I thought asparagus liked to be pretty deep, in sandy soil. In fact they recommend you dig a trench, plant it and fill only part way, then add soil later. I guess this way the new plants can find the surface and get some sun, and they adapt to the additions just fine. I don't think it would hurt to fill it in. Probably best to do it while it's dormant, I would think.

You're right tox! I forgot about the trench thingy! I'll do it this fall when I cut them back. Thanks, Nancy

I fill in as it grows until the trench it was planted in is full.

I am not sure if this helps, (but I thought it kinda stupid of me, at first, then I thought it was kinda neat).
When I started my "gus" bed, I didn't wear my good reading glasses and I misread Rodales (organic gardening book) instructions and dug a hole 4 feet down put in a foot of food waste, six inches of soil, the asparagus roots and then filled the whole crater back up with the remaining soil. the next year a few peepers showed up (which I left) and the next year a lot more (which I left) and the third year I started to harvest the 1/2 inch thick stalks, and since I don't like asparagus, my wife said they were good
I did try some this year and as long as I picked and cooked them a few days after they appear they are ok, if I wait too long they can be bitter.
Proving once again that mother nature is forgiving and looks out for idiots and babies.
IALBTC

No danger of that here ryan - it would take me a week to dig 4 ft. down in the clay we live on. :-o