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Radiolocation Errors

There are 5 main sources of error in the Radiolocation method used at Wakulla Springs:

1) Beacon Errors:
Leveling Error: The 22 inch underwater Beacon loops were leveled by the divers to make the magnetic field axis as vertical as possible. The bubble level mounted on each loop was adjusted to be accurate (relative to the loop) to within a fraction of a degree.  If the divers were only able to split the bubble with the levels' circular reference mark, the loop would be tilted 1 degree, which results in an error of 0.5 meter in ground zero at 300 foot (90 meter) depth. This is a worst case. The divers reported that they had little trouble centering the bubble.
Loop Error: The loops are quite precise, giving an error in ground zero location of <0.25mtr at 300 foot (90m) depth in "free space" when perfectly leveled.

2) Error Caused By the Rock: The geology at Wakulla was ideal for Radiolocation, with flat lying limestone extending from well below the cave passages right to the surface with only a little quartz sand on top. The water table was also nearly at the surface, with all of the cave passages filled with water of similar electrical conductivity to the rock. The rock should have little effect on ground Zero location.
It should be noted that at depths greater than 250 feet (76m), "anisotropy" was observed. There were variations in the sharpness of the nulls as ground zero was approached from different directions. There was always one direction where a perfect null was observed. The result was that during the final locating, one Line-of-Position was very precise while the second one (perpendicular) had a broad null, making it less precise. The reason for this effect is not known, but may be caused by vertical joints in the rock aligning in a particular direction.
There was no reasonable way to do an accuracy check. The only practical method (other than drilling a perfectly vertical hole at a Radiolocated point) is to lower a perfectly leveled Beacon loop at least 200 feet (60 m) into a water filled vertical well open to the surface, then locate the vertical magnetic axis with a beacon receiver.  This position can be compared to the line physically supporting the loop to obtain the error. The drawback is that the Radiolocation would likely have to be done from a boat, a difficult task at best!

3) Receiver Error: Due to the extremely high signal strength there is no error due to the receiver electronics. Any errors in the receiver loop and its bubble level can be compensated for by creating a "box" of 4 measurements around ground zero.  After the initial location, the loop was "flipped" 180 degrees and a second location done. A second pair of measurements was done perpendicular to the first. Ground zero was in the center of the box, which varied in size from <0.1 meter up to 0.5 m. There were a few cases near buildings and power lines where interference prevented use of this "boxing" technique (see 4).

4) Ground Zero Location Error: At the usual 300 foot (90m) depth, this error varied from <0.1 meter in the best conditions with no power line or atmospheric noise, to about 1 meter in the worst conditions with both severe noise and anisotropy.

5) In-Cave buoy Error: This is not an actual source of Ground Zero error. In the cave, each Radiolocated point was marked with a reflective buoy floating some height above the floor with its anchor placed exactly where the center of the Beacon was located. This was done so the DWM driver could easily see the points while keeping away from the silt. It is assumed that the driver always pressed the mark button exactly as the SONAR array passed over the buoys.  Any water flow in the tunnels caused the buoys to be offset downstream, which caused a slight shift in the map, but no cross-tunnel errors.  The large main tunnels had little current, allowing the buoys to be several meters above the silt. In the small high-flow B-Tunnel, the buoys were set < 1 meter off the floor which reduced the offset.

Surveying Errors

1) DGPS Error: DGPS was used only for initial Ground Zero locations, usually on the same day as the Radiolocations. These points were subsequently surveyed to centimeter level accuracy when the time and equipment became available and thus did not contribute to the error budget. However, this allowed exact determination of the accuracy of my DGPS setup for 38 Ground Zero points, many of which were deep in old growth forest. It also made an excellent reality check for the precision surveying.  At least 300 fixes were recorded and plotted for each location. The size of the plot was related to how much multipath was present (from the trees), and the average could be found from the center of the plot. This largely eliminated the degradation due to multipath. The measured average DGPS error for 38 points was 3.78 meters.  The USCG error estimate for my setup follows:

USCG  DGPS Error Source
Error (meters)
Error close to Reference Station 
Distance from Reference Station (320km)
2.0 (1.0m for150km distance)
User Equipment Error (typical)

Apparently I was successful in eliminating the effects of multipath!

2) Phase Differential GPS (RTK-GPS) Error: The Trimble Base Station was established to an accuracy of <1cm. The roving Trimble Receiver reported accuracies of <1cm. The combined accuracy is about 1cm (or better). Each point is independent of the others.

3) Total Station Error: This error depends on distance, and is cumulative. For our purposes, the error was no more than a few mm. The dominant error was the RTK-GPS errors in setting the two reference points for the start of each Total Station survey. It is reasonable to assume that Total Station surveyed Ground Zero points are accurate to 1cm.

Total Error

The only significant errors are in using the receiver to do the Ground Zero Locations (#4 above), and in leveling of the Beacon loop by the divers (#1 above).  The Error varied from about 0.3 meter in the quietest locations to 1.1  meters in the noisest. It is safe to say that we tied most of the underground points to the surface UTM grid to within 1 meter.