Since the men are recruited from all three branches of the military, they are represented in the insignia as:

Air Force

Navy

Army 

The clarification on the Air, Water, Earth and Fire portion is as follows:

The longevity of this unit is represented in the Infinity sign. For as long as there are brave and highlyskilled soldiers willing to fight the good fight, the 8th Special Warfare Logistics Group will exist.

ARTE, MARTE, VIGORE means by skill, valor, and energy.