My cat is a bit too tenacious in digging in his litter box. Not matter how clean it is, no matter how much litter is inside, he spends quite some time digging it, both before and after doing his business. This results in a complete mess, with considerable amount of the litter outside of the the box. The box is big and deep.
How to tell my cat he isn't an archaeologist?
Some cats are diggers and there's not much you can do about it. A covered box is an option but traps odors, so monitor the situation carefully. (One of my cats wouldn't go into a covered box at all, even clean -- claustrophic, I guess.) I just keep a broom and dustpan handy; it's less hassle than cleaning up outside-of-box rebellions.
A suggestion I've seen but never tried myself: get one of those big, deep plastic tubs, and cut an entrance in one of the short sides (down to the normal litterobox height) wide enough for the cats to easily negotiate. Kicked litter will still come out the "door" but the other three sides will be more resistant, and because you're not putting a top on it you don't have odor-containment issues.
Rather than trying to change behavior I use a top entry litter box like the one from Clever cat.
This goes a long way to prevent litter from getting outside of the box. They also make mats that catch it outside of the box.
I don't think you're going to change his behavior and you really, really, want to avoid making the litter box a place where punishment happens. Cleaning up litter is less of a bother than the other options...
At any rate, you might look at getting a covered litter box. These will, help contain litter and come in a few varieties (I've just used the ones that look like little houses).
My kitten used one brand of litter for the first 6 months and when I changed the brand of litter she started digging it out while standing on the outside of the box. I went back to the original litter she stopped. Also I have heard that some cats hate the scented odor eliminating brands because the smell detracts them.
I had a similar situation. My cat would run into her litterbox and start throwing litter around like she was playing with it. My solution was to get one of those covered litter boxes like the one's you can buy at Target or WalMart. She doesn't throw the litter around anymore. And she still seems content.
One thing I do is to buy a sheet of plastic carpet protector (with the pointy side to keep it in place) and cover the area around the box with it. Then scattered litter becomes a broom and dustpan issue rather than a vacuum cleaner issue.
