NCT Controller described a descent below MVA when an arrival on the JAWWS2 STAR was at 3;000 in lieu of the standard 8;000; the Supervisor caught the error and the aircraft was issued a climb clearance.

Narrative

On-the-job training was being administered by myself on Licke/Hooks when the FLM on duty queried the CPC-in-training (CPC-IT) about the altitude of an air carrier on the JAWWS 2 arrival to SJC. The aircraft was between GILRO Intersection and WVI airport and the data block indicated 030. The CPC-IT queried the pilot and the pilot confirmed he was at 030. The aircraft was westbound leaving a 040 MVA; entering a 045 MVA. The CPC-IT told the pilot to continue on his westbound heading and climbed him to 060 for the MVA. Normally; Licke receives jets on the JAWWS 2 arrival at or descending to 080; so when the aircraft checked in on frequency; neither me nor the CPC-IT caught the aircraft reporting his descent to 030. The CPC-IT issued the current SJC altimeter and went back to sequencing the SJC arrivals closer to SJC. Recommendation; as a trainer; I should have caught the incorrect altitude when the air carrier checked in on Licke frequency. The CPC-IT is progressing well with his/her training; so I was more focused on his sequencing techniques than what the aircraft stated when he checked in.