Seismic Porosity Prediction via Semi-Supervised Learning: Integrating a Low-Frequency Model and a Closed-Loop Network Structure

Porosity estimation from seismic data is crucial for understanding subsurface rock properties and enhancing reservoir characterization across Earth and Energy sciences. Although deep learning (DL) has emerged as a promising solution for porosity prediction, conventional supervised approaches face inherent limitations in seismic applications due to restricted seismic bandwidth constraints and insufficient labeled training data. To address these challenges, we propose a semi-supervised strategy that integrates a low-frequency porosity model (LowF) porosity model and a domain-specific closed-loop (CL) network structure. The LowF component, constructed through geostatistical modeling, incorporates essential geological prior knowledge to compensate for bandwidth limitations of seismic data. Concurrently, the CL structure (seismic-to-porosity-to-seismic) fully uses the abundant unlabeled seismic data while enforcing direct constraints on porosity predictions. We also perform a supervised porosity-to-seismic mapping to optimize the CL process. Comparative analyses through cross-well masked tests demonstrate the proposed method’s superior performance over a conventional supervised learning approach. Furthermore, the incorporation of LowF and CL remarkably enhances the geological continuity and stability of the seismic porosity predictions. Purely supervised model yields geologically implausible predictions, CL-only implementation fails to capture vertical porosity trends, and LowF-only model may introduce bias. The proposed strategy offers insights into various geophysical inversion problems, particularly valuable for reservoir characterization with limited well constraints.