SAME RWY ASSIGNMENT ASSUMED. NMAC IN MULTIPLE RWY OP PARALLEL RWYS.

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WE WERE FLYING A 747 FROM JAPAN TO SEA AND WERE ENTERING ELLIOTT BAY FOR A BAY VISUAL TO RWY 16R AT SEA. WE WERE AT 3000 FT WITH CEILING OF ABOUT 3300 FT IN OUR AREA. SEA APCH TOLD US THAT ACR Y WAS 5 MI N OF OUR POS -- WE ONLY ACKNOWLEDGED 'ROGER' AS WE DID NOT HAVE THE ACFT INSIGHT AND IT WAS NOT GIVEN TO US AS TFC. AS WE APCHED BOEING FIELD (5 MI N OF SEA) WE WERE ON THE RWY 16R GS AND WE SUDDENLY NOTICED TFC ON TCASII 800 FT BELOW US. OUR INITIAL REACTION WAS EITHER A TFC ACFT OR BOEING TFC. HOWEVER; THE SEPARATION DECREASED TO 700-600 FT AND AT THAT POINT WE HAD A TCASII RA TO 'STOP DSCNT.' I ASKED SEA TWR IF THEY KNEW THE ACFT WAS AS WE HAD HAD AN RA. SEA SAID THAT IT WAS ACR Y ON A VISUAL TO RWY 16L. SEPARATION GOT TO 400 FT VERT DURING ALL OF THIS AND WHEN I LOOKED DOWN OUT OF MY L SIDE WINDOW ALL I COULD SEE WAS THE L WING OF THE DASH 8. AT NO TIME WERE WE EVER INFORMED OF AN ACFT ON APCH TO RWY 16L WHICH IS A VERY CLOSE PARALLEL RWY. WHAT HAPPENED STAGGERED APCHS WITH CLOSE RWYS? WHAT HAPPENED TO ATC NOTIFYING BOTH ACFT IF PARALLEL VISUALS ARE GOING TO BE USED? HOW CAN VISUAL SEPARATION BE MAINTAINED IF 1 ACFT IS ALLOWED TO PASS ANOTHER? WHAT HAPPENED TO WAKE TURB. CAUTION AND EDUCATION? THE ATC SYS NEEDS TO SLOW DOWN AND EVALUATE ITSELF.