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Distributed acoustic sensing (DAS) is a promising technology for monitoring for instance geo-energy and geohazards applications. However, the large amount of data generated by DAS can be challenging to analyze, and there is a need for developing tools that can process data effectively for decision support systems. We propose a two-step approach for detecting events in DAS data. First, we use DBSCAN to cluster the data into groups of points that are likely to be caused by the same event. Then, we use multiple convolutional neural networks (CNNs) to classify the clusters into different event types. The proposed approach has several advantages: it is able to detect events of arbitrary shape and size, it is robust to noise, and it is able to classify events into a variety of different types. We evaluate the methods on a DAS dataset collected at the Gløshaugen campus of the Norwegian University of Science and Technology. Our results show that the approach can achieve an accuracy of 87% in classifying events.