Very mysterious. (Well, not all that mysterious if you know the park is right next to NMIT. We assume students are practising some sort of esoteric skill, like the time we saw groups with chain saws up the trees, looking like a flock of huge birds.)
At last, the mystery has been solved. They must be marks to show the horticulture students, or the park rangers, where to spray, so that indigenous plants can be put in.
I dislike the use of herbicides, especially Roundup, but I do realise it's an effective way to restore indigenous plantings.
Once we knew what to look for, it was clear that the grass was indeed dying. (We made sure Penny didn't walk on any place we knew had been sprayed.)
It will be interesting over the next few months to see the new plants grow.