Is there anything I can do to keep squirrels from digging up my yard?

https://www.tomcatbrand.com/en-us/library/using-repellents/how-keep-squirrels-out-yard-and-garden

\you can Lay chicken wire just under your Lawn or borders so they can't dig in far......They may be after Bulbs or wanting to plant Acorns .............

a cat or dog

Yes. Squirrels can be a nuisance. If you have food sources that the squirrels like--the squirrels will just keep coming back. I do not feed my birds in the summer--so there is nothing extra available for the squirrels--they stay away. I feel sorry for them in the winter--and they can't dig holes then!! However--if you have trees and shrubs--acorns especially--it would be hard to deter the squirrels unless you are willing to remove those food sources.

There's a lot of good information about preventing predation of gardens & plants on Mother Earth Website. Some excellent advice & reading.

I use cayenne pepper powder and Irish Spring soap shredded to keep the squirrels, chipmunks and rabbits from eating everything. If you have one or two areas that are picked on more often, bait a mouse trap with peanut butter. It will not catch them, but the snap really scares them and they tend to stay away from that area for a good while.

This sound like Chipmunks. I am about to purchase a couple of plastic owls in hopes it will deter these little devils as the claim!

Bring in a "predator": A decoy predator, like a motion-activated owl, can scare chipmunks away from your yard. You can also buy a spray product made from the urine of predator animals like red foxes and cats. The smell will convince chipmunksthat they're in danger - and they'll stay away.