B757 CAPT REPORTS EXERCISING EMERGENCY AUTHORITY TO DEVIATE AROUND TSTMS ON ATLANTIC ROUTE.

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WE HAD JUST RECEIVED A SIGMET FROM ATC ABOUT A LINE OF TSTMS IN OUR AREA. OUR RADAR WAS ON AND WE COULD SEE THE RETURNS ON THE NAV DISPLAY. RETURNS SHOWED TSTMS FOR APPROX 80 MI IN FRONT. WE WERE ON A COURSE DIRECT TO WAYDE. WE WERE EXPERIENCING LIGHT CHOP. I WAS DISCUSSING THE SITUATION WITH THE FLT ATTENDANTS. AS THE CHOP WAS NOW GETTING WORSE; I ADVISED THEM TO BE SEATED. LIGHT CHOP WAS NOW MODERATE. FO WAS ON THE RADIO WITH OCEANIC HF. I ASKED HIM TO GET A CLRNC TO DEVIATE FOR WX. HF RECEPTION WAS VERY POOR WITH A LOT OF STATIC INTERFERENCE AND WAS VERY DIFFICULT TO UNDERSTAND. WE HAD ST ELMO'S FIRE ALL OVER WINDSHIELD. ATC TOLD US TO STANDBY; AGAIN BARELY READABLE. I DID NOT HEAR EVERYTHING THEY SAID BUT FO ADVISED ME UNABLE DUE TO TFC. AT THAT MOMENT WE EXPERIENCED MODERATE TURB; LIGHTNING AND SOME LOSS OF AIRSPD. I IMMEDIATELY DEVIATED TO AVOID THE TSTM. FO THEN ADVISED ATC WE WERE DEVIATING 15 MI L. WE HEARD ATC TO SAY ROGER RPT BACK ON COURSE. LNAV AND VNAV WERE ENGAGED. AS WE DID NOT HAVE AN ATC CLRNC; ONCE ON THE OFFSET; AS WE BELIEVED OUR COURSE WAS 180 DEGS WE CLBED 300-37300 FT. WE WERE LEVEL FOR ABOUT 20 MINS. WHEN CLR OF WX WE RETURNED TO COURSE. AT ABOUT THAT TIME WE RECEIVED A TA FOR TFC WE SAW. ALL LIGHTS WERE ON AND FO TRIED TO CALL ON 123.45 TO NO AVAIL. I INITIATED A RETURN TO ALT. AT ABOUT THAT TIME WE RECEIVED AN RA; MONITOR VERT SPD. I CONTINUED WITH THE DSCNT TO 37000 FT. ACFT WENT OVERHEAD. AT NO TIME WERE WE CLOSER THAN 800 FT TO THE OTHER ACFT. WHEN IT WENT OVERHEAD WE WERE ABOUT 200 FT OFF OUR ALT. AT NO TIME WERE WE OR THE OTHER ACFT IN DANGER AS WE HAD THEM IN VISUAL CONTACT. IT WAS CERTAINLY NOT A LOSS OF SEPARATION. WE WERE FOLLOWING OUR PROCS AS STATED.