This thesis presents the underlying probabilistic model, the parameter estimation, and the inference algorithm of NET-VISA, Network Processing Vertically Integrated Seismic Analysis. NET-VISA is an Open Universe Probability Model (OUPM) for seismic events, the transmission of seismic waves through the earth, and their detection (or misdetection) at stations, as well as a model for spurious detections. The probabilistic model allows for seamless integration of various disparate sources of information. Applied in the context of the International Monitoring System (IMS), a global sensor network developed for the Comprehensive Nuclear-Test-Ban Treaty (CTBT), NET-VISA achieves a reduction of around 60% in the number of missed events compared to the currently deployed system. It also finds events that are missed by the human analysts who post-process the IMS output.