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In this paper we report a Geant4 simulation study to investigate the characteristic prompt gamma (PG) emission in a water phantom for real-time monitoring of the Bragg peak (BP) during proton beam irradiation. The PG production, emission spatial correlation with the BP, and position preference for detection with respect to the BP have been quantified in different PG energy windows as a function of proton pencil-beam energy from 100 to 200MeV. The PG response to small BP shifts was evaluated using a 2cm-thick slab with different human body materials embedded in a water phantom. Our results show that the prominent characteristic PG emissions of 4.44, 5.21 and 6.13MeV exhibit distinctive correlation with the dose deposition curve. The accuracy in BP position identification using these characteristic PG rays is highly consistent as the beam energy increases from 100 to 200MeV. There exists a position preference for PG detection with respect to the BP position, which has a strong dependence on the proton beam energy and PG energies. It was also observed that a submillimeter shift of the BP position can be realized by using PG signals. These results indicate that the characteristic PG signal is sensitive and reliable for BP tracking. Although the maximization of the PG measurement associated with the BP is difficult, it can be optimized with energy and detection position preferences.