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As an essential process in subsurface exploration and characterization, estimating elastic properties of the rocks such as compressional wave velocity (Vp), shear wave velocity (Vs) and density from 3D seismic has been a research focus in the past decades and recently is greatly promoted by the advancements in machine learning particularly convolutional neural networks (CNNs). However, most of the CNNs fail to incorporate the priori geophysical rules/principles, such as the AVO response in conventional seismic inversion; correspondingly, they are purely data driven and prone to the overfitting issue when wells are sparse. In this work, we propose integrating angle-stack seismic with well logs by a new CNN architecture, which not only introduces the concept of AVO analysis for constraining the network training but also simulates the process of stacking for enhancing the CNN generalization capability. As demonstrated on the Poseidon dataset, given as few as six wells, the proposed method can build a robust mapping relationship between the near-/mid-/far-stack amplitude and Vp/Vs/Rhob properties and produce the corresponding elastic property models with high lateral consistency throughout Poseidon area. The proposed CNN can be readily modified for accommodating more seismic angle stacks, incorporating more pre-defined geophysical principles, and estimating more elastic properties.