Page 1
HİD 473 Yeraltısuyu Modelleri
Sayısal Analiz
Sonlu Farklar Yaklaşımı
Levent Tezcan2013-14 Güz Dönemi
Modelleme
Problemin Tanımlanması
Kavramsal Modelin Geliştirilmesi
Hidrojeolojik Süreçler Sınır Koşulları
Matematiksel Modelin Geliştirilmesi
Diferansiyel Eşitlikler Analitik & Sayısal Yöntemler
Modelin Kurulması Kalibrasyon & Veri Toplama
Sonuçların Elde Edilmesi
Page 2
SAYISAL YÖNTEMLER
• Yeraltısuyu Akımını ifade eden Diferansiyel Eşitlik, Cebirsel DoğrusalMatris eşitliklerine dönüştürülür.
• İki dönüştürme yaklaşımı yaygın olarak kullanılır:
• SONLU FARKLAR YAKLAŞIMI
• SONLU ELEMANLAR YAKLAŞIMI
SONLU FARKLAR YAKLAŞIMI
dfdt
f t t f ttt
lim
( ) ( )
0
Page 3
dfdt
f t f t 0 1( )
f t t f tt
f t( ) ( )
( )
f t t f t t f t( ) ( ) ( )
f t t f t t f t( ) ( ) ( ) t=0.1
0.20.1
t
0.0
0.30.40.50.60.70.80.91.0
f(t)
1.00000.90000.81000.72900.65610.59050.53140.47830.43050.38740.3487
Page 4
0.0010.01
t
0.1
f(1)
0.34870.36600.3677
dfdt
f
f t e t( )
f e( ) .1 0 36791
f t t f t t f t( ) ( ) ( ) t 0
t 0 f tf t t
t( )
( )
1
f t t f tt
t( ) ( )
( )
( )
112
112
f( ) .1 0 3855
f( ) .1 0 3676
Page 5
Taylor Seri Açılımı
f f x xdfdx
x xd f
dx
x xd f
dx
i i i i
i i
i i
1 1
12
2
2
13
3
3
12
13
( )
( )
!( ) ....
x x f x f x x fi i i i ( ) :1 1
Taylor Seri Açılımı
x x f x f x x fi i i i ( ) :1 1
f f x xdfdx
x xd f
dx
x xd f
dx
i i i i
i i
i i
1 1
12
2
2
13
3
3
12
13
( )
( )
!( ) ....
Page 6
birincidfdx
türev:
dfdx
f fx x
x xx x
d f
dx
x xx x
d f
dx
i i
i i
i i
i i
i i
i i
1
1
12
1
2
2
13
1
3
3
12
13
( )
( )( )
!( )( )
....
dfdx
f fx x
xi i
i i
1
1
0( )
birincidfdx
türev:
dfdx
f fx x
x xx x
d f
dx
x xx x
d f
dx
i i
i i
i i
i i
i i
i i
1
1
12
1
2
2
13
1
3
3
12
13
( )
( )( )
!( )( )
....
dfdx
f fx x
xi i
i i
1
1
0( )
Page 7
ikincid f
dx türev:
2
2
d f
dx
f f f
x xxi i i
i i
2
21 1
12
220
( )
dfdx
f fx x
xi i
i i
1
1
0( )
dfdx
f fx x
xi i
i i
1
1
0( )
d f
dx
f f f
x xxi i i
i i
2
21 1
12
220
( )
Page 8
2D DENGELİ YAS AKIM EŞİTLİĞİ‘NİN SONLU FARKLAR ŞEKLİ
2
2
2
2 0x y
x
y
i,j
xi
yi i+1,j
xi+1
i-1,j
xi-1
i,j-1yi-1
i,j+1yi+1
xi
yj
i,j i+1,j
i,j+1 i+1,j+1
Page 9
İleri Farklar Yaklaşımı
( ) ( ) ....
( ) ( )
x x x xddx
ddx
x x xxx
Geri Farklar Yaklaşımı
( ) ( ) ....
( ) ( )
x x x xddx
ddx
x x xxx
Page 10
Orta Farklar Yaklaşımı
ddx
x x x xxx
( ) ( ) 2
xi
(x)
x
B
xi+1
x+x
(x+x)
xi-1
(x-x)
x-x
İleri Farklar
Geri Farklar
Orta Farklar
Page 11
ikincid
dx türev:
2
2
d
dx
x x x x x
xx
2
2 2
2
( ) ( ) ( )
2D DENGELİ YAS AKIM EŞİTLİĞİ‘NİN SONLU FARKLAR ŞEKLİ
2
2
2
2 0x y
Page 12
2
2
2
2 0x y
i j i j i j i j i j i j
x y
1 12
1 12
2 20, , , , , ,
x y
i j i j i j i j i j
, , , , ,
14 1 1 1 1
2D DENGESİZ YAS AKIM EŞİTLİĞİ‘NİN SONLU FARKLAR ŞEKLİ
2
2
2
2x yST t
Page 13
Zamana göre türev
t tt k t
k k
1
İFY
t tt k t
k k
1
GFY
İleri ve Geri Farklar Yaklaşımı
i jk,
xx
y
y
i jk1,
i jk, 1
i jk, 1
i jk1,
t
t
i jk,1
i jk,1
t=(k+1)t
t=(k-1)t
Page 14
İleri Farklar Yaklaşımı (t)
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
x y
ST t
1 12
1 12
1
2 2, , , , , ,
, ,
i jk
i jk
i jk
i jk
i jk
1 1 1 1, , , , ,,, , , i jk,
1
Açık=Belirtik (Explicit) Çözüm
Geri Farklar Yaklaşımı (t)
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
x y
ST t
11 1
11
211 1
11
2
1
2 2, , , , , ,
, ,
i jk,
i j
ki jk
i jk
i jk
i jk
11 1
11
11
11
, , , , ,,, , ,
Kapalı=Örtük (Implicit) Çözüm
Page 15
Açık ve Kapalı Çözümler
k
k+1
x
t Bilinenleri
k i+1ki-1
k
ik+1 Aranan
k
k+1
x
t Bilinenleri
k i+1ki-1
k
ik+1 Aranani-1
k+1 i+1k+1
b
Örnek
L R
R
(t>0)
ki
ki+1
ki-1
x
=sbt =sbti i+1i-1
xi xi+1
1 2 3 4 5
Başlangıç ve SınırKoşulları
b=1.5 mx=3 mK=0.5 m/gS=0.02
L= 1= 6.1m t
R= 5= 6.1m t
R= 5= 1.5m t
2= 3= 4= 6.1m t
Page 16
Örnek
i j
ki jk
i jk
i jk
i jk
x
ST t
1 1
2
12, , , , ,
i j
ki jk
i jk
i jk
i jkT
St
x, , , , ,
1
2 1 12
i j
ki jk
i jk
i jk
i jkT
St
x, , , , ,
1
2 1 12
TS
t
xt
2
12
0 1
. gün
Page 17
i j
ki jk
i jk
i jk
i jkT
St
x, , , , ,
1
2 1 12
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
, , , , ,
, , , , ,
. ..
.
.
12 1 1
11 1
0 5 150 02
0 1
32
0 416 2
Çözüm
k i=1 i=2 i=3 i=4 i=50 6.10 6.10 6.10 6.10 6.101 6.10 6.10 6.10 6.10 1.502 6.10 6.10 6.10 4.18 1.503 6.10 6.10 5.30 3.86 1.504 6.10 5.77 5.04 3.48 1.505 6.10 5.60 4.69 3.30 1.506 6.10 5.43 4.49 3.13 1.507 6.10 5.32 4.32 3.02 1.508 6.10 5.23 4.19 2.93 1.509 6.10 5.16 4.10 2.86 1.50
10 6.10 5.11 4.02 2.81 1.50
Page 18
k
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0 5 10 15 20 25 30 35 40 45 50
i=4
i=3
i=2
t=0.1 gün
k
t=0.15 gün
i=4
i=3i=2
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0 5
10 15
Page 19
Geri Farklar DenklemiKapalı ‐ Örtük Çözüm
i j
ki jk
i jk
i jk
i jk
x
ST t
1
1 111
2
12, , , , ,
i j
ki jk
i jk
i jk
i jk
x
ST t
1
1 111
2
12, , , , ,
i jk
i jk
i jk
i jk
ST
x
t
ST
x
t
11
21
11
2
2, , ,
,
Page 20
b
Örnek
L R
R
(t>0)
ki
ki+1
ki-1
x
=sbt =sbti i+1i-1
xi xi+1
1 2 3 4 5
Başlangıç ve SınırKoşulları
b=1.5 mx=3 mK=0.5 m/gS=0.02
L= 1= 6.1m t
R= 5= 6.1m t
R= 5= 1.5m t
2= 3= 4= 6.1m t
i jk
i jk
i jk
i jk
ST
x
t
ST
x
t
11
21
11
2
2, , ,
,
i jk
i jk
i jk
i jk
11
21
11
2
20 02
0 5 1530 1
0 020 5 15
30 1
, , ,
,
.. . .
.. . .
Page 21
i jk
i jk
i jk
i jk
1
1 1114 4 2 4, , , ,. .
k+1=1t=(k+1)t=0.1
i=2 2 11
21
2 11
204 4 2 4 . .
10 1
20 1
30 1
204 4 2 4. . .. .
11
21
31
204 4 2 4 . .
6 1 4 4 2 4 6 121
31. . . .
i jk
i jk
i jk
i jk
1
1 1114 4 2 4, , , ,. .
k+1=1t=(k+1)t=0.1
i=2 11
21
31
204 4 2 4 . .
i=3 21
31
41
304 4 2 4 . .
i=4 31
41
51
404 4 2 4 . .
Page 22
i
i
i
2 4 4 2 4
3 4 4 2 4
4 4 4 2 4
11
21
31
20
21
31
41
30
31
41
51
40
. .
. .
. .
6 1 4 4 14 64
4 4 14 64
4 4 1 5 14 64
21
31
21
31
41
31
41
. . .
. .
. . .
Page 23
4 4 1 0 20 74
1 4 4 1 14 64
0 1 4 4 16 14
21
31
41
21
31
41
21
31
41
. .
. .
. .
4 4 1 0
1 4 4 1
0 1 4 4
20 74
14 64
16 14
21
31
41
.
.
.
.
.
.
21
31
41
6
5 8
5
m
m
m
.
Page 24
Gauss Yoketme Yöntemi
a a a
a a a
a a a
x
x
x
b
b
b
110 120 130
210 220 230
310 320 330
1
2
3
10
20
30
E
E
E
10
20
30
a a
a a
x
x
b
b
Ea
Ea
Ea
Ea
a x bEa
Ea
221 231
321 331
1
2
21
31
10
110
20
210
10
110
30
310
332 3 3221
221
31
331
E
E
E
21
31
32
Gauss Yoketme Yöntemi
Page 25
a a a
a a
a
x
x
x
b
b
b
ba
b aa
b a aa
110 120 130
221 231
332
1
2
3
10
21
32
332
332
221 231 3
221
310 120 2 130 3
110
0
0 0
x
xx
xx x
Gauss Yoketme Yöntemi
4 2 1
3 6 4
2 1 8
12
25
32
11
21
31
X
X
X
Gauss Yoketme Yöntemi
Page 26
Crank‐Nicholson Yaklaşımı
Orta Farklar YöntemiTek Yönlü Akım
12
2 211 1
11
1 12
1
( ) ( )
( )
( )
ik
ik
ik
ik
ik
ik
ik
ik
x
ST t
Crank‐Nicholson Yaklaşımı
( ) ( )( )
( ) ( )( )
, , , , , ,
, , , , , ,
, ,
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i jk
i
x
y
ST
11 1
11
1 12
11 1
11
1 12
1
2 1 2
2 1 2
jk
t
0<<1
Page 27
Duraylılık
TS
t
x
t
y
2 2
12
b
Örnek
L R
R
(t>0)
ki
ki+1
ki-1
x
=sbt =sbti i+1i-1
xi xi+1
1 2 3 4 5
Başlangıç ve SınırKoşulları
b=1.5 mx=3 mK=0.5 m/gS=0.02
L= 1= 6.1m t
R= 5= 6.1m t
R= 5= 1.5m t
2= 3= 4= 6.1m t
Page 28
Crank‐Nicholson Denklemi
12
2 211 1
11
1 12
1
( ) ( )
( )
( )
ik
ik
ik
ik
ik
ik
ik
ik
x
ST t
k+1=1t=(k+1)ti = 2
1
2
2 231
21
11
30
20
11
2 21
20( ) ( )
( )( )
x
S
T t
i=21
2
2 231
21
11
30
20
10
2 21
20( ) ( )
( )( )
x
S
T t
i=3 1
2
2 241
31
21
40
30
20
2 31
30( ) ( )
( )( )
x
S
T t
i=41
2
2 251
41
31
50
40
30
2 41
40( ) ( )
( )( )
x
S
T t
Page 29
1
2
2 6 1 6 1 2 6 1 6 1
3
0 02
0 0756 13
121
2 21( . ) ( . . . )
( )
.
.( . )
x
1
2
2 6 1 2 6 1 6 1
3
0 02
0 0756 14
131
21
2 31( ) ( . . . )
( )
.
.( . )
x
1
2
15 2 6 1 2 6 1 6 1
3
0 02
0 0756 14
131
2 41( . ) ( . . . )
( )
.
.( . )
x
1
2
2 211 1
11
1 12
1
( ) ( )
( )
( )
ik
ik
ik
ik
ik
ik
ik
ik
x
S
T t
(( )
)
( )
ik
ik
ik
ik
ik
ik
S x
T t
S x
T t
11
21
11
1
2
1
2 1
2 1
Page 30
ik
ik
ik
ik
ik
ik
11 1
11
1 16 8 2 8. .
31
21
11
30
20
106 8 2 8 . .
41
31
21
40
30
206 8 2 8 . .
51
41
31
50
40
306 8 2 8 . .
ik
ik
ik
ik
ik
ik
11 1
11
1 16 8 2 8. .
31
216 8 6 1 6 1 2 8 6 1 6 1 . . . . . .
41
31
216 8 6 1 2 8 6 1 6 1 . . . . .
1 5 6 8 6 1 2 8 6 1 6 141
31. . . . . .
Page 31
31
216 8 6 1 29 28 . . .
41
31
216 8 29 28 . .
1 5 6 8 29 2841
31. . .
6 8 1 0 35 38
1 6 8 1 29 28
0 1 6 8 30 78
21
31
41
21
31
41
21
31
41
. .
. .
. .
6 8 1 0
1 6 8 1
0 1 6 8
35 38
29 28
30 78
21
31
41
.
.
.
.
.
.
Page 32
Birinci ve ikinci satırlar birinci elemanına bölünür:
1 0 147 0
1 6 8 1
0 1 6 8
5 203
29 28
30 78
21
31
41
.
.
.
.
.
.
Gauss Eliminasyon
Birinci satırdan ikinci satır çıkartılarak yeni ikinci satır elde edilir:
1 0 147 0
0 6 653 1
0 1 6 8
5 203
34 483
30 78
21
31
41
.
.
.
.
.
.
Gauss Eliminasyon
Page 33
Gauss Eliminasyon
İkinci ve üçüncü satırlar ikinci elemanlarına bölünür:
1 0 147 0
0 1 0 150
0 1 6 8
5 203
5 183
30 78
21
31
41
.
.
.
.
.
.
Gauss Eliminasyon
İkinci satırdan üçüncü satır çıkartılarak yeni üçüncü satır elde edilir:
1 0 147 0
0 1 0 150
0 0 6 650
5 203
5 183
35 963
21
31
41
.
.
.
.
.
.
Page 34
1 0 147 0
0 1 0 150
0 0 6 650
5 203
5 183
35 963
21
31
41
21
31
41
21
31
41
.
.
.
.
.
.
41
31
41
21
31
35 9636 650
5 408
5 183 0 150 5 994
5 203 0 147 6 084
..
.
. . .
. . .
m
m
m
İterasyon Tekniği
x y
x y
3
2 4
x y
yx
3
42
Page 35
Jacobi ‐ İterasyonİterasyon
No x y
1 0 0
2 x = 3 - 0 = 3 y = (4-0)/2 = 2
3 x = 3 - 2 = 1 y = (4-3)/2 = 1/2
4 2.5 1.5
5 1.5 0.75
6 2.25 1.25
n 2 1
Gauss‐Seidel ‐ İterasyonİterasyon
No x y
1 0 0
2 x = 3 - 0 = 3 y = (4-3)/2 = 0.5
3 x =3 - 0.5 =2.5 y=(4-2.5)/2 =0.75
4 2.25 0.875
5 2.125 0.9375
6 2.0625 0.9687
n 2 1
Page 36
3D Sonlu Farklar Akifer Modeli
Akifer Modeli
Page 37
Hücre Merkezli Grid Sistemi
(Block Centered Grid Sys.)
i,j i+1,j
i,j+1
i-1,j
i,j-1
xi
yj
xi+1/2xi-1/2
xx x
yy y
ii i
jj j
1 21
1 21
2
2
/
/
3D
i,j i+1,ji-1,j
Page 38
2D Yeraltısuyu Akımı
y
x
i
j
2D Yeraltısuyu Akımı
x
Tx y
Ty
W Stxx yy( ) ( )
x
Qy
Q W Stxx yy( ) ( )
Q
x
Q Q
xi j i j i j
i
, / , / ,
1 2 1 2
Page 39
x
Tx x
Tx
Txxx
ixx
i jxx
i j
1
1 2 1 2 / , / ,
11 2 1 2
1
1 2
1
1 2 xT
xT
xixx
i jk
i jk
ixx
i jk
i jk
ii j i j/ , / ,
, ,
/
, ,
/
yT
y
yT
yT
y
yy
jyy
i jk
i jk
jyy
i jk
i jk
ji j i j
11 2 1 2
1
1 2
1
1 2 , / , /
, ,
/
, ,
/
Page 40
2D YAS Akımı Sonlu Farklar Eşitliği
1
1
1 2 1 2
1 2 1 2
1
1 2
1
1 2
1
1 2
1
1 2
xT
xT
x
yT
yT
y
ixx
i jk
i jk
ixx
i jk
i jk
i
jyy
i jk
i jk
jyy
i jk
i jk
j
i j i j
i j i j
/ , / ,
, / , /
, ,
/
, ,
/
, ,
/
, ,
/
W St
ki j
i jk
i jk
,, , 1
yT
xx
T
y
yT
xx
T
y
yT
xx
T
y
j
xx
ii jk
i
yy
ji jk
j
xx
ii jk
i
yy
ji jk
j
xx
ii
yy
j
i j i j
i j i j
i j i j
1 2 1 2
1 2 1 2
1 2 1 2
1 21
1 21
1 21
1 21
1 2 1 2
/ , , /
/ , , /
/ , , /
/,
/,
/,
/,
/ /
yT
xx
T
y
x y W x yS
t
j
xx
ii
yy
ji jk
i jk
i ji j
i jk
i jk
i j i j1 2 1 2
1 2 1 2
1
/ , , /
/ /,
,, ,
Page 41
B xT
y
D yT
xF y
T
x
H xT
y
i j i
yy
j
i j j
xx
ii j j
xx
i
i j i
yy
j
i j
i j i j
i j
,/
,/
,/
,/
, /
/ , / ,
, /
1 2
1 2 1 2
1 2
1 2
1 2 1 2
1 2
E B D F H x yS
t
Q x yS
th W
i j i j i j i j i j i ji j
i jk
i ji j
i jk k
, , , , ,,
,,
,
1 1
Page 42
j B
j D E F
j H
i i i
1
1
1 1
D H E F B Qi j i jk
i j i jk
i j i jk
i j i jk
i j i jk
i jk
, , , , , , , , , , , 1 1 1 1
1
Page 43
Hücreler Arası Transmissivite
T xT T
x T x Txx
xx xx
xx xxi j i j
i j i j
i j i j i j i j
1 2 1 2
1
1 1
2/ , / ,
, ,
, , , ,
T xT T
x T x Txx
xx xx
xx xxi j i j
i j i j
i j i j i j i j
1 2 1 2
1
1 1
2/ , / ,
, ,
, , , ,
T yT T
y T y T
T yT T
y T y T
yy
yy yy
yy yy
yy
yy yy
yy yy
i j i j
i j i j
i j i j i j i j
i j i j
i j i j
i j i j i j i j
, / , /
, ,
, , , ,
, / , /
, ,
, , , ,
1 2 1 2
1
1 1
1 2 1 2
1
1 1
2
2
Page 44
D E F Qi j i jk
i j i jk
i j i jk
i jk
, , , , , , , 1 1
1
D E F Qk k k k1 1 0 1 1 1 1 1 1 1 2 1 1 1
1, , , , , , ,
E F Q
D E F Q
D E F Q
D E F Q
D E Q
k k k
k k k k
k k k k
k k k k
k k k
1 1 1 2 11
2 1 2 2 2 3 21
3 2 3 3 3 4 31
4 3 4 4 4 5 41
5 4 5 5 51
E F
D E F
D E F
D E F
D E
Q
Q
Q
Q
Q
k
k
k
k
k
k
k
k
k
k
1 1
2 2 2
3 3 3
4 4 4
5 5
1
2
3
4
5
11
21
31
41
51
'0
0
1D KatsayıMatrisi
Page 45
2D KatsayıMatrisinin Yapısı
EBD
HEBD
HEBD
HEBD
HEBD
FHEB
FHEB
FHEB
FHEB
FHE
NCOL
NCOL1
2D YAS AKIMI SONLU FARKLAR PROBLEMİ
Page 46
PROBLEM
j
i
i=1 i=2 i=3
j=3j=2
j=1
Veriler
xi yj Sij Txij Tyij N ij
50 100 3050 100 3050 100 30
250 80 0.02 200 100 0.01 26250 240 0.01 300 150 0.01 29250 100 0.02 200 100 0.01 27300 80 0.03 350 175 0.01 20300 240 0.04 400 200 0.009 27300 100 0.02 200 100 0.01 25400 80 0.01 310 155 0.01 19400 240 0.01 290 145 0.01 22400 100 0.03 180 90 0.01 19
50 100 1850 100 1850 100 18
N=0.01 m/günQw=-100 m3/sW=N+Qw
Page 47
i j T xi-1/2 T xi+1/2 T yj-1/2 T yj+1/21 1 1.143 0.949 0.000 0.8331 2 1.500 1.263 0.833 0.7691 3 1.143 0.727 0.769 0.0002 1 0.949 0.931 0.000 1.2072 2 1.263 0.939 1.207 0.9092 3 0.727 0.537 0.909 0.0003 1 0.931 1.117 0.000 0.9213 2 0.939 1.064 0.921 0.7233 3 0.537 0.735 0.723 0.000
Dij Fij Bij H ij Eij Qij91.43 75.93 0.00 208.33 -775.69 -10600.00
360.00 303.16 208.33 192.31 -1663.80 -18000.00114.29 72.73 192.31 0.00 -879.32 -13750.0075.93 74.51 0.00 362.07 -1232.51 -14640.00
303.16 225.43 362.07 272.73 -4043.38 -78380.0072.73 53.73 272.73 0.00 -999.19 -15300.0074.51 89.37 0.00 368.44 -852.32 -6400.00
225.43 255.41 368.44 289.20 -2098.48 -22080.0053.73 73.47 289.20 0.00 -1616.40 -23200.00
Page 48
1 2 3 4 5 6 7 8 91 E11 H11 0.00 F11 0.00 0.00 0.00 0.00 0.00 Q11-D1112 B12 E12 H12 0.00 F12 0.00 0.00 0.00 0.00 Q12-D1223 0.00 B13 E13 H13 0.00 F13 0.00 0.00 0.00 Q13-D1334 D21 0.00 B21 E21 H21 0.00 F21 0.00 0.00 Q215 0.00 D22 0.00 B22 E22 H22 0.00 F22 0.00 Q226 0.00 0.00 D23 0.00 B23 E23 H23 0.00 F23 Q237 0.00 0.00 0.00 D31 0.00 B31 E31 H31 0.00 Q31-F3118 0.00 0.00 0.00 0.00 D32 0.00 B32 E32 H32 Q32-F3229 0.00 0.00 0.00 0.00 0.00 D33 0.00 B33 E33 Q33-F333
1 -775.69 208.33 0.00 75.93 0.00 0.00 0.00 0.00 0.00 -13342.862 208.33 -1663.80 192.31 0.00 303.16 0.00 0.00 0.00 0.00 -28800.003 0.00 192.31 -879.32 0.00 0.00 72.73 0.00 0.00 0.00 -17178.574 75.93 0.00 0.00 -1232.51 362.07 0.00 74.51 0.00 0.00 -14640.005 0.00 303.16 0.00 362.07 -4043.38 272.73 0.00 225.43 0.00 -78380.006 0.00 0.00 72.73 0.00 272.73 -999.19 0.00 0.00 53.73 -15300.007 0.00 0.00 0.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.658 0.00 0.00 0.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.439 0.00 0.00 0.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.200.00 7.72 -0.92 -0.10 -1.46 0.00 0.00 0.00 0.00 155.440.00 192.31 -879.32 0.00 0.00 72.73 0.00 0.00 0.00 -17178.570.00 -0.27 0.00 16.13 -4.77 0.00 -0.98 0.00 0.00 210.000.00 303.16 0.00 362.07 -4043.38 272.73 0.00 225.43 0.00 -78380.000.00 0.00 72.73 0.00 272.73 -999.19 0.00 0.00 53.73 -15300.000.00 0.00 0.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.650.00 0.00 0.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 0.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45
Page 49
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.140.00 4.45 -0.01 -0.19 -0.38 0.00 0.00 0.00 109.470.00 -0.12 60.06 -17.94 0.00 -3.65 0.00 0.00 802.060.00 -0.12 -1.21 13.15 -0.90 0.00 -0.74 0.00 278.690.00 72.73 0.00 272.73 -999.19 0.00 0.00 53.73 -15300.000.00 0.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.650.00 0.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14
1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.580.00 502.14 -150.06 -0.08 -30.55 0.00 0.00 6730.430.00 -10.09 109.89 -7.61 0.00 -6.22 0.00 2354.620.00 0.00 -3.79 13.65 0.00 0.00 -0.74 234.960.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.650.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14
1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.400.00 10.59 -0.75 -0.06 -0.62 0.00 246.660.00 -1331.66 4793.42 -0.06 0.00 -259.37 82499.640.00 -0.30 0.00 11.38 -4.95 0.00 120.890.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14
1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40
1.00 -0.07 -0.01 -0.06 0.00 23.300.00 3.53 -0.01 -0.06 -0.19 85.250.00 -0.07 38.07 -16.61 0.00 427.840.00 -0.07 -1.64 9.25 -1.28 141.640.00 53.73 0.00 289.20 -1616.40 -24522.45
Page 50
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14
1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40
1.00 -0.07 -0.01 -0.06 0.00 23.301.00 0.00 -0.02 -0.06 24.160.00 530.59 -231.45 -0.06 5986.930.00 -23.04 129.94 -18.08 2013.870.00 0.00 -5.40 30.03 480.55
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14
1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40
1.00 -0.07 -0.01 -0.06 0.00 23.301.00 0.00 -0.02 -0.06 24.16
1.00 -0.44 0.00 11.280.00 5.20 -0.78 98.680.00 -3289.78 18295.24 292800.32
1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14
1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40
1.00 -0.07 -0.01 -0.06 0.00 23.30
1.00 0.00 -0.02 -0.06 24.161.00 -0.44 0.00 11.28
1.00 -0.15 18.975.41 107.97
1 2 31 27.14 22.60 20.882 28.77 26.52 21.983 27.95 25.66 19.96