, allowing model values to pass through the CNN module during forward computation and model gradients to pass through the CNN module during backpropagation. Experiments have shown that filtering the model parameters during forward computation and the model gradients during backpropagation can ultimately yield high-quality inversion results.

Figures (6)

• Figure 1: The proposed FWI_CNN framework introduces a CNN module, represented by the blue shaded area, to filter model parameters and gradients. The red dashed box outlines the main iterative process of FWI_CNN, while the black dashed box denotes the main iterative process of conventional FWI. If the blue shaded area is removed from FWI_CNN, the remaining framework corresponds to the conventional FWI process. The entire FWI_CNN framework is fully differentiable, allowing it to leverage deep learning libraries’ backpropagation tools to optimize both model parameters and CNN parameters simultaneously. The forward computation and backpropagation processes are indicated by blue and red arrows, respectively.
• Figure 2: Computation graph for the convolution operation of a CNN layer.
• Figure 3: Comparison of the filter effects for model parameters and gradients by the CNN module. From top to bottom are the Karst cave model, the fracture model and the fault model. From left to right are the real model, grad before CNN, grad after CNN, model before CNN and model after CNN. To facilitate comparison with the real model, post-processing steps such as clipping and scaling were applied to both the model before CNN and the model after CNN to standardize the color maps.
• Figure 4: The structure of CNN module. The network consists of four modules: two downsampling modules and two upsampling modules, ultimately producing an output $m'_k$ with the same shape as the input model parameters $m_k$.
• Figure 5: The visual comparison of inversion results is shown as follows: from left to right are the real model, the inversion results for conventional FWI, FWI_TV and FWI_CNN. From top to bottom are the Karst cave model, the fracture model and the fault model. Consistent with Fig. \ref{['grad']}, post-processing operations, including clipping and scaling, were applied to the results to standardize the color maps for better comparison with the real model.