An Improved Semi-Supervised Clustering Method with Differential Privacy Technology for Seismic Attributes Analysis Problems

Seismic attribute analysis is inherently confronted with three intertwined challenges: scarce labels, high dimensionality and, critically, data sensitivity that can expose reservoir locations and well positions to privacy breaches. To reconcile accurate clustering with strict confidentiality, we propose Differential privacy pairwise constrained K-means (DP-PCSKM), a semi-supervised clustering framework that fuses sparse-weighted K-means with Gaussian differential privacy (GDP). Pairwise constraints and feature selection are embedded into a single objective, enabling simultaneous cluster refinement and attribute weighting. GDP noise is carefully injected into both centroid and weight-update steps, while a soft-threshold operator reduces dimensionality—and thus sensitivity—before perturbation, yielding a controllable privacy-utility trade-off. Blind well tests conducted on two 2-D horizon slices extracted from real 3-D seismic volumes (containing 398,871 and 274,284 grid points, respectively) demonstrate that, under strong privacy protection conditions ( μ = 0.6 ), the DP-PCSKM algorithm outperforms other DP-based methods in terms of both visualization and accuracy, proving that strong privacy protection has only a minor impact on geological interpretability.