As far as I know, the late Miocene volcano preserved at Sibley Volcanic Reserve doesn’t have a name, so no one will mind if I dub it Sibley Volcano. This is what it’s mostly made of, a dark basaltic lava as exposed in the rock face behind the water tank.
The bullseye pattern is the result of spheroidal weathering. A thick body of fresh, solid rock generally is quickly cracked by sets of joints (a joint is fault that has not yet moved, or a fault is a joint with displacement on it). Joints let groundwater, among other things, into the rock. As the groundwater does its thing on the rock, it works its way into the jointed blocks and, to paraphrase an old Grateful Deadhead saying, the smaller they grow the rounder they get. Spheroidal weathering.
The wonderful rounded granite forms of Joshua Tree National Park result from the same process. They were gradually exposed by erosion and, being coarse-grained granite, they don’t display a dramatic onion-skin structure. This was abruptly exposed by quarrying. It’s a miniature version of the exfoliation domes in the Sierra Nevada granites.
Oakland Geology 
2 April 2009 at 4:18 pm
Hi Andrew,
I don’t have a lot of experience with geology, so forgive me if my question is naive. Does the weathering cause the spheroidal shape all on its own, or is that due to some internal structure of the basalt? Maybe it was a pillow lava, and it formed in rounded layers? Or are the joints really just naturally round, even if the rock has no round characteristics? That is so weird. I wonder why that happens.
-Holly
2 April 2009 at 5:55 pm
Holly, it’s the same reason that a square bar of soap turns round the more you use it: the edges of the block are attacked from two sides, the corners from three sides, the faces from just one side.
6 April 2009 at 9:26 am
Oh, that makes sense! Great explanation. Thanks.
15 May 2009 at 4:35 pm
And the jointing facilitated significant groundwater intrusion, as evidenced by the numerous quartz-filled amygules one finds in the “Sibley basalt” vesicles toward the northern extent of the park trails
22 March 2012 at 4:14 pm
A majority of the ppl in the bay area don’t know about this. I learned this in my Geology course at CC that this volcano is 10 million years old and it has been sealed for years. Amazing, but scary