1. 120731 VAC (UI&YS) KAGRA Vacuum System Layout ** How to decide the positions of optical instruments in the tunnel map? Coordinate of the KAGRA interferometer Tunnel NO.100 XNO.130 YNO.130 Benchmark

2. 120731 VAC (UI&YS) KAGRA Vacuum System Layout Tunnel map coordinate (two-dimension) NO. 100 Ho=373 m (45705.612, 12491.972) XNO. 130 Ho=382 m (48311.858, 11006.212 ) 3000 m ** Benchmarks are set based on geodetic survey. YNO. 130 Ho=362 m (47191.372, 15098.218) Benchmark ** Positions of these benchmarks is described by the terms of X, Y, and Orthometric height (Ho). Gauss-Kluegel projection

3. ** C onvert the two-dimensional values to the three-dimensional ones. KAGRA Vacuum System Layout 120731 VAC (UI&YS) Tunnel map coordinate (Xmap, Ymap, Ho) Latitude, Longitude, Height (B, L, H+He=H+Hg+Ho) Geocentric coordinate (X, Y, Z) Takayama origin, zone VII, Japan Ho: height from geoid surface H; radius of GRS80 of ellipsoid earth Hg; height of geoid surface from GRS80 surface He(ellipsoid height) = Ho(orthometric height) + Hg(geoid height) Z X Y Xmap Ymap B L H GRS80 Tunnel map coordinateGeocentric coordinate X mapY mapHoHgLatitudeLongitudeHo+HgXYZ NO.100 45705.61212491.972372.00040.9809362442.69671371821.4418412.9809-3777335.3233484897.7613765312.972 XNO.130 48311.85811006.212362.00040.8067362607.32251371721.9349402.8067-3775185.6443484931.1983767406.006 YNO.130 47191.37215098.218382.00041.1138362530.76771372006.1631423.1138-3778463.2273482388.8643766511.429

4. x y Yopt horizontal plane at center room horizontal plane at X end Y arm optical plane of interferometer X arm Xopt O (BS) horizontal plane at Y end ** Coordinate of the KAGRA interferometer is inclined by 1/300 against horizontal plane at center room. KAGRA Vacuum System Layout 120731 VAC (UI&YS) Coordinate of the KAGRA interferometer XY BS 00 IXV 26506.96575748010000-16.38063719570170 EXV 3026490.296029720000 00 -16.38063719570170 IYV -7.3324946184763923221.84698866390000 EYV 26.00065355565930 3023205.184275680000 00 ** X end room has a higher altitude and Y end room has a lower one, than that of horizontal plane at center room.

5. KAGRA Vacuum System Layout 120731 VAC (UI&YS) Tunnel map coordinateGeocentric coordinate X mapY mapHoHgLatitudeLongitudeHo+HgXYZ NO. 100 45705.61212491.972372.00040.9809 362442.696 7 1371821.441 8 412.9809 - 3777335.323 3484897.7613765312.972 XNO. 130 48311.85811006.212362.00040.8067 362607.322 5 1371721.934 9 402.8067 - 3775185.644 3484931.1983767406.006 XNO. 130+27 48331.83910994.821361.92840.8052 362607.971 2 1371721.478 6 402.7332 - 3775169.165 3484931.4543767422.050 YNO. 130 47191.37215098.218382.00041.1138 362530.767 7 1372006.163 1 423.1138 - 3778463.227 3482388.8643766511.429 YNO. 130+23 47204.74315121.674382.09541.1152 362531.200 2 1372007.105 7 423.2102 - 3778473.377 3482366.2853766522.214 Coordinate of the KAGRA interferometer Geocentric coordinate XYXYZ BS 00 Calculating now IXV 26506.96575748010000-16.38063719570170 EXV 3026490.296029720000 00 -16.38063719570170 IYV -7.3324946184763923221.84698866390000 EYV 26.00065355565930 3023205.184275680000 00 ** We are calculating exact each coordinate value of optical instruments on KAGRA tunnel.