3DD: 3D Coordinate Difference

This record specifies the beginning of a 3D coordinate difference observation set.

The format for a 3D coordinate observation group is as follows:

3DD [optional sigma ID]
[Set of 3D coordinate records or DXYZ records]
[Covariance matrix header record]
[Matrix elements records]

The "Set of 3D coordinate records or DXYZ records" must contain only PLH, PLO, NEH, NEO, XYZ coordinate records, or DXYZ coordinate difference records (it may also contain HI, HT, 4PAR, and 7PAR records).

If DXYZ records are not used, GeoLab will automatically subtract the first of these records from the others to arrive at the actual coordinate difference measurement values (in which case the covariance matrix elements entered must correspond to these computed coordinate differences).

The "Covariance matrix header record" can be one of the following records: COV, WGT, CORR, or GENC.

The matrix elements records are set up as described in Input Matrix Formatting.

The format of the 3DD record is as follows:

Columns 002-005: 3DD
Columns 007-009: Sigma record identifier (see the SIGM record)

If we have the following three sets of coordinate difference observations:

• Station 1 to station 2: d1= X2 - X1; d2 = Y2 - Y1; d3 = Z2 - Z1;

• Station 2 to station 3: d4 = X3 - X2; d5 = Y3 - Y2; d6 = Z3 - Z2;

• Station 3 to station 1: d7 = X3 - X1; d8 = Y3 - Y1; d9 = Z3 - Z1;

for a total of nine observations (3 sets of dX, dY, and dZ), we would input them in three DXYZ records as follows:

3DD
DXYZ12 d1 d2 d3
DXYZ23 d4 d5 d6
DXYZ31 d7 d8 d9

If we denote a covariance matrix element as sij (where s11 is the variance of d1, and s12 is the covariance between d1 and d2) the upper-triangular portion of the covariance matrix for these observations is as follows (note that the order of the covariance elements depends only on the order in which the observations are given as DXYZ records).

s11 s12 s13 s14 s15 s16 s17 s18 s19
s22 s23 s24 s25 s26 s27 s28 s29
s33 s34 s35 s36 s37 s38 s39
s44 s45 s46 s47 s48 s49
s55 s56 s57 s58 s59
s66 s67 s68 s69
s77 s78 s79
s88 s89
s99

The ELEM records for this observation would therefore be:

ELEM s11 s12 s13
ELEM s14 s15 s16
ELEM s17 s18 s19
ELEM s22 s23 s24
ELEM s25 s26 s27
ELEM s28 s29
ELEM s33 s34 s35
ELEM s36 s37 s38
ELEM s39
ELEM s44 s45 s46
ELEM s47 s48 s49
ELEM s55 s56 s57
ELEM s58 s59
ELEM s66 s67 s68
ELEM s69
ELEM s77 s78 s79
ELEM s88 s89
ELEM s99