CITATION FO REPORTS DESCENDING BELOW MSA WHILE VISUALLY SEARCHING FOR TVL ARPT.

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WHILE DSNDING FOR TVL WE REQUESTED VECTORS HOPING TO GET THE VISUAL APCH. WE THEN DECIDED SINCE WE WERE BOTH UNFAMILIAR WITH THE AREA WE SHOULD ASK FOR THE LDA/DME-1 RWY 18. WE THEN RECEIVED A VECTOR AND LOWER ALT FOR THE LDA/DME-1 RWY 18 APCH AT TVL. WE WERE ASKED BY CTR IF WE WERE GOING TO BE ABLE TO MAKE THE APCH FROM THERE. WE DECIDED THEY MUST THINK WE ARE TOO HIGH TO MAKE THE DSCNT. WE RESPONDED INDICATING WE WOULD BE ABLE TO MAKE IT. WE WERE HANDED OFF TO RENO APCH. WE WERE VMC AND THE CAPT STATED; THIS IS THE LAKE (BY THE ARPT). I BELIEVED I COULD SEE THE RWY AND STATED WHERE I THOUGHT IT WAS. THE CAPT STATED THE ARPT WOULD NOT BE IN THE POS INDICATED. WE LOOKED AT THE APCH PLATE AND AGREED IT WAS NOT THE ARPT I WAS SEEING. THE CAPT THEN INITIATED A DSCNT OVER THE LAKE. I POINTED OUT WE HAD NOT INTERCEPTED THE LDA AND WERE NOT RECEIVING ANY DME. I STATED WE SHOULD NOT DSND UNTIL WE ARE ON THE LDA AND HAD REACHED A STEP DOWN POINT. THE CAPT INDICATED WE WERE VISUAL SO IT DID NOT MATTER. RENO APCH CALLED US AND TOLD US TO CHK ALT AND GAVE US AN ALTIMETER SETTING. RENO APCH THEN CALLED US AND STATED AN ALT ALERT; STATED THE MINIMUM ALT; AND WHAT ALT THEY WERE SHOWING US AT. THE CAPT IMMEDIATELY CLBED TO THE MINIMUM ALT. WE THEN REALIZED THE LAKE WE WERE DSNDING OVER WAS NOT THE LAKE BY THE ARPT WE WERE LNDG AT. WE HAD BEEN DSNDING OVER A SMALLER LAKE TO THE NE. CONTRIBUTING FACTORS: NOT ADHERING TO SOP. LOSS OF SITUATIONAL AWARENESS. LACK OF CRM. FATIGUE.