  Xu [Jianwei Xu, J. Phys. A: Math. Theor. 45 405304 (2012)] generalized
geometric quantum discord [B.Dakic, V. Vedral, and C . Brukner, Phys. Rev.
Lett. 105 190502 (2010)] to multipartite states and proposed the geometric
global quantum discord. In this paper, we first derive the analytical formulas
of the geometric global quantum discord and geometric quantum discord for
two-qubit X states, respectively. Second, we give five concrete examples to
demonstrate the use of our formulas. Finally, we prove that the geometric
quantum discord is a tight lower bound of the geometric global quantum discord.
