  Geometric description of quantum correlations are favored for their distinct
physical significance. Geometric discord based on the trace distance and the
Bures distance are shown to be well-defined quantum correlation measures. Here,
we examine their particular dynamical behaviors under independent as well as
common structured reservoirs, and reveal their robustness against decoherence.
We showed that the two well-defined geometric discord may be preserved well, or
even be improved and generated by the noisy process of the common reservoir.
Moreover, we also provided a strategy for long-time preservation of these two
geometric discord in independent reservoirs.
