LGT TURNED FROM ASSIGNED SID HDG TOWARD MOUNTAINS WHILE STILL BELOW MIN XING ALT.

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OUR CLRNC AS RECEIVED FROM SLC CLRNC DELIVERY WAS '...TO STL VIA SLC 3 DEP THEN AS FILED EXCEPT CHANGE RTE TO READ J154 OCS; MAINTAIN 8000; DEP FREQ 135.5; SQUAWK XXXX.' AFTER RECEIVING THE CLRNC; THE CAPT AND FO DISCUSSED THE DEP AND RTE CHANGE. I WAS ABLE TO REVIEW THE RTE CHANGE ON MY CHART; BUT AS FLT ENGINEER; I DO NOT POSSESS A COPY OF THE SID. CREW MEMBER DUTIES FOR THIS LEG WERE CAPT AS PNF AND FO AS PF. AFTER BEING CLRED INTO POS AND HOLD ON RWY 34R; THE TWR CTLR ADVISED '...CLRED FOR TKOF.' AFTER BEING SWITCHED TO DEP CTL; WE WERE CLRED TO 16000 FT. DURING THIS PORTION OF THE CLB; WHILE IN IMC AND WITH TSTMS RPTED ON SLC ATIS; THE CAPT WAS ADJUSTING THE WX RADAR AND I WAS OBSERVING THE TEMP SINCE ENG ANTI ICE WAS ON AND THE TOTAL AIR TEMP WAS INCREASING. AT APPROX 8000 TO 9000 FT MSL; THE FO INITIATED A R TURN (FROM OUR HDG OF 340 DEG) AND; BASED ON OUR PROX TO SLC VOR; THE CAPT AND I ASSUMED THAT THE TURN WAS TO INTERCEPT J154 EBOUND. DURING THE TURN DEP CTL ASKED US TO STATE OUR HDG. THE CAPT REPLIED 'COMING THROUGH 030 DEG IN THE TURN'; WHEREBY THE CTLR ISSUED 'AN IMMEDIATE L TURN TO 340 DEGS; EXPEDITE CLB THROUGH 12000.' A L TURN WAS INITIATED AT A 30 DEG BANK WHILE CLBING AT 210 KIAS. DURING THE TURN BACK TO 340 DEGS; THE RADAR ALTIMETER INDICATORS REMAINED OUT OF VIEW (ABOVE 2500 FT AGL). DEP CTL INFORMED US THAT WE WERE TO MAINTAIN RWY HDG UNTIL RECEIVING VECTORS ON COURSE. A SUBSEQUENT REVIEW OF THE SLC 3 SID CONFIRMED THIS. SUPPLEMENTAL INFO FROM ACN 193934: WHEN DEP FIRST QUESTIONED US WE WERE AT 3 DME NE OF SLC VOR CLBING THROUGH 8800 FT. I THINK THAT THERE WAS CONFUSION WHEN WE WERE CLRED VIA SLC #3 EXCEPT TO JOIN J-154. THE WX WAS IFR.