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This letter proposes a SInk-initiated Geographic Multicast (SIGM) protocol for mobile sinks in wireless sensor networks. To reduce location updates from sinks to a source and to achieve fast multicast tree construction and data delivery, SIGM allows sinks to construct their own data delivery paths from a source to them and a geographic multicast tree to be automatically constructed by merging the data delivery paths. Then, the source forwards data to the sinks down the multicast tree. This paper also proposes a round-based virtual infrastructure with a radial shape for growing the merging probability of data delivery paths and reducing the reconstruction frequency of the multicast tree due to mobility of sinks.