There are 2 primary ways you can reduce soil compaction:
1) Expand the area where mulched is applied under a tree.
As the mulch decomposes it will break up some of that compaction. It will also create an above ground buffer which acts like a spring to prevent the soil from experiencing the full impact from the sources of compaction, namely machinery and frequent foot traffic.
In the ideal world the area mulched under a tree would extend out as far as the branch tips or even further. This option isn’t always practical as oftentimes there simply isn’t enough space to do so. There usually are too many obstacles competing with where mulch can go from sheds to patios to driveways to fences.
Which leads to another option…
2) Air Spading
Air spading involves the use of high pressure air focused directly into the soil, in line with all the primary roots of the tree. When performed in multiple locations under the trees canopy it fractures the soil allowing for air and water to circulate better. Air spading is opening up the underground network to provide more room for the exchange of nutrients between the soil and the rest of the tree.