1. Gravity Interpretation
Lecture 3
Gravity Interpretation

3. Gravityis the negative gradient of potential
Since from
Given a gravity survey you can sum the normal gravity field
Times area to obtain the anomalous mass.

4. Calculate excess mass:
Sum area times g divide answer by 2πG

6. Gravity measures the force of attraction of the Earth which
Depends on the mass distribution through Newton’s law of
Gravity
Force= G m1m2/r2=m1g

9. Gravity from an Infinite Slabgz R h gz

10. Gravity changes at different
elevations in mines
tunnels or buildings
g2=gE2+gb gb
g1-g2= gE1 -gE2 -2gb
g1=gE1-gb gE

11. Gravity Cylinder z dy x R z

12. Terrain corrections
Bouguer correction assumes and infinite slab. Effect of hills or valley cause
Gravity to be less. To correct both must be added.

13. Hammer Charts
Terrain corrections can be computed using transparent template, called a Hammer Chart, which is placed over a topographic map.
Chart is centred on gravity station and topography read off at centre of each segment.

14. Terrain chart for topographic effects

17. Global Free Air Gravity Map
See topographic effect Andes, Himalayas, Deep ocean basins

20. Infinite vertical sheet (Dike)
G=2Gdensity t ln[{(h+L)^2+x^2}/(x^2+h^2)]
t=thickness
L= length of sheet
Telford et al. Eq. 2.65

26. Matlab Program for Cylinder
x=[-10:.1:10];
%depth
a(1)=1;
%radius
a(2)=0.5;
%density
drho=1e3;
x1=x;
G=6.67e-11;
R=sqrt(x1.^2+a(1)^2);
dg=2*G*drho*pi*a(2)^2*a(1)./R.^2;
f=dg*1e5;
figure(1)
plot(x,f,'r')
axis([-10,10,-2,2])

27. Program for Talwani Polygon
close all
xs=[-10:.1:10];
sumzee=0.0;
for i=1:length(xd)-1;
x=xd(i)-xs;xp=xd(i+1)-xs;
z=zd(i); zp=zd(i+1);
th=atan2(z,x);
thp=atan2(zp,xp);
phi=atan2((zp-z),(xp-x));
if z-zp==0, zp=0.0001;end
a=xp+zp*((xp-x)./(z-zp));
term1=(th-thp);
num=cos(th).*(tan(th)-tan(phi));
den=cos(thp).*(tan(thp)-tan(phi));
term2=tan(phi).*log(num./den);
den
zee=a.*sin(phi).*cos(phi).*(term1+term2);
sumzee=zee+sumzee;
end
G=6.672e-11;
rho=1e3;

29. Gravity across the US and its relationship with tectonic
features. Thick crust or thin lithosphere = low gravity because
of less mass.

30. Problem 3, page 123
An extensive dolerite sill was intruded at the interface between horizontal sandstones. Sketch the gravity profiles expected if the sill and beds have been displaced by (a) A steeply dipping normal fault, (b) A shallow thrust fault, and © A strike slip fault.

31. Problem 4, page 124
Calculate how much gravity changes, and whether it is an increase or a decreas, on going one km north from (a) the equator, (b) 45 deg. North, and © 45 deg. South.

32. Problem 6, page 124
A spherical cavity of radius 8 m has its center 15 m below the surface. If the cavity if full of water and is in rocks of density 2.4 g/cm3, what is the maximum size of its anomaly?

33. Problem 8, page 124
Suppose g = m/s2 at sea level. What would be the value of g at 1 km above the same location.

34. Problem 9, page 124
Suppose you take a gravimeter 1 km down a mine in rock with density 2.3 g/cm3. How much would gravity change?