To me, this looks like it is most likely skunk damage. Skunks will sometimes dig in lawns in the spring and fall, but the behavior often ceases pretty quickly. It could indicate you have a high grub population, but not necessarily as skunks will eat a variety of arthropods in lawn soil.

There isn't much in the way of research-based solutions. The efficacy of castor oil based repellants is questionable.

It's worth investigating whether you have a grub problem, but I wouldn't jump straight to treatment.

The damage is fairly superficial, and the behavior will almost certainly stop as we go through spring. 

You can explore a variety of management ideas here: http://ipm.ucanr.edu/PMG/PESTNOTES/pn74118.html

Wishing you good luck.