NO API 653 deals ONLY with aboveground storage tanks
For horizontal and vertical AST UL 142 is the fabrication standard and Steel Tank Institute SP001 Standard for The Inspection of Aboveground Storage Tanks, 4th Edition Issued July 2006
For UST's fabrication UL 58 Standard for Safety: Steel Underground Tanks for Flammable and Combustible Liquids
API does not have a standard for UST's. They do have API Recommended Practice 1615 Installation of Underground Petroleum Storage Systems and API Standard 2610 Design, Construction, Operation, Maintenance, and Inspection of Terminal & Tank Facilities among others.
Inspection falls under Petroleum Equipment Institute PEI RP900 Recommended Practices for the Inspection and Maintenance of UST Systems
refer:
http://www.epa.gov/swerust1/cmplastc/standard.htm