High-resolution pre-stack seismic data are essential for exploring complex and thin-layered reservoirs, and can enhance the reliability of resource evaluation. However, traditional pre-stack seismic data resolution enhancement methods are single-trace processing unable to preserve the amplitude-versus-offset (AVO) relationships, thus compromising the accuracy of subsequent inversion and interpretation. To address the limitation, a novel semi-supervised learning framework is proposed, enhancing the resolution of pre-stack seismic data and preserving AVO relationships of resolution-enhanced seismic data. The proposed approach integrates physical models with well-log data to train neural networks within a hybrid data- and model-driven framework. The labelled dataset, constructed from well-log data and corresponding amplitude-versus-angle (AVA) gathers, eliminates the assumptions inherent in traditional single-trace reflection coefficient inversion methods. Meanwhile, the physics-guided component utilizes unlabeled seismic data to train neural networks, improving the generalizability of the method. Importantly, this approach preserves AVO relationships during resolution enhancement by leveraging well-log data and the Zoeppritz equation that are essential for elastic parameters inversion. Experiments on both two-dimensional synthetic data and a three-dimensional field data demonstrate that the proposed method can stably extend the frequency bandwidth by 40%, proving its feasibility and effectiveness of the proposed approach.