Joint Inversion of GPR and VES Data Using Physics-Guided Siamese Networks

Accurate delineation of subsurface lithological and structural characteristics is essential for applications ranging from groundwater exploration to environmental geophysics. Traditional single-modality inversion techniques often suffer from resolution trade-offs and ambiguity in petrophysical interpretation. In this work, we propose a novel multimodal deep learning framework for the joint inversion of Ground Penetrating Radar (GPR) and Vertical Electrical Sounding (VES) data, enabled through physics-informed Siamese neural network architecture. This network is explicitly designed to learn shared subsurface representations by encoding signal-specific features via dual 1D convolutional pathway, which are subsequently fused into a common latent embedding. From this shared space, the network predicts three key geophysical outputs: (i) layer-wise resistivity, (ii) normalized thicknesses , and (iii) geological model classification from eight lithological types.

To ensure physical consistency between modalities, the architecture incorporates an empirical dielectric–resistivity relationship derived from soil physics literature as a physics-informed regularization loss, coupling the inferred resistivity profile with dielectric behavior. The resistivity head uses a Huber loss on log-transformed outputs to reduce the effect of noise and outliers, while the thickness head is stabilized with Batch Normalization and dropout layers to prevent over fitting. A multi-class cross-entropy loss is used for geological classification, and a joint loss function ensures simultaneous optimization across modalities.

Training is conducted on a synthetically generated dataset comprising 24,000 4-layer models, covering diverse resistivity-thickness scenarios and geological facies. A dedicated subset includes thin-layer configurations, simulating challenging cases where GPR contributes enhanced resolution beyond VES capabilities. The network achieves a classification accuracy of 95.4%, a resistivity RMSE of 1.76 Ω·m, and thickness RMSE of 1.85 m on unseen validation data, validating its predictive performance. An ablation study with three independent random seeds (42, 123, 2025) confirms the network’s stability and generalizability.

Visual comparison of predicted vs. true resistivity and thickness profiles exhibits strong structural alignment, even in geologically complex models. Further, input-output attention diagnostics and multimodal fusion behavior reveal interpretable latent correlations between GPR and VES responses.

This work introduces a scalable and domain-aware inversion framework that learns geophysical realism, respects petrophysical coupling laws, and demonstrates potential for field-deployable AI-assisted subsurface mapping. The integration of empirical physics, attention mechanisms, and synthetic realism places this methodology at the frontier of modern geophysical inversion strategies.