Article Index

4. Example

Adjust the same level circuit from Chapter D, Figure F-5.

Figure F-5
Level Circuit

Additional information are the number of instrument setups on each line.

Obs Line dElev Setups        Obs Line dElev Setups
1 BMA-Q +8.91 3   5 BMA-R -3.56 3
2 BMB-Q -2.92 2   6 BMC-R -17.12 4
3 BMC-Q -4.67 1   7 BMD-R -21.10 2
4 BMD-Q -8.66 3   8 Q-R -12.47 3

a. Observation equations

The observation equations are the same as in the Chapter D example.

b. Set up matrices

 The [C], [U], [K], and [V] matrices are also the same.

 

Compute weights from number of setups. Weights are inversely proportional to number of setups.

Obs Line Setups Weight          Obs Line Setups Weight
1 BMA-Q 3 1/3     5 BMA-R 3 1/3
2 BMB-Q 2 1/2     6 BMC-R 4 1/4
3 BMC-Q 1 1/1     7 BMD-R 2 1/2
4 BMD-Q 3 1/3     8 Q-R 3 1/3

The weights can be multiplied by 12 to make them integers. The weight matrix is:

 

c. Solve Unknowns: [U] = [Q] x [CTWK]

Multiply [CT ] x [W] and [CTW] x [C]

 

Multiply [CTW] x [K]

 

Invert [CTWC]

Since this is a 2x2 matrix, it can be quickly inverted using its the determinant.

 

Compute the elevations

Carry enough significant figures to avoid rounding errors.

 

d. Adjustment Statistics

Residuals: [V] = [CU] - [K]

 

 

 

e. Comparison of Unweighted and Weighted Adjustment

Point Unweighted, So=±0.028 Weighted; So=±0.067
Q 815.418 ±0.013 815.424 ±0.012
R 802.962 ±0.014 802.958 ±0.016

Weighing observations changed the elevations changed slightly. Although So increased, it's a better overall indicator of the mixed quality observations.

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