A B737-300 ON APCH TO TUL 18L FROM THE WEST RCVD GPWS CAUTION AFTER DSNDING EARLY ON A R BASE. NO OBSTACLE WAS SEEN AND PLT ERROR ASSUMED.

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I WAS THE PF. ATC BROUGHT US ALONG THE W SIDE OF TUL FOR A NIGHT VISUAL APCH TO RWY 18L. AFTER DSNDING US TO 4000 FT AND STILL SLIGHTLY SW OF THE FIELD; WE RPTED THE FIELD IN SIGHT. WE WERE THEN CLRED FOR THE VISUAL RWY 18L. WE THEN DSNDED TO 2400 FT. AT ABOUT 6-7 MI (DME FROM ILS) I STARTED A R BASE TURN. AFTER ESTABLISHED ON THE BASE LEG; CORRECTED FOR A STRONG WIND OUT OF THE SW. AT THIS TIME I BELIEVE; I STARTED A GRADUAL DSCNT (WE WERE ALREADY AT FLAPS 5 DEGS) AND SOMEWHERE BTWN RWY 18R AND RWY 18L; THE GPWS CAUTION OBSTACLE WARNING SOUNDED. I ADDED PWR; STARTED A FAIRLY RAPID CLB (DID NOT RECONFIGURE AS WE WERE STILL FLAPS 5 DEGS GEAR UP) UNTIL THE ALERT ENDED. (IT ONLY SOUNDED THE ONE TIME.) WE THEN CONTINUED THE APCH AND LANDED UNEVENTFULLY. AFTER THE EVENT; THE FO AND I TRIED TO FIGURE OUT WHAT OBSTACLE CAUSED THE WARNING. WE COULD FIND NONE THAT WERE CHARTED AT THAT DISTANCE OR LOCATION (BTWN RWY 18R AND RWY 18L). ALSO; ODDLY; THERE WAS NO LOW ALT WARNING FROM ATC. AFTER 5 DAYS OF GOING OVER AND OVER THIS IN MY HEAD; I THINK I HAD SPOTTY SITUATIONAL AWARENESS TO BEGIN WITH AND THEN IT DEGRADED FURTHER. I THINK I STARTED A PREMATURE DSCNT AND WHAT THE GPWS SAW AS AN OBSTACLE WAS REALLY TERRAIN. THE FO AFTERWARDS SAID HE WAS ABOUT TO QUESTION MY ALT BASED ON RADAR ALT; BUT DID NOT. I (WE) HAD SOME CREW PERSONALITY ISSUES THAT IN HINDSIGHT I DID NOT DEAL WITH EFFECTIVELY. SUPPLEMENTAL INFO FROM ACN 761668: WE WERE ON THE VISUAL APCH TO RWY 18L IN TULSA. WHILE ON THE R BASE TO THE RWY AT APPROX 6 MI FROM THE ARPT; WE RECEIVED A GPWS OBSTACLE WARNING. AS WE RECEIVED THE WARNING; WE WERE AT APPROX 1500 FT RA. WE INITIATED A FULL PWR CLB IMMEDIATELY TO APPROX 2500 FT ON THE RA. AT THIS POINT ALL WARNINGS WERE GONE. WE CONTINUED ON THE APCH TO A LNDG WITHOUT FURTHER INCIDENT. I WAS ON THE SIXTH LEG OF MY DAY COMING OFF A REDUCED REST OVERNIGHT; AFTER A 14 HR 30 MIN DUTY DAY THE DAY BEFORE. I SHOULD HAVE BEEN WATCHING THE PF MORE. TO HIS CREDIT; HE RESPONDED WITHOUT ANY DELAY TO THE GPWS WARNING.