was about 3. At epoch 1 the comparable variance factor
was 1. The results listed in Table 1 are those after the a
priori standard deviations of the observations of the aerial
photographs have been increased globally so that the
resulting variance factor was 1.
Analysis of plots of residuals on the plate measurements
for the aerial photography for epoch 2 have shown that
each plate has a systematic array of residuals but that
between plates and over the block as a whole the residuals
are random. The most probable cause of this is effects of
film unflatness with the cut film stuck to the glass plates.
Therefore it is apparent that if suitable glass plates could
be found for the UMK that a high precision could be
obtained from the aerial photography alone. It is
fortuitous, therefore, that the decision to take back-up
photography from the ground was taken as this has
enabled the original specification to be achieved.
4. Analysis of deformation
The next stage in the data processing was to input the GAP
outputs from epochs 1 and 2 into a program called ANDEF
(ANalysis of DEFormation). The data from GAP that
ANDEF uses are the coordinates of both sets of target
points (x, and x,), the cofactor matrices of these two sets
(Q, and Q,), the degrees of freedom for each epoch (r, and
r,) and the estimated variance factors 0,” and 0,7).
ANDEF checks that the same datum of inner constraints
has been used in both epochs and also tests that both
results have the same variance factor ( 5% significance
level). A common variance factor is then computed from
Figure 6 300mm UMK photograph taken from high level close in position - epoch1
(Note obstructions owing to construction plant)
2 2
o
Ir +1,
The matrix of displacement vectors is calculated from :-
d=x,-x,
The cofactor matrix for these displacements is :-
Qu= Qi +Q,
A global congruency test is then carried out using :-
Q =d'Q,;* d
where Q,* is the pseudoinverse of the singular cofactor
matrix Q, which, in this case, is rank deficient by 7.
These are then used in a series of congruency tests to
isolate a set of targets which, at a specific confidence level,
can be regarded as stable. The displacements of the other
targets relative to this sub-set are derived. Tests based on
hypotheses about the geotechnical and structural
properties of the wall should be included in this process;
it is intended to do this later in this project.