Diving data loop closures altering depths

[Olly Betts]

On Mon, Jun 17, 2013 at 02:38:04PM +0100, Footleg wrote:
> Trying to track down why some underwater data was several metres higher
> than a sump water surface, I discovered that closing loops between stations
> at the same depth in diving data alters the depth of surrounding data. This
> was not expected!
> 
> I've attached a fragment of the data which illustrates this. Without the
> loop closed:
> 
> Station entrance.030 is at depth -5.30

Is this a typo?  I get -5.20 as the depth for this station.

> Closing the loop:
>  *equate Entrance.010 EntranceLoopNorth.019
> 
> where both these stations are at the same depth, but horizontally displaced
> (a common scenario as depths are absolute but length and compass errors
> accumulate in diving data), now:
> 
> Station entrance.030 is at depth -5.48
> 
> Is this a bug, or have I not understood something here?

I've had a look - I think this is something that can reasonably happen.

Each leg in a diving survey gives the slope length, the vertical change,
and a bearing.  Although the two ends are the same height, when you tell
survex to "pull them together", the diving legs in between don't simply
have the constraints of the depth readings, they also have the
constraints of the bearings and slope lengths.

If you take this individual underwater leg with a slope length of 5m and
a depth change of 4m (and so the horizontal distance is 3m, by
Pythagoras' Theorem):

     ---->
      B   ^
     /    4m
    /     |
   A      v
   <3m> 

(best viewed in a monospace font...)

The leg says that the length "wants" to be 5m and the vertical change
"wants" to be 4m.

If you close a loop such that the horizontal distance needs to increase,
then simply moving B horizontally preserves the vertical reading but
forces the length to change.  But there's no reason to suppose that the
depth gauge is totally precise and the tape measure is lousy, so it's
more reasonable change the length by less but also change the depth a
bit (so rotate the leg, rather than shearing it).  If you think of
simulating the readings and their errors as a system of springs, then
pulling B to the right stretches the length spring, causing B to also
be pulled down.  B moving down compresses the depth spring, which tends
to push B back up.  B will end up in some equilibrium position,
depending on the strength of the two springs (which corresponds to what
the standard deviations given for the readings are) and the force
applied to move B right.

In your example it's a lot more complex as there are many legs involved,
but I think this is probably the effect behind what you are seeing.

I tried playing with some simpler examples, which show similar effects,
but I did find something odd that happens that I can't explain.  For
example, this survey lies entirely in an E-W vertical plane, but closing
the loop causes the survey to rotate out of that plane:

;*equate sump2dry sump2wet

*fix sump1 0 0 0

; Dry route between the sumps:
sump1 2 10.00 090 045
2 sump2dry 10.00 090 -045

; Wet route between the sumps:
*data diving from to length bearing fromdepth todepth
sump1 3 8.00 090 0 -6.00
3 sump2wet 8.00 090 -6.00 0

; These are the unclosed positions of the stations:
*fix 2_        reference  7.07 0.00  7.07
*fix sump2dry_ reference 14.14 0.00  0.00
*fix 3_        reference  5.29 0.00 -6.00
*fix sump2wet_ reference 10.58 0.00  0.00

While there's no reason to trust the compass readings as being perfect,
I'd expect the symmetry of the situation to mean that the survey stayed
in the plane.

Cheers,
    Olly