UNIVERSITATEA TEHNICA DE CONSTUCTII BUCURESTI

FACULTATEA DE GEODEZIE

Geodezie Fizica 2:Lucrarea 1:

Determinarea diferentelor de gravitate (ɗ gij) intr-o retea gravimetrica

IRIMIA MADALINA Anul IV ,Grupa 3

An universitar 2012-2013

Tema lucrarii: Intr-o retea gravimetrica alcatuita din 6 puncte materializate in teren s-au realizat determinari gravimetrice cu ajutorul unui gravimetru relativ de tip La Coste & Romberg (Scintrex). In urma efectuarii masuratorilor au rezultat lecturile mediate in diviziuni Li``(div). Pentru momentul observatiilor se poate determina valoarea corectiei de variatie diurna CVD (ΔgVD) avand in vedere ca masuratorile s-au realizat in data de 3 iunie 2010, intre orele 7-11 si ca se cunosc valorile erorilor de variatie diurna (eVD) exprimate in µgal (date din ora in ora pentru ziua in care s-au efectuat masuratorile) . Se cunoaste constanta de scara a intrumentului utilizat k, valabila pentru intervalul de diviziuni cuprins intre 3900-4100 div. Se presupune ca asupra lecturilor efectuate au fost deja aplicate corectiile fizice (de presiune si de temperatura).Se cere:

I. Sa se determine diferentele de gravitate ɗ 0gij intre punctele masurate prin metoda grafica;

II. Sa se determine diferentele de gravitate ɗ0gij intre punctele masurate prin metoda analitica;

III. Sa se realizeze o comparatie intre rezultatele obtinute intre cele 2 metode (tabel comparativ);Se vor prezenta si preciziile de determinare.

Etape de calcul:

I.1. Calculul lecturilor corectate tinand cont de constanta de scara a instrumentului;L`=L``*K

L``=L``+(-1)N*L``/1000NN=12- numarul de ordine;

k ∈ [3900, 4000)= 0.99244 mgal/divk ∈ [4000, 4100)= 0.99254 mgal/divk ∈ [4100, 4200)= 0.99261 mgal/div

k=Δ gABΔLAB

mgal/div

Nr. mas.

Operator Pilastru Timp [h]

Lectura in div. L``

Const. scara K (mgal/div)

Lectura in mgal L`=L``*K

1 1 4 7.21 4080.7655

0.992540 4050.3230

2 1 5 7.43 4080.8071

0.992540 4050.3643

3 2 5 7.47 4080.7990

0.992540 4050.3563

4 1 6 8.03 4080.5507

0.992540 4050.1098

5 2 6 8.07 4080.5391

0.992540 4050.0983

6 1 3 8.17 4080.3899

0.992540 4049.9502

7 2 3 8.21 4080.3398

0.992540 4049.9005

8 1 2 8.31 4080.5227

0.992540 4050.0820

9 2 2 8.35 4080.5182

0.992540 4050.0775

10 1 1 8.45 4080.7680

0.992540 4050.3255

11 2 1 8.48 4080.7594

0.992540 4050.3170

12 2 4 9.02 4080.7425

0.992540 4050.3002

13 1 4 9.04 4080.7479

0.992540 4050.3056

14 1 5 9.11 4080.7941

0.992540 4050.3514

15 2 5 9.15 4080.8000

0.992540 4050.3573

16 1 6 9.23 4080.5366

0.992540 4050.0958

17 2 6 9.26 4080.531 0.992540 4050.0905

2

18 1 3 9.34 4080.3469

0.992540 4049.9075

19 2 3 9.37 4080.3333

0.992540 4049.8940

20 1 2 9.53 4080.5241

0.992540 4050.0834

21 2 2 9.56 4080.5292

0.992540 4050.0885

22 1 1 10.04 4080.7831

0.992540 4050.3405

23 2 1 10.06 4080.7705

0.992540 4050.3280

24 2 4 10.19 4080.7580

0.992540 4050.3156

I.2 Calculul corectiei de variatie diurna;cVD=-eVD, [cVD]-µgalSe interpoleaza valorile in tabel pentru erorile de variatie diurna in functie de ora in care s-au realizat

masuratorile. Schimbam semnul si rezulta corectia de variatie diurna in µgali.Eroarea de variatie diurna reprezinta influenta fenomenului de maree terestra care se transpune in varatia

absoluta si relativa a gravitatii in functie de timp pentru acelasi punct sau aceeasi zona de pe suprafata terestra.

Eroarea de variatie diurna 03.06.2010Ora eVD [µgal] Ora eVD [µgal] cVD [µgal]

0 64.2 7.21 -64.7 64.71 67.4 7.43 -67.8 67.82 60.2 7.47 -68.4 68.43 42.3 8.03 -70.0 70.04 16.1 8.07 -69.7 69.75 -13.8 8.17 -68.9 68.96 -41.6 8.21 -68.6 68.67 -61.7 8.31 -67.8 67.88 -70.2 8.35 -67.5 67.59 -65.5 8.45 -66.7 66.7

10 -49.1 8.48 -66.4 66.411 -24.8 9.02 -65.0 65.012 2.1 9.04 -64.4 64.413 26.2 9.11 -62.5 62.514 43.4 9.15 -61.4 61.415 51.4 9.23 -59.2 59.2

16 50.7 9.26 -58.4 58.417 43.5 9.34 -56.2 56.218 33.9 9.37 -55.4 55.419 26.0 9.53 -51.0 51.020 23.2 9.56 -50.2 50.221 27.1 10.04 -47.5 47.522 36.9 10.06 -46.7 46.723 50.0 10.19 -41.4 41.4

I.3. Determinarea lecturilor corectate;L[mgal]=L`[mgal]+cVD*1/1000 [µgal]

Nr. mas.

Operator

Pilastru Timp

Lectura in div. L``

Const. scara K (mgal/div)

Lectura in mgal L`=L``*K

cVD [µgal]

Lectura corectata L

(mgal)

1 1 4 7.21 4080.7655

0.992540 4050.3230 64.7 4050.3877

2 1 5 7.43 4080.8071

0.992540 4050.3643 67.8 4050.4321

3 2 5 7.47 4080.7990

0.992540 4050.3563 68.4 4050.4246

4 1 6 8.03 4080.5507

0.992540 4050.1098 70.0 4050.1798

5 2 6 8.07 4080.5391

0.992540 4050.0983 69.7 4050.1679

6 1 3 8.17 4080.3899

0.992540 4049.9502 68.9 4050.0191

7 2 3 8.21 4080.3398

0.992540 4049.9005 68.6 4049.9690

8 1 2 8.31 4080.5227

0.992540 4050.0820 67.8 4050.1498

9 2 2 8.35 4080.5182

0.992540 4050.0775 67.5 4050.1450

10 1 1 8.45 4080.7680

0.992540 4050.3255 66.7 4050.3922

11 2 1 8.48 4080.7594

0.992540 4050.3170 66.4 4050.3834

12 2 4 9.02 4080.7425

0.992540 4050.3002 65.0 4050.3651

13 1 4 9.04 4080.7479

0.992540 4050.3056 64.4 4050.3700

14 1 5 9.11 4080.7941

0.992540 4050.3514 62.5 4050.4139

15 2 5 9.15 4080.8000

0.992540 4050.3573 61.4 4050.4187

16 1 6 9.23 4080.5366

0.992540 4050.0958 59.2 4050.1550

17 2 6 9.26 4080.5312

0.992540 4050.0905 58.4 4050.1488

18 1 3 9.34 4080.3469

0.992540 4049.9075 56.2 4049.9637

19 2 3 9.37 4080.3333

0.992540 4049.8940 55.4 4049.9494

20 1 2 9.53 4080.5241

0.992540 4050.0834 51.0 4050.1344

21 2 2 9.56 4080.5292

0.992540 4050.0885 50.2 4050.1387

22 1 1 10.04

4080.7831

0.992540 4050.3405 47.5 4050.3880

23 2 1 10.06

4080.7705

0.992540 4050.3280 46.7 4050.3747

24 2 4 10.19

4080.7580

0.992540 4050.3156 41.4 4050.3570

Pentru realizarea graficului se alege pentru fiecare din cei 6 pilastri cate o valoare de referinta Oi fata de care se calculeaza prin diferenta valorile Li’ cu care se merge pe grafic.

I.4. Determinarea diferentelor de gravitate ɗ0gij intre punctele masurate prin metoda grafica;

Diferentele de gravitate se calculeaza astfel:g0

ij=( Oj- Oi)+(nij(1)+nij

(2))/2000

Punct Originea Latura nij (1) [µgal]

nij (2) [µgal]

Media [µgal] δgij [mgal]

4 4050.3 45 -52 -47.2 -49.6 δg45 0.0504

5 4050.4 56 44.6 37.5 41.05 δg56 -0.2590

6 4050.1 63 4.5 5.6 5.05 δg63 -0.1949

3 4049.9 32 -21.6 -21.7 -21.65 δg32 0.1783

2 4050.1 21 43.4 51.3 47.35 δg21 0.2474

1 4050.3 14 -42.1 16.6 -12.75 δg14 -0.0128

II.Sa se determine diferentele de gravitate ɗ0gij intre punctele masurate prin metoda analitica;

Mi0+vi=x0k+tioy ,unde:

Mi0-lectura efectuata intr-un punct de statie ti-momentul efectuarii acestei lecturi t0-moment de timp de referinta (7h) tio=ti-t0

x0k-valoarea cea mai probabila a lecturii efectuate intr-un punct k

y-eroarea de drift instrumental i-nr lecturii efectuate intr-un punct,i=1..n vi-corectia care se aplica lecturii Mi0

x0k=( x0

k)*+dxk

Valorile provizorii se determina prin medierea celor 4 lecturi din fiecare din cele 6 puncte de statie:

Valori provizorii [mgal]x0

1= 4050.3846x0

2= 4050.1420x0

3= 4049.9753x0

4= 4050.3699x0

5= 4050.4223x0

6= 4050.1629

Eroarea de drift instrumental - deplasare, translatie a lecturilor care se datoreaza imbatranirii sistemului elastic al unui gravimetru. Se asimileaza aceasta eroare cu panta dreptei de regresie sau a familiei de drepte

Nr dx4 dx5 dx6 dx3 dx2 dx1 Δt lik [µgal]

1 1 0 0 0 0 0 0.35 -17.752 0 1 0 0 0 0 0.72 -9.783 0 1 0 0 0 0 0.78 -2.314 0 0 1 0 0 0 1.05 -16.88

5 0 0 1 0 0 0 1.12 -5.05

6 0 0 0 1 0 0 1.28 -43.76

7 0 0 0 1 0 0 1.35 6.28

8 0 0 0 0 1 0 1.52 -7.82

9 0 0 0 0 1 0 1.58 -3.0410 0 0 0 0 0 1 1.75 -7.6311 0 0 0 0 0 1 1.80 1.1512 1 0 0 0 0 0 2.03 4.8013 1 0 0 0 0 0 2.07 -0.0114 0 1 0 0 0 0 2.18 8.4215 0 1 0 0 0 0 2.25 3.6616 0 0 1 0 0 0 2.38 7.8717 0 0 1 0 0 0 2.43 14.0518 0 0 0 1 0 0 2.57 11.5819 0 0 0 1 0 0 2.62 25.9020 0 0 0 0 1 0 2.88 7.5521 0 0 0 0 1 0 2.93 3.3122 0 0 0 0 0 1 3.07 -3.4223 0 0 0 0 0 1 3.10 9.9024 1 0 0 0 0 0 3.32 12.96

0.00Ecuatia de corectie se scrie astfel:

vi= dxk+tioy+lik

lik=( x0k)*- Mi0

Verificare: [lik]=0Matriceal se scrie sub forma:

V(24,1)=A(24,7)X(7,1)+L(24,1)

N=ATPA ,unde P=I24

X=-N-1ATPL A-matricea coeficientilor parametrilor necunoscuti; N-matricea sistemului normal; P-matricea ponderilor; L-matricea termenului liber; X-matricea parametrilor necunoscuti.

A

1 0 0 0 0 0 0.35

L [µgal]

-17.75

0 1 0 0 0 0 0.72 -9.78

0 1 0 0 0 0 0.78 -2.31

0 0 1 0 0 0 1.05 -16.88

0 0 1 0 0 0 1.12 -5.05

0 0 0 1 0 0 1.28 -43.76

0 0 0 1 0 0 1.35 6.28

0 0 0 0 1 0 1.52 -7.82

0 0 0 0 1 0 1.58 -3.04

0 0 0 0 0 1 1.75 -7.63

0 0 0 0 0 1 1.80 1.15

1 0 0 0 0 0 2.03 4.80

1 0 0 0 0 0 2.07 -0.01

0 1 0 0 0 0 2.18 8.42

0 1 0 0 0 0 2.25 3.66

0 0 1 0 0 0 2.38 7.87

0 0 1 0 0 0 2.43 14.05

0 0 0 1 0 0 2.57 11.58

0 0 0 1 0 0 2.62 25.90

0 0 0 0 1 0 2.88 7.55

0 0 0 0 1 0 2.93 3.31

0 0 0 0 0 1 3.07 -3.42

0 0 0 0 0 1 3.10 9.90

1 0 0 0 0 0 3.32 12.96

N

4 0 0 0 0 0 7.7670 4 0 0 0 0 5.9330 0 4 0 0 0 6.9830 0 0 4 0 0 7.8170 0 0 0 4 0 8.9170 0 0 0 0 4 9.717

7.767 5.933 6.983 7.817 8.917 9.717 108.382

4 5 6 3 2 1 Y

N¯¹

0.5282 0.2125 0.2501 0.2799 0.3193 0.3480 -0.1433 40.2125 0.4123 0.1911 0.2139 0.2440 0.2658 -0.1094 50.2501 0.1911 0.4749 0.2517 0.2871 0.3129 -0.1288 60.2799 0.2139 0.2517 0.5317 0.3214 0.3502 -0.1442 30.3193 0.2440 0.2871 0.3214 0.6166 0.3995 -0.1645 2

0.3480 0.2658 0.3129 0.3502 0.3995 0.6854 -0.1792 1

-0.1433 -0.1094 -0.1288 -0.1442 -0.1645 -0.1792 0.0738 Y

X [µgal]

23.99x04

Valori provizorii [mgal]

Corectii[mgal]

Valori compensate[mgal]

18.33 x05 x01= 4050.3846 0.0300 4050.4146

21.57 x06 x02= 4050.1420 0.0275 4050.1695

24.14 x03 x03= 4049.9753 0.0241 4049.9994

27.54 x02 x04= 4050.3699 0.0240 4050.3939

30.01 x01 x05= 4050.4223 0.0183 4050.4407

-12.36 [µgal]/h y

x06= 4050.1629 0.0216 4050.1845

V [µgal]

1.91-0.316.34-8.282.73

-35.4713.750.984.940.778.923.67-1.56-0.23-5.810.00

5.56

4.01

17.72

-0.53

-5.39

-11.30

1.61-4.03

δg45= 0.0467 [VV] 2259.177δg56= -0.2562 n 24δg63= -0.1850 [mgal] h 7δg32= 0.1701 So [µgal] 11.53δg21= 0.2451 Svi [µgal] 9.70δg14= -0.0206

Ab st. a unitatii de pondere (s0)

[µgal]

Ab st. a unei mas. comp. [µgal] Sδij [µgal]

11.53

sx1= 9.54 Sδg45 8.277

sx2= 9.05 Sδg56 8.193

sx3= 8.41 Sδg63 8.178

sx4= 8.38 Sδg32 8.197

sx5= 7.40 Sδg21 8.175sx6= 7.94 Sδg14 8.293sy= 3.13

Valorile relative ale gravitatii s-au calculat cu formulele: g0

45=x05-x0

4 g056=x0

6-x05

g063=x0

3-x06 g0

32=x02-x0

3

g021=x0

1-x02 g0

14=x04-x0

1

Calculul preciziiloro Abaterea standard (eroarea medie patratica) a unitatii de pondere

s0=±√ [vv ]m−n

=±√V T ·Vm−nm-nr de masuratori (24)n-nr de necunoscute (7)

s0=11.53 [gal]o Erorile de determinare a diferentelor de gravitate

Sδij= s0√Qxixi+Q xjxj−2Q xixj

Pentru a elimina masuratorile gresite se face testul Pope (de determinare a masuratorilor eronate)svi-abaterea standard a unei corectii

svi=√ n−hn s0√ pi

=9.70 [gal]

Se calculeaza pentru cele 24 masuratori |visvi| si se compara cu valoarea cn,n-h=2.785, unde n-nr de masuratori, h- nr

de necunoscute.

Daca |v isvi|< cn,n-h,atunci masuratorile sunt bune, iar in caz contrar avem masuratori gresite care trebuie inlaturate.

In cazul nostru masuratoarea cu nr 6 este gresita si astfel trebuie eliminata reluandu-se compensarea.

Reluarea calculelor eliminand masuratoarea 6.

Nr dx4 dx5 dx6 dx3 dx2 dx1 Δt lik [µgal] vi [µgal] Nr. vi/svi c

1 1 0 0 0 0 0 0.35 -17.75 1.91 4 0.20

2.785

DA

2 0 1 0 0 0 0 0.72 -9.78 -0.31 5 -0.03 DA

3 0 1 0 0 0 0 0.78 -2.31 6.34 5 0.65 DA

4 0 0 1 0 0 0 1.05 -16.88 -8.28 6 -0.85 DA

5 0 0 1 0 0 0 1.12 -5.05 2.73 6 0.28 DA

6 0 0 0 1 0 0 1.28 -43.76 -35.47 3 -3.66 NU

7 0 0 0 1 0 0 1.35 6.28 13.75 3 1.42 DA

8 0 0 0 0 1 0 1.52 -7.82 0.98 2 0.10 DA

9 0 0 0 0 1 0 1.58 -3.04 4.94 2 0.51 DA

10 0 0 0 0 0 1 1.75 -7.63 0.77 1 0.08 DA

11 0 0 0 0 0 1 1.80 1.15 8.92 1 0.92 DA

12 1 0 0 0 0 0 2.03 4.80 3.67 4 0.38 DA

13 1 0 0 0 0 0 2.07 -0.01 -1.56 4 -0.16 DA

14 0 1 0 0 0 0 2.18 8.42 -0.23 5 -0.02 DA

15 0 1 0 0 0 0 2.25 3.66 -5.81 5 -0.60 DA

16 0 0 1 0 0 0 2.38 7.87 0.00 6 0.00 DA

17 0 0 1 0 0 0 2.43 14.05 5.56 6 0.57 DA

18 0 0 0 1 0 0 2.57 11.58 4.01 3 0.41 DA

19 0 0 0 1 0 0 2.62 25.90 17.72 3 1.83 DA

20 0 0 0 0 1 0 2.88 7.55 -0.53 2 -0.05 DA

21 0 0 0 0 1 0 2.93 3.31 -5.39 2 -0.56 DA

22 0 0 0 0 0 1 3.07 -3.42 -11.30 1 -1.16 DA

23 0 0 0 0 0 1 3.10 9.90 1.61 1 0.17 DA

24 1 0 0 0 0 0 3.32 12.96 -4.03 4 -0.41 DA

Nr dx4 dx5 dx6 dx3 dx2 dx1 Δtlik

[µgal]1 1 0 0 0 0 0 0.35 -17.752 0 1 0 0 0 0 0.72 -9.783 0 1 0 0 0 0 0.78 -2.314 0 0 1 0 0 0 1.05 -16.885 0 0 1 0 0 0 1.12 -5.056 0 0 0 1 0 0 1.35 6.287 0 0 0 0 1 0 1.52 -7.828 0 0 0 0 1 0 1.58 -3.049 0 0 0 0 0 1 1.75 -7.63

10 0 0 0 0 0 1 1.80 1.1511 1 0 0 0 0 0 2.03 4.8012 1 0 0 0 0 0 2.07 -0.0113 0 1 0 0 0 0 2.18 8.4214 0 1 0 0 0 0 2.25 3.6615 0 0 1 0 0 0 2.38 7.8716 0 0 1 0 0 0 2.43 14.0517 0 0 0 1 0 0 2.57 11.5818 0 0 0 1 0 0 2.62 25.9019 0 0 0 0 1 0 2.88 7.5520 0 0 0 0 1 0 2.93 3.3121 0 0 0 0 0 1 3.07 -3.4222 0 0 0 0 0 1 3.10 9.9023 1 0 0 0 0 0 3.32 12.96

Valori provizorii [mgal]

x0

1=4050.384

6x

02=

4050.1420

x0

3=4049.960

7x

04=

4050.3699

x0

5=4050.422

3x

06=

4050.1629

A

1 0 0 0 0 0 0.35

L [µgal]

-17.75

0 1 0 0 0 0 0.72

-9.78

0 1 0 0 0 0 0.78

-2.31

0 0 1 0 0 0 1.05

-16.88

0 0 1 0 0 0 1.12

-5.05

0 0 0 1 0 0 1.35

6.28

0 0 0 0 1 0 1.52

-7.82

0 0 0 0 1 0 1.58

-3.04

0 0 0 0 0 1 1.75

-7.63

0 0 0 0 0 1 1.80

1.15

1 0 0 0 0 0 2.03

4.80

1 0 0 0 0 0 2.07

-0.01

0 1 0 0 0 0 2.18

8.42

0 1 0 0 0 0 2.25

3.66

0 0 1 0 0 0 2.38

7.87

0 0 1 0 0 0 2.43

14.05

0 0 0 1 0 0 2.57

11.58

0 0 0 1 0 0 2.62

25.90

0 0 0 0 1 0 2.88

7.55

0 0 0 0 1 0 2.93

3.31

0 0 0 0 0 1 3.07

-3.42

0 0 0 0 0 1 3.10

9.90

1 0 0 0 0 0 3.32

12.96

N

4 0 0 0 0 0 7.770 4 0 0 0 0 5.930 0 4 0 0 0 6.980 0 0 3 0 0 6.530 0 0 0 4 0 8.920 0 0 0 0 4 9.72

7.77 5.93 6.98 6.53 8.92 9.72 106.74

4 5 6 3 2 1 Y

N¯¹

0.5410 0.2223 0.2617 0.3264 0.3341 0.3641 -0.1499 40.2223 0.4199 0.1999 0.2494 0.2553 0.2782 -0.1145 50.2617 0.1999 0.4853 0.2935 0.3004 0.3274 -0.1348 60.3264 0.2494 0.2935 0.6995 0.3748 0.4084 -0.1681 30.3341 0.2553 0.3004 0.3748 0.6336 0.4180 -0.1721 20.3641 0.2782 0.3274 0.4084 0.4180 0.7055 -0.1875 1-0.1499 -0.1145 -0.1348 -0.1681 -0.1721 -0.1875 0.0772 Y

X [µgal]

19.23 x04

Valori provizorii [mgal]

Corectii [mgal]

Valori compensate [mgal]

14.69 x05

x01= 4050.3846 0.0241 4050.4086

17.29 x06

x02= 4050.1420 0.0221 4050.1641

6.99 x03 x03= 4049.9607 0.0070 4049.9677

22.08 x02

x04= 4050.3699 0.0192 4050.3892

24.06 x01

x05= 4050.4223 0.0146 4050.4370

-9.91 [µgal/h]

x06= 4050.1629 0.0173 4050.1802

δg45= 0.0478

[mgal]

[VV] 503.523 V

[µgal]

-1.98-2.18

4.63

-9.98

1.18

-0.11

-0.76

3.36

-0.907.383.89-1.251.49-3.931.567.24-6.866.971.07-3.67-9.733.25-0.66

δg56= -0.2568 [mgal] n 23δg63= -0.2125 [mgal] h 7δg32= 0.1964 [mgal] So [µgal] 5.610δg21= 0.2446 [mgal] Svi [µgal] 4.679δg14= -0.0194 [mgal]

Ab st. a unitatii de

pondere (s0) [µgal]

Ab st. a unei mas. compensate

[µgal] Sδij [µgal]

5.61

sx1= 4.71 Sδg45 4.031sx2= 4.47 Sδg56 3.988sx3= 4.69 Sδg63 4.337sx4= 4.13 Sδg32 4.285sx5= 3.63 Sδg21 3.979sx6= 3.91 Sδg14 4.039

sy= 1.56

Aplicand din nou testul Pope se poate observa ca toate masuratorile sunt in regula

Nr dx4 dx5 dx6 dx3 dx2 dx1 Δt lik

[µgal]vi

[µgal] Nr. vi/svi c

1 1 0 0 0 0 0 0.35 -17.75 -1.98 4 -0.424

2.755

DA

2 0 1 0 0 0 0 0.72 -9.78 -2.18 5 -0.467 DA

3 0 1 0 0 0 0 0.78 -2.31 4.63 5 0.989 DA

4 0 0 1 0 0 0 1.05 -16.88 -9.98 6 -2.134 DA

5 0 0 1 0 0 0 1.12 -5.05 1.18 6 0.253 DA

6 0 0 0 1 0 0 1.35 6.28 -0.11 3 -0.023 DA

7 0 0 0 0 1 0 1.52 -7.82 -0.76 2 -0.163 DA

8 0 0 0 0 1 0 1.58 -3.04 3.36 2 0.718 DA

9 0 0 0 0 0 1 1.75 -7.63 -0.90 1 -0.192 DA

10 0 0 0 0 0 1 1.80 1.15 7.38 1 1.577 DA

11 1 0 0 0 0 0 2.03 4.80 3.89 4 0.832 DA

12 1 0 0 0 0 0 2.07 -0.01 -1.25 4 -0.267 DA

13 0 1 0 0 0 0 2.18 8.42 1.49 5 0.318 DA

14 0 1 0 0 0 0 2.25 3.66 -3.93 5 -0.841 DA

15 0 0 1 0 0 0 2.38 7.87 1.56 6 0.333 DA

16 0 0 1 0 0 0 2.43 14.05 7.24 6 1.548 DA

17 0 0 0 1 0 0 2.57 11.58 -6.86 3 -1.466 DA

18 0 0 0 1 0 0 2.62 25.90 6.97 3 1.489 DA

19 0 0 0 0 1 0 2.88 7.55 1.07 2 0.229 DA

20 0 0 0 0 1 0 2.93 3.31 -3.67 2 -0.784 DA

21 0 0 0 0 0 1 3.07 -3.42 -9.73 1 -2.080 DA

22 0 0 0 0 0 1 3.10 9.90 3.25 1 0.695 DA

23 1 0 0 0 0 0 3.32 12.96 -0.66 4 -0.140 DA

IV. Realizarea unei comparatii intre rezultatele obtinute intre cele 2 metode (tabel comparativ);

δgij δgij grafic

δgij analitic 1 [mgal] δgij analitic 2 [mgal] Sδgij 1 [µgal]

Sδgij 2 [µgal] Δ [mgal]

δg45 0.0504 0.0467 0.0478 8.277 4.031 0.0026δg56 -0.25895 -0.2562 -0.2568 8.193 3.988 -0.0021δg63 -0.19495 -0.1850 -0.2125 8.178 4.337 0.0175δg32 0.17835 0.1701 0.1964 8.197 4.285 -0.0180δg21 0.24735 0.2451 0.2446 8.175 3.979 0.0028δg14 -0.01275 -0.0206 -0.0194 8.293 4.039 0.0067

Datorita eventualelor pante ale dreptelor de regresie reprezentate, se obtin valori relative ale gravitatii mai putin precise decat in urma folosirii metodei analitice (in special in urma compensarii efectuate dupa eliminarea masuratorii eronate).