Hello soares, interesting pic, for me it doesn't change the advice replace the removed soil, incorporate compost and spread mulch treat the soil with the diluted solutions and the molasses. To locate certified tree care services and consultants in your area visit here;
http://www.treesaregood.com/FindTree...reService.aspx
and follow the step by step directions.
Remember despite having cut some of the roots radiating out from the stem the remaining roots still have a connection with the soil profile beneath, there are no "tap roots" as such but there are numerous sinker roots heading down from the laterals, whilst these remain intact the tree will recover, though any significant root damage always reduces the life span of the tree, and increases its vulnerability to insect and fungal pathogens.