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

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.

Lecture 7 ended here, Thurs Sept 30th

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

Predicting magnetic field variations

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

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

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

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.

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.

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

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:

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 :

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).

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

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).

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.

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.

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.

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 (www.getech.com).

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 (www.getech.com). Psuedo-magnetic field Psuedo-gravity field