  The Hellings-Downs (HD) curve plays a crucial role in search for nano-hertz
gravitational waves (GWs) with pulsar timing arrays. We discuss the angular
pattern of correlations for pulsar pairs within a celestial hemisphere. The
hemisphere-averaged correlation curve depends upon the sky location of a GW
compact source like a binary of supermassive black holes. If a single source is
dominant, the variation in the hemisphere-averaged angular correlation is
greatest when the hemisphere has its North Pole at the sky location of the GW
source. Possible GW amplitude and source distance relevant to the current PTAs
by using the hemisphere-averaged correlation are also studied.
