  As a precious global resource in quantum information, genuine tripartite
nonlocality(GTN) can be quantified by violating Svetlichny inequality. However,
there is still no analytical expression for the general three-qubit states due
to the difficulty of theoretical calculations. In this paper, we achieve highly
accurate quantization of GTN for arbitrary three-qubit quantum states
numerically. As an example, we study the dynamics of GTN and genuine tripartite
entanglement(GTE) for the W state. Moreover, the complementarity of GTN is
verified by examining the nonlocality between the tripartite and the bipartite.
Finally, we also find a useful strategy to protect the correlation of GTN and
GTE under decoherence by utilizing the Zeno effect.
