Small Aircraft; Low Wing; 1 Eng; Fixed Gear
Distraction
ATC Issue All Types; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Human Factors; Environment - Non Weather Related
I was the Trainer. Trainee was talking to Aircraft X and Aircraft Y inbound and separating Aircraft Y; from a non participating VFR aircraft. Aircraft X went below the MVA while we were focused on other duties. Once the low altitude alarm went off; the Trainee issued instructions to climb Aircraft X and vector them away from the obstruction. Aircraft X pilot told us that he believed he had already been cleared for the visual approach; which is why he descended.This was just an instance of us being distracted from the scenario and made a mistake. However; due to the Low Altitude alert; we were able to recover in a timely manner.
TRACON instructor reported an aircraft went into a higher MVA; the MSAW alert went off and the controllers turned and climbed the aircraft. The pilot reported they thought they were cleared for the Visual Approach; which is why they descended.