TRACON controller described a loss of separation with terrain when an incorrect read back was missed...

Attributes
ACN	1209267
Time
Date	201410
Local Time Of Day	1801-2400
Place
Locale Reference	ZZZ.TRACON
State Reference	US
Aircraft 1
Make Model Name	Bombardier Learjet Undifferentiated or Other Model
Operating Under FAR Part	Part 135
Flight Phase	Initial Approach Descent
Route In Use	Vectors
Flight Plan	IFR
Person 1
Function	Approach
Qualification	Air Traffic Control Fully Certified
Person 2
Function	Captain Pilot Flying
Qualification	Flight Crew Air Transport Pilot (ATP)
Experience	Flight Crew Last 90 Days 40 Flight Crew Total 6000 Flight Crew Type 2500
Events
Anomaly	Airspace Violation All Types Deviation - Altitude Excursion From Assigned Altitude Deviation - Procedural Published Material / Policy Deviation - Procedural Clearance

Narrative:

I vectored a lear jet off the arrival to the zzzzz intersection on the runway xx localizer at ZZZ; with a descent clearance to 3000. The aircraft's flight path would take him over an MVA of 3000; that was the reason for the altitude assignment. I observed the aircraft about a mile west of the MVA between 3100-3000 and it appeared to be leveling. The next time I noticed his altitude he was over the MVA through 2200. I issue the low altitude alert and an immediate climb. The aircraft climbed back to 3000 without incident. He stated that I cleared him to descend to 2000 and read it back that way. I thought I clearly assigned him 3000. I should have checked his altitude sooner to verify he did stop at 3000.

Original NASA ASRS Text

Title: TRACON Controller described a loss of separation with terrain when an incorrect read back was missed by ATC.

Narrative: I vectored a Lear Jet off the arrival to the ZZZZZ intersection on the RWY XX localizer at ZZZ; with a descent clearance to 3000. The aircraft's flight path would take him over an MVA of 3000; that was the reason for the altitude assignment. I observed the aircraft about a mile west of the MVA between 3100-3000 and it appeared to be leveling. The next time I noticed his altitude he was over the MVA through 2200. I issue the low altitude alert and an immediate climb. The aircraft climbed back to 3000 without incident. He stated that I cleared him to descend to 2000 and read it back that way. I thought I clearly assigned him 3000. I should have checked his altitude sooner to verify he did stop at 3000.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

TRACON controller described a loss of separation with terrain when an incorrect read back was missed by ATC.