Medium Large Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Other / Unknown; Situational Awareness
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance
Human Factors
Aircraft X was in the downwind at 110. My instructions were 'Reduce speed to one eight zero then descend and maintain nine thousand.' Aircraft X read back the clearance correctly. I later observed Aircraft X at 082 and assigned 085 to meet the MVA requirement. Aircraft X climbed back up to 085. Separation with terrain was lost. I should have noticed the incorrect altitude sooner. Aircraft X was 800 feet below their assigned altitude before I noticed it and took action. I also did not issue a safety alert. Although in my opinion 080 is not an unsafe altitude with terrain in this area; there are other factors such as mountain wave and canyon winds that could cause additional safety risks for the aircraft. I do not know what could have been done in the cockpit to prevent the event. Perhaps if they were unsure of the altitude assignment; they could have requested that I verify the altitude assignment.
S56 TRACON Controller reported aircraft descended below clearance altitude and entered a higher MVA.