Vertical mulching will also lessen damage due to excessive water, preserve necessary aeration during wet periods, allow sub-soil water penetration during dry periods, and promote the formation of fine feeder roots.
To vertically mulch your tree, power auger or drill two inch wide, 18" deep holes in the soil on 12-20" centers under the affected trees starting at about 8 feet from the trunk and out to the drip line of the branches (where fine feeder roots are located). This area is also called the edge of the critical root zone. If you hit a large root, just move over and complete the hole. You should have a grid of holes toward the outer edge of the CRZ.
Fill holes with a mixture of pea gravel, or sand, or a mixture of compost with pea gravel or sand. A 3-4 inch layer of good quality organic mulch, such as aged wood chips, leaves, compost, or pine straw spread evenly over the entire critical root zone will also help trees substantially.