The distances Y. of each one of the SCP are measu- 
red as follows: first by means of an instrument 
(telemeter is the best alternative) and secondly - 
photogrammetrically. The differences between the 
double determined distances is AY., where "j" is 
the number of SCP (in this case jl= I - IIl). 
These differences give rise to corrections in the 
distances of the CP which can be determined with 
sufficient accuracy using the proportional depend- 
ence between the distances and the horizontal  pa- 
parallax, i.e. 
Pp. 
A. ai rem ^t; (2) 
1 
1 
where p, is the horizontal parallax of the respec- 
tive SCP; P; is the horizontal parallax of the 
CP. 
The formulas (2) are used to determine corrections 
(1). 
After the photogrammetric determination, the spa- 
cial photogrammetric co-ordinates X;, MIA of the 
CP are corrected with the help of (1 and T. i.e. 
X, = XX + Ax, ; 
i 1 1 
= : + ° 
X Y Ay, : (3) 
27. = 725 4-A2.. 
1 d li 
The transformational image co-ordinates x,, 7 z 
are determined using (3). The differences between 
them and the measured image co-ordinates are 
AX = a + a, x, x + a,x, 2 + 442 + a,x 3 
(4) 
Az = i + cz. X + e zz + C4X + cz 
The formulas (4) are figured out by means of the 
principle of least squares and result in the coef- 
ficients Ya” and "c". 
The same formulas (4) are used also to receive the 
corrections of the image co-ordinates of the  exa- 
minated points (EP),(Fig.l, points 1, 2, 3, ....). 
The iterative method is applied. For the first ap- 
proximation the measured values of x_ and z are 
used. The iterations continue until the following 
conditions are observed: 
  
k+1 k < 
AX, m AX, | = Mx ’ 
k+1 k < 
| Az, - Az. 3 M. ; (5) 
  
where and Ju, are apriori values; "n" is the 
x 
number Of the EP and "k" is the number of the 
iterations. 
The image transformational co-ordinates are recei- 
ved using the calculated corrections and through 
them - the spacial photogrammetric  transformatio- 
nal co-ordinates of the EP. These co-ordinates can 
serve to calculate the  geodetic co-ordinates or 
the relative displacements as it is very often 
done: 
acl 5. oe: 
AX = 2a An ? 
= i = o 
AY, = ln Y 3 (6) 
i 0 
A7, ® elds Far! 
0 0 o ; ; 
where X , Y , Z are the spacial photogrammetric 
transformational co-ordinates of the EP at the ze- 
i i i > ; 
ro cycles X, Y? Z are similar co-ordinates at 
the deformational cycle "i" ("i" depends on the fun- 
ction of the structure and on its size and shape); 
"n" is the number of EP. 
3. PRACTICAL RESULTS. 
The deformations of a reinforced reservoir ( size 
28/14/5 m), which is supported by 45 pillars, are 
examinated. Photographic parameters: f = 194.82 mm 
(Photheo 19/1318, Carl Zeiss); B = 13.020 m; Y = 
62.000 m. 
Nineteen EP are observed in two cycles: a zero (an 
emrty reservoir) and a deformational cycle (a full 
reservoir). Geodetis measurements are used to get 
the displacements: range (using the theodolite Theo 
010A, Carl Zeiss) and levelling (using the level Ni 
007, Carl Zeiss). 
The photogrammetric displacements are compared to 
the latter, which are accept as most probable. 
In each cycle three photographs are taken and they 
are measured with the help of Stekometer, Carl 
Zeiss. Each of the points is measured three times. 
  
  
In calculations a computer is used and software 
respectively. The final results are given in 
TABLE 1. 
TABLE 1 
o 
Ne AX n^ X, €. AY u^ Ts E, |^ Z n^ ag €, 
mm | mm | mm| mm | mm |mm mm | mm | mm 
1 15 6 91-34 1-25 1-9 ]|- 9 | -3] -6 
2 18 12 61-37 |-28 | -9 -13 | -4] -9 
3 13 8 5]-29 ]-20 | -9 -13 mû | -9 
4 8 5 31-14 |- 9 | -5 -7 -3] -4 
5]-6|- 1 —-5 1-20 |-14 1-6 |-10 | -4 | -6 
6 14 8 6 | -16 1-11 | -5 - 9 -4 | -5 
7177 |-3 —-4 1-19 ]-11 1-8. | —11 -4 | -7 
81-9 1-1 -8|-12|-61|-6 |-8]| -3] -5 
917-7 1-2 -51-9]-5]-4 1-10 | -4 | -6 
10 4 2 21-61-21-4 1-7 -4 1 -3 
11 6 2 4|-5]|-1[|-4 [-10]| -4]| -6 
12 6 3 31]-51-2]1]-3 ]-10] -4| -6 
13 5 2 31-3 51-8 |-5 -3 | -2 
14 7 2 5173 31-6 — 5 -3] -2 
15 6 3 3I1-31—5 2 - 6 3 | -3 
16 |- 2 6| -8/-31-6 3 = / -4 | -3 
17 6 1 $1-7251-.21-3 -10 | -4 | -6 
18 7 1 61-3 0[-3 1-9] -31.-6 
19 7 1 6 1 ==3 01-3 1-8 | -3 -5 
  
  
  
  
  
  
  
  
  
  
  
  
There AX h? AY h? AZ are photogrammetric dis- 
placements; AX, AYP AZ are geodetic displace- 
ments; €., £5 E, “are tPue errors of the photo- 
grammetric displacements. The results of the exami- 
nation of only one of the walls are shown, i.e. of 
the wall with the biggest displacements. 
The displacements of the EP are illustrated graphi- 
cally in Fig.2. 
Using the true errors the standard errors of the 
displacements are calculated: 
2 
+ es + |/ 550 
  
à 
  
TAX = n = = 7519; 5.4 mm, 
2 
AE ES: ue te, 
m Y n 19 . mm,