Pre-stack seismic inversion is used to calculate elastic parameters, including P-wave and S-wave velocities, as well as densities. These parameters play an integral role in the characterization of reservoirs, thereby enhancing the exploration and production process. Deep learning-based seismic inversion does not need a known physical system and can give satisfactory results with sufficient training data. The acquisition of such datasets for seismic inversion poses a significant challenge due to the exorbitant costs associated with drilling activities. Integrating domain knowledge, physical systems, and well log data into a deep learning-based seismic inversion framework is crucial for improving its efficiency and effectiveness. Nevertheless, existing data-driven approaches do not adequately exploit such information, thereby constraining their overall performance and applicability. Therefore, we develop a double dual neural network structure built upon the closed-loop neural network framework, which incorporates both physics and model information to mitigate the dependency on extensive labeled datasets. The information from the different domains is linked through a loss function, where one dual network is responsible for constraining the inversion results using physics information to ensure the physics consistency of the predictions, and the other dual network is responsible for constraining the inversion results using a priori model information to enhance the reliability of the predictions. The method makes full use of well-log data for network training when wells are available, as well as providing unsupervised learning and inversion under well-free conditions. The integration of qualitative and quantitative analyses proves instrumental in demonstrating the effectiveness of the proposed methodology through the use of synthetic and field pre-stack examples.