Delineating subsurface interfaces is a crucial step in site selection and characterization for various subsurface applications, such as the geologic carbon sequestration, the radioactive waste disposal and hydrocarbon exploration and production. 3D seismic surveys are widely used for identifying subsurface interfaces and geologic features. Due to the large volumes and the complexity of seismic data, manual interpretation of subsurface interfaces is extremely time-consuming and the interpretation results can be greatly affected by the subjectivity of a particular interpreter. With the latest advances in deep neural networks (DNNs), automatic seismic interpretation methods based on DNNs emerged. Most of the DNN-based seismic interpretation methods are supervised learning methods, which require large amount of labeled data for network training. We have developed an unsupervised learning method with deep fully convolutional networks (FCNs) for rapid subsurface interface identification based on self-learning algorithms, which does not require manual data labeling and specific training datasets. The characteristics of subsurface interfaces are represented as numerical constraints added to the specially designed loss function for constructing the FCN model. Application of the unsupervised learning method on a real seismic dataset collected at a potential CO2 storage site demonstrates that the proposed method yields rapid and accurate identification of subsurface interfaces with relatively strong acoustic impedance contrast in seismic images. The proposed approach may assist in automatic subsurface interface identification in real time and facilitate building geological models for subsurface applications.