A BAYESIAN PHYSICS-DRIVEN NEURAL NETWORK FOR ELASTIC LOG PREDICTION VIA CROSS-BASIN TRANSFER LEARNING

Driven by the demands of reservoir characterization, accurate elastic log prediction remains a critical research priority that bridges rock physical properties with seismic responses for hydrocarbon exploration. Elastic logs are conventionally estimated using rock physics models (RPMs) or, more recently, machine learning (ML) frameworks. However, these RPMs are constrained by idealized assumptions and fail to account for uncertainty, whereas existing ML approaches often lack physical constraints. To address this, Bayesian Neural Networks (BNNs) have proven successful in quantitative log prediction by simultaneously enhancing accuracy and quantifying model uncertainty. We introduce a novel BNN framework designed for the quantitative estimation of elastic properties from well logs. By integrating rock physics constraints via a physics-based loss term derived from synthetic velocity realizations, the proposed method ensures physically consistent predictions and calibrated uncertainty. Using variational inference (VI) governed by the Kullback-Leibler divergence objective function, the framework approximates the neural network’s posterior distribution to generate ensemble predictions that closely align with the target logs. To bridge the gap between velocity measurements and rock physical properties, the network incorporates a physics-dependent loss term derived from various combinations of velocity realizations. Furthermore, we employ cross-domain adaptation via a two-stage fine-tuning transfer learning strategy to predict seismic velocities in an unseen basin. By utilizing selective layer updates and regularization on a limited subset of target well data, the framework adapts the pre-trained BNN without sacrificing prior knowledge, ensuring physically meaningful predictions and physically consistent trends despite domain shift. When tested on field datasets from the Canning Basin (Western Australia) and the Sichuan Basin (China), our proposed approach outperformed the standard BNN, delivering higher correlation coefficients, lower prediction errors, and lower uncertainties. Remarkably, this framework offers a scalable, robust paradigm for subsurface characterization in complex, data-limited regimes by synthesizing physics-informed constraints with cross-domain transfer learning.