1. Gravity and Magnetic Surveying
Lecture 4
Gravity and Magnetic Surveying

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

3. 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.

4. Terrain chart for topographic effects

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

15. 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])

16. 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;

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

19. Magnetic Field Measurements and Interpretation

20. Roberts and Jachens, USGS, 1999

22. The dipole Can be caused by a bar magnet
or a loop of current carrying wire

23. Dipole (two poles) Note direction of field
Earth’s field is mainly a dipole, but not only.
North pole is south magnetic pole, but that may flip

24. Geomagnetic Field
Dynamo in outer core generates the geomagnetic field.

25. Geographic north is determined by the spin axis.
Magnetic north (actually a south magnetic pole) is
Determined by currents in the core. It is presently near Greenland
The geomagnetic field. Declination is angle field makes with
geographic north. Inclination is the angle the field makes with
The horizontal (dip). D=13.5o and I=60o in LA

26. Location North Magnetic Pole Year Latitude ( °N) Longitude ( °W) 2001
81.3
110.8
2002
81.6
111.6
2003
82.0
112.4
2004
82.3
113.4
2005
82.7
114.4

27. Principle of the geodynamo
A dynamo makes electrical current by moving a coil relative to a magnetic field
(e.g. that from a magnet).
One way to make a magnetic field is to generate an electric current. The geodynamo
Is thought to be caused by electric currents (a billion amperes) in the liquid iron core.
Motion of the iron as the core convects regenerates the current.

28. Change in declination of compass at the geomagnetic observatory London

29. Contours of geomagnetic field
Contours are in units of 5000 nT (nanoteslas) and range from 25, nT

30. Non-Dipole Geomagnetic Field
This pattern changes in time drifting hundreds of km across the globe/year.
Thought to be due to eddy currents in the outer core it shows that these
Motions are a million times faster than plate tectonics; Why?

31. Magnetism in rocks records the Earth’s magnetic field at time of cooling
Hot (above Curie
Point) magnetism
is random.
Cool (below Curie
Point) magnetism
locks in to direction
of the magnetic field
at that time. It is then
stable w.r.t. future
Reversals.
Blocking temperature is temperature below the Curie
Point that magnetism locks in.