Nowadays ships are usually equipped with a system of marine instruments, one of which is an Automatic Identification System (AIS) transponder. The availability of the global AIS ship tracking data opened the possibilities to develop maritime security far beyond the simple collision prevention. The research work summarized in this thesis explores this opportunity, with the aim of developing an intuitive and comprehensible method for traffic modeling and anomaly detection in the maritime domain. The novelty of the method lays in employing the technique of artificial potential fields. The general idea is for the potentials to represent typical patterns of vessels' behaviors. A conflict between potentials, which have been observed in the past, and the potential of a vessel currently in motion, indicates an anomaly. The developed potential field based method has been examined using a web-based anomaly detection system STRAND (for Seafaring TRansport ANomaly Detection). Its applicability has been demonstrated in several publications, examining its scalability, modeling capabilities and detection performance. The experimental investigations led to identifying optimal detection resolution for different traffic areas (open sea, harbor and river), and extracting traffic rules, e.g., with regard to speed limits and course, i.e., right-hand sailing rule. The map-based display of modeled traffic patterns and detection cases has been analyzed as well, using several demonstrative cases. The massive AIS database created for this study, together with a dataset of real traffic incidents, provides an abundance of challenges for future studies.