From Physics Constraints to Trustworthy Bayesian Reasoning: Synergies of PINN, iPINN, and iBPINN in Prestack AVO Inversion

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Abstract
Physics-Informed Neural Networks (PINNs) enable unsupervised inversion by integrating seismic forward modeling equations directly into neural network loss functions, operating on angle-domain seismic data. The inverse PINN (iPINN) extends this framework by treating the central frequency of the Ricker wavelet as a trainable parameter, thereby enhancing adaptability to spectral mismatch and improving lateral continuity in inversion results. However, iPINN do not provide uncertainty quantification for their predictions. To address this limitation, a Bayesian Physics-Informed Neural Network (iBPINN) is proposed, incorporating Flipout-based Bayesian convolutional and fully connected layers into the iPINN architecture. Through variational inference, iBPINN enables probabilistic modeling of both network weights and wavelet frequency, yielding not only predicted physical parameters but also posterior standard deviation (std) maps for direct visualization and quantitative assessment of predictive uncertainty. Numerical experiments on the Marmousi2 synthetic model show that PINN achieves rapid convergence for large-scale stratigraphic structures, while iPINN provides more consistent inversion results for deeper layers and weakly sensitive parameters via dynamic frequency correction. iBPINN maintains comparable inversion consistency and, crucially, enables intuitive mapping of predictive uncertainty through std analysis, particularly in fault zones, high-impedance contrasts, and low-SNR regions. Field application to seismic data from a CO₂ injection site further demonstrates that the uncertainty maps provided by iBPINN offer additional insights into fluid substitution and reservoir connectivity. This methodological progression—from PINN (“statistics + logic”), to iPINN (“logic + adaptability”), and ultimately to iBPINN (“logic + reasoning”)—mirrors the broader evolution of AI in geophysical inversion: from statistical models, to logic-embedded frameworks, and finally to reasoning-enhanced architectures. The proposed iBPINN framework thus offers a unified, interpretable, and trustworthy approach for next-generation seismic inversion in complex geological environments.
Funding Information
  • Geophysical Research Institute, Sinopec Shengli Oilfield Company, through the Project “Research on CO2 Flooding Non-Uniformity Time-Lapse Seismic Monitoring Technology” (30200020-23-ZC0613-0023)

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