For trees to get old they depend very much on the condition of the root system.
A root system is in some ways a reflection of the canopy as far as composition is concerned. Large-sized roots anchor the tree down and branch out into smaller-sized roots to which the fine fibrous roots are attached. The canopy has large limbs that branch out into smaller limbs which have fine twigs attached. Yet the root system is not an exact mirror image of the tree above ground.
The depth and thus the length of the roots are mainly determined by the depth of the top soil, the density of the sub-soil and by the prevailing water table.
The Westchester region has very shallow top soils and the "sub-soil" is rock. This is the reason why root systems look like pancakes, as illustrated in the pictures. Most of the trees in our area are rooting at a depth between 5 and 12 inches!
There is a general thought that tree roots do not spread any further than the canopy projection of the tree. In soil profiles that allow exclusively shallow rooting such as ours, this is not true. Roots can extend as wide as three times the canopy diameter. Root systems do not adhere to property fence lines and, therefore, it is more than likely that a tree on your property depends on rooting space in your neighbor’s property. Building activity on your property or next door can affect the stability of your tree. Road construction affects the development of healthy root systems as does any form of trenching nearby trees. Impairment of the root system of a tree does affect the tree’s stability and extreme weather conditions, such as those displayed during Hurricane Sandy, quickly reveals which trees have a weakened root system.
Checking out your trees for stability is a good start to reducing the risk of calamities.