## 3DD: 3D Coordinate Difference Header

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.

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

**The format for this observation set 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 this record is as follows (from column - to column: description):**- 002-005: 3DD
- 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