1. Predicting magnetic field variations
the presence of a magnetized object creates a dipolar disturbance
the disturbance is then measured as an “anomaly” by the magnetometer
the magnetometer may measure the horizontal or vertical component of the disturbance
other magnetometers measure the total magnetic field (see later)
the maximum vertical field will be measured where the dipole field points straight down
the horizontal field anomaly will be maximum (or minimum) when the dipole field points horizontally

2. Top: a buried dipole with an internal magnetization vector, induced by the external field of the earth. This sets up a perturbation to the external field, ΔB.
Bottom: You should sketch the horizontal field anomaly, ΔBh and the vertical field anomaly ΔBv recorded over this anomaly by a two-component magnetometer.

3. Lecture 7 ended here, Thurs Sept 30th

4. Predicting magnetic field variations
some magentometers measure the “total magnetic field”
we need to predict the anomaly in the total field caused by the buried anomaly
The total field: this is the magnitude
The total field anomaly: this is the difference between the total field and the background, i.e.,
Note that

5. Predicting magnetic field variations

6. Predicting magnetic field variations
The total field anomaly is approximately equal to the anomaly in the component of the field parallel to the direction of the total field, B

7. Now: sketch the total field anomaly on top of your sketch of the vertical and horizontal field anomalies

8. Instrumentation for magnetic prospecting
“fluxgate magnetometers measure the vector components of the field
“proton-precession” magnetometers measure the total field anomaly
high precision magnetometers are also available – “optically pumped” magnetometers operate on quantum mechanical observations on alkali metal vapours

9. Fluxgate magnetometer
Fluxgate magnetometers The principle of the operation of a uxgate magnetometer is shown in Figure 3.7. Two high permeability magnetic cores (usually ferrite or permalloy) are magnetized in opposite directions by induction using an alternating electric current. The current is large enough to drive the
induced magnetic elds into saturation. The resultant B eld therefore attens at its saturation value, as in Figure 3.7b). If there is an additional, external eld (i.e., the natural magnetic eld) then the saturation will occur slightly earlier for one core, and slightly later for the second core, as in Figure
3.7c). The two elds, when summed will then no longer be zero valued at all times. The time variation in the sum of the two elds causes a voltage in the secondary windings around the cores, as in Figure3.7c). Further technical details are given in the textbook by Telford et al. The net result is a signal that is proportional to the component of the external eld that is parallel with the axis of the cores. Three component uxgate magnetometers have similar cores arranged in three mutually orthogonal directions so that the three Cartesian components of the magnetic eld will be measured.

10. Proton precession magnetometer
Proton precession magnetometers These instruments operate on an entirely dierent physical principle, that of nuclear magnetic resonance. The atomic nuclei of hydrogen (think of them as magnetic dipoles) will tend to align themselves with any external magnetic eld. If this eld is disrupted (by an articial
magnetic eld) the protons will re-align themselves. If the articial eld is once more removed, the protons will return to their original orientation. However they return by precessing about the earth's eld, much like a spinning top precesses as it spins in an external gravitational eld. The precession takes place with a well dened frequency, known as the Lamour frequency, given by fL = 2pjBj (3.32) where pis the \gyromagnetic ratio" for protons, a physical constant known to within an accuracy of .001 %
Proton precession magnetometer require a uid rich in protons (usually water), a coil to create the articial eld and to sense the precession frequency. They are sensitive to the magnitude of the external eld, rather than any particular component.

11. Poisson relationship: relating gravity and magnetics
More complex geological models are often required
The gravity anomaly is easier to predict
The “Poisson relationship” relates the magnetic anomaly to the gravity anomaly
The following assumptions are required:
The buried anomaly has a density contrast, and a magnetization contrast
The boundaries for both contrasts is the same
The density and magnetization of the target is uniform

12. Poisson relationship: relating gravity and magnetics
Revisit the dipole model:
Magnetic potential is
And, recall the gravity potential is:
where M is the dipole moment per unit volume (i.e., the magnetization) and is the excess mass per unit volume (i.e., the density contrast). These relationships show in a simple way that the magnetic potential varies faster than the gravity eld (because it has one additional spatial derivative due to the gradient operator).
Rewriting both of these by dividing by volume:

13. Poisson relationship: relating gravity and magnetics
We get gravity from potential with
Note the similarity of magnetic potential and gravity acceleration!
where M is the dipole moment per unit volume (i.e., the magnetization) and is the excess mass per unit volume (i.e., the density contrast). These relationships show in a simple way that the magnetic potential varies faster than the gravity eld (because it has one additional spatial derivative due to the gradient operator).
Isolate :

14. Poisson relationship: relating gravity and magnetics
Substituting, we obtain the “Poisson relationship”:
Note that the dot product measures the component of gravity in the direction of magnetization, so that
where M is the dipole moment per unit volume (i.e., the magnetization) and is the excess mass per unit volume (i.e., the density contrast). These relationships show in a simple way that the magnetic potential varies faster than the gravity eld (because it has one additional spatial derivative due to the gradient operator).

15. Poisson relationship: relating gravity and magnetics
Magnetic potential:
Magnetic field:
The key term, tells us to:
Project g in the direction M
Take the gradient
where M is the dipole moment per unit volume (i.e., the magnetization) and is the excess mass per unit volume (i.e., the density contrast). These relationships show in a simple way that the magnetic potential varies faster than the gravity eld (because it has one additional spatial derivative due to the gradient operator).
Note that the component of the gradient in any direction is the rate of change in that direction, so for example the x component of is

16. Poisson relationship: relating gravity and magnetics
Horizontal components:
For non-horizontal components it is less obvious. For example, for the total field anomaly we need
(i.e., pointing in the direction of the B field)
where M is the dipole moment per unit volume (i.e., the magnetization) and is the excess mass per unit volume (i.e., the density contrast). These relationships show in a simple way that the magnetic potential varies faster than the gravity eld (because it has one additional spatial derivative due to the gradient operator).

17. Poisson relationship: relating gravity and magnetics
For the total field anomaly we need
(i.e., pointing in the direction of the B field)
Imagine instead, we move the target a small amount in the B direction, and change the sign of the gravity field
the sum of the two fields is equal to the required derivative
To solve this, imagine instead that we could move the anomaly a small amount in the B direction, and change the sign of the gravity eld. These are both impossible in reality, but straightforward in a computer model. The sum of the original gravity eld and the new (negative) gravity eld would be exactly equivalent to the required derivative. The diagram in Figure 3.14 shows how this construction can be used to compute the total eld anomaly for a buried object.

18. Poisson relationship: relating gravity and magnetics
To solve this, imagine instead that we could move the anomaly a small amount in the B direction, and change the sign of the gravity eld. These are both impossible in reality, but straightforward in a computer model. The sum of the original gravity eld and the new (negative) gravity eld would be exactly equivalent to the required derivative. The diagram in Figure 3.14 shows how this construction can be used to compute the total eld anomaly for a buried object.
The construction is equivalent to a new body, with positive and negative monopoles on the two surfaces.

19. Poisson relationship: relating gravity and magnetics
Common applications:
Model the magnetic anomaly from the predicted gravity anomaly
Calculate the “pseudo-gravity” directly from the magnetic field data
Calculate the “pseudo-magnetic field” directly from the gravity field
Common applications of the Poisson relationship are
1. As we have shown, the Poisson relationship allows us to calculate (i.e., to model) the magnetic anomaly if we have a way of calculating the gravity anomaly { this is useful for approximate sketches (such as the ones above) and for quantitative calculations.
2. The Poisson relationship allows us to calculate a \pseudo-gravity" anomaly directly from the magnetic eld data. This is useful to eliminate the skew in magnetic eld proles with respect to the location of the magnetic targets. It also creates a eld that i) no longer exhibits a skew with respect to the
location of the target, and ii) is much smoother than the magnetic eld data.
3. The Poisson relationship allows us to compute \pseudo-magnetic elds" from gravity surveys, for comparison with observed magnetic proles. This is useful for testing the assumptions above (homogeneous, self-contained bodies) and detecting the presence of remanent magnetization.

20. Poisson relationship: examples
a) A geological map of Poland, showing the division between shallower crystalline basement of the East European platform to the NE, and the thick Paleozoic and Mesozoic sedimentary cover to the SW. b) The Bouguer anomaly gravity eld over central Poland, c) the total magnetic eld anomaly, d) the pseudo-magnetic eld anomaly calculated from the gravity, and e) the pseudo-gravity anomaly calculated from the magnetics. From Geophysical Exploration Ltd (

21. Poisson relationship: examples
Bouguer gravity anomaly
Total magnetic field anomaly
a) A geological map of Poland, showing the division between shallower crystalline basement of the East European platform to the NE, and the thick Paleozoic and Mesozoic sedimentary cover to the SW. b) The Bouguer anomaly gravity eld over central Poland, c) the total magnetic eld anomaly, d) the pseudo-magnetic eld anomaly calculated from the gravity, and e) the pseudo-gravity anomaly calculated from the magnetics. From Geophysical Exploration Ltd (
Psuedo-magnetic field
Psuedo-gravity field