Date: 201606
Local time of day: 1201-1800
Location: PSP.Airport, CA
Flight conditions: VMC
Aircraft: Large Transport
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class E SCT
ATC / advisory: TRACON SCT
Reporter organization: Air Carrier
Reporter function: First Officer; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion
Second reporter function: Pilot Not Flying; Captain
Anomaly: Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Cleared direct SBONO and descend to 7000 feet on the RNAV Visual 13R. Approximately 6-8 miles past SBONO; with the airport and terrain in sight; I initiated a descent to 4000 feet believing the controller had issued us clearance for the RNAV Visual. Passing through approximately 6700 feet the controller asked for confirmation of altitude and indicated that the minimum vectoring altitude was 7000 feet. I corrected pitch and power to recover quickly to 7000 feet. Prior to reaching 7000 feet the controller asked if we had the field in sight; we responded we did and for what I thought was the second time issued approach clearance. I then corrected to descend to 4000 feet approaching TOTAV. The airport and terrain was in sight throughout the sequence of events and the rest of the approach and landing was uneventful.In hindsight; after mentally reviewing the sequence of events; I believe the controller may have said 'Direct SBONO and descend to 7000 feet FOR the RNAV Visual' and I incorrectly interpreted that as approach clearance. While I had no doubt that we had received clearance I had reviewed both the 19-0-1 and 19-0 pages; and briefed the procedure. All that said I would suggest this is a case where I should re-confirm approach clearance prior to leaving 7000 feet.


Second narrative: Upon checking in with SOCAL Approach we were asked what approach we wanted at PSP. We requested the RNAV Visual 13R. He asked again to confirm and we acknowledged. We both understood him then to say we were cleared direct SBONO; maintain 7000; cleared the RNAV Visual RWY 13R; advise the field in sight. First Officer (FO) was flying and passing SBONO we set 4000 for TOTAV and began descent following Vertical Deviation Indicator. We were VMC and FO had just advised me he had the field in sight. Passing approximately 6600 MSL Approach asked our altitude and advised us of a low altitude alert and directed us to climb. We began our climb and advised the field in sight. He then re-cleared us for the RNAV Vis 13R and advised us of a possible pilot deviation. We flew the profile and landed uneventfully.


Synopsis: Flight crew misunderstood ATC routing and altitude clearance for the expected approach procedure. ATC alerted the crew to the fact that they had descended below minimum vectoring altitude. The crew regained the assigned altitude and completed the approach and landing uneventfully.