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In this work, we propose a novel method to improve the generalization ability of CNN-based face forgery detectors. Our method considers the feature anomalies of forged faces caused by the prevalent blending operations in face forgery algorithms. Specifically, we propose a weakly supervised Second Order Local Anomaly (SOLA) learning module to mine anomalies in local regions using deep feature maps. SOLA first decomposes the neighborhood of local features by different directions and distances and then calculates the first and second order local anomaly maps which provide more general forgery traces for the classifier. We also propose a Local Enhancement Module (LEM) to improve the discrimination between local features of real and forged regions, so as to ensure accuracy in calculating anomalies. Besides, an improved Adaptive Spatial Rich Model (ASRM) is introduced to help mine subtle noise features via learnable high pass filters. With neither pixel level annotations nor external synthetic data, our method using a simple ResNet18 backbone achieves competitive performances compared with state-of-the-art works when evaluated on unseen forgeries.