Date: 201911
Local time of day: 1201-1800
Location: MMFR.ARTCC, FO
Flight conditions: VMC
Weather elements / visibility: Thunderstorm
Aircraft: Large Transport
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
ATC / advisory: Center MMFR
Reporter organization: Air Carrier
Reporter function: Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Communication Breakdown; Confusion
Anomaly: ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Contributing factors: Chart Or Publication; Human Factors; Weather; Procedure
Primary problem: Procedure

Narrative: Deviated around weather north of MMSD; FO (First Officer) monitored terrain on ND (Navigation Display) and 'Own Ship' display and minimum required altitudes on Radar Minimum Altitudes chart. I monitored weather radar. Numerous requests from us to ATC to fly a particular heading and/or proceed direct to a fix in order to avoid weather were ignored; misunderstood or responded to slowly by ATC. ATC asked if we could proceed to the IAF (Initial Approach Fix) for the approach (there are 9 IAFs) without specifying which one. We proceeded direct to D346K 11 DME (Distance Measuring Equipment) Fix on VOR DME 2 Runway 16 - not an IAF; it is charted as an IF (Initial Fix) based on weather and terrain and assumed ATC understood. ATC cleared us for the approach; we began descent to 3;600 feet; and maintained; VMC conditions with terrain in sight. ATC asked if we had terrain in sight; provided terrain warning and told us we were supposed to have maintained 5;000 feet. I now believe ATC thought we were proceeding direct to D005O (we initially asked to proceed direct to it and ATC stated he didn't know where that fix was) and cleared us for the visual approach. Numerous aircraft in the area were deviating and having difficulty reading back and understanding clearances. Arrival and approach charts use similar fixes (MARUX and MARAK) which sound similar in Spanish and English and add to the confusion in determining where the best deviation options exist. Numerous other points on charts show in FMS (Flight Management System) database but ATC is apparently unfamiliar with alpha-numeric points. I believe ATC was unsure of where we were (we knew where we were) and which fix we were headed to even though we were in a radar environment. Reconsider naming conventions for fixes on charts and databases and ensure ATC familiarity/access to said points and/or ensure quick way to identify alpha-numeric fixes. Biggest lessons learned: continue emphasizing importance of constant verification of ATC clearances and altitude assignments and use of 'Own Ship' on Radar Minimum Altitudes chart. While it would have helped if ATC stated 'maintain 5;000 feet until established' (ATC did not); confirmation with ATC prior to descent would have alleviated Controller's concerns. Maintaining 5;000 feet until on a published segment of the approach would have left us high but would also have alleviated Controller's concerns.




Synopsis: Air carrier flight crew reported miscommunication with ATC over clearances.