Here's a hugelkultur-like idea that may be a little better (for well established trees). Within the drip line, bore some holes in the ground (a water hose with a pressure nozzle works great) and then cram them full of all the dead branches that the pecans drop (plus any other rotten
wood laying around). That way, you will be adding organic matter and building up the soil life. It's also less disturbance than digging a big trench at the drip line to bury some wood.
One thing that they do here in Georgia is to
seed the ground under the pecans with crimson clover. The best looking pecan orchards here are the ones that have clover as a ground cover. This is also the time of year to be seeding crimson clover. I bought some last week and seeded the front
yard last weekend.
We've had a really wet year so far, and I'm wondering how big the yield will be. A couple years ago, when we were in drought (not as bad as yours), the pecan crop was very poor.