Dipole field Emerges from North poles, converges on South poles Falls off at a high 1/r3 rate of decay Thus we expect that magnetic anomalies are much more localized The field anomaly responds mainly to shallow targets 1. The magnitude of the eld falls o as a function of 1=r3. This is signicantly dierent from the gravi ty eld, which falls o as a function of 1=r2. We can understand this qualitatively as being the result of the close proximity of the North and South pole of the dipole, which tend to cancel each other | it is perhaps surprising that they do not cancel each other completely, even though they are assumed to be very close together. 2. When = 0 and = 180 (i.e., at the North and South poles of the dipole), the tangential component B = 0. Thus, at the poles the eld is purely radial as we expect. At the South pole ( = 0) the radial component Br is negative: the eld therefore converges on South poles and emerges from North poles, as we also expect.

Buried vertical dipole – magnetic field profiles Profile of vertical component Profile of horizontal component 1. The magnitude of the eld falls o as a function of 1=r3. This is signicantly dierent from the gravi ty eld, which falls o as a function of 1=r2. We can understand this qualitatively as being the result of the close proximity of the North and South pole of the dipole, which tend to cancel each other | it is perhaps surprising that they do not cancel each other completely, even though they are assumed to be very close together. 2. When = 0 and = 180 (i.e., at the North and South poles of the dipole), the tangential component B = 0. Thus, at the poles the eld is purely radial as we expect. At the South pole ( = 0) the radial component Br is negative: the eld therefore converges on South poles and emerges from North poles, as we also expect. Note how depth is related to width of profiles!

Buried vertical dipole – magnetic field maps Contour map of vertical component Contour map of horizontal component 1. The magnitude of the eld falls o as a function of 1=r3. This is signicantly dierent from the gravi ty eld, which falls o as a function of 1=r2. We can understand this qualitatively as being the result of the close proximity of the North and South pole of the dipole, which tend to cancel each other | it is perhaps surprising that they do not cancel each other completely, even though they are assumed to be very close together. 2. When = 0 and = 180 (i.e., at the North and South poles of the dipole), the tangential component B = 0. Thus, at the poles the eld is purely radial as we expect. At the South pole ( = 0) the radial component Br is negative: the eld therefore converges on South poles and emerges from North poles, as we also expect. Note how depth is related to width of profiles!

Lecture 6 ended here, Tues Sept 28th

Dipole field Widely used to explain Atomic scale magnetic fields – the “Bohr magneton” – arising from spin and orbit of charged particles Grain scale magnetic fields in rocks – arising from the macroscopic alignment of Bohr magnetons Magnetic anomalies in exploration geophysics – can often be approximated by dipolar fields Planetary scale geophysics – the entire observed field of the earth is nearly perfectly dipolar 1. The magnitude of the eld falls o as a function of 1=r3. This is signicantly dierent from the gravi ty eld, which falls o as a function of 1=r2. We can understand this qualitatively as being the result of the close proximity of the North and South pole of the dipole, which tend to cancel each other | it is perhaps surprising that they do not cancel each other completely, even though they are assumed to be very close together. 2. When = 0 and = 180 (i.e., at the North and South poles of the dipole), the tangential component B = 0. Thus, at the poles the eld is purely radial as we expect. At the South pole ( = 0) the radial component Br is negative: the eld therefore converges on South poles and emerges from North poles, as we also expect.

Magnetization In understanding dipolar fields, a key parameter is the orientation of the “magnetic moment”: For a collection of dipoles, i.e. a magnetic mineral, the field is due to the alignment of individual dipoles. We define, the magnetization, M as the vector sum

How does magnetization contribute to the observed field? Recall, but now is the “macroscopic current”, and is the “magnetization current” Thus

How does magnetization contribute to the observed field? Magnetic field intensity: H is that portion of the magnetic field arising only from macroscopic currents.

Units of B, H, M: B is the Magnetic induction: Units are Tesla [N C-1 m-1 s] H is the Magnetic field intensity: Units are [A m-1] M is the Magnetization: Units are also [A m-1] In “free space” there is no magnetization, thus

Induced magnetization and magnetic “susceptibility” Inside magnetic material, B and H are different Magnetic minerals acquire a magnetization by “induction” from an external field (such as the earth’s) Empirical evidence is that note, the subscript indicates this is not the only kind of magnetization (see later) thus, magnetization is parallel (or anti-parallel) to the external field the “susceptibility”, k is a rock property

Induced magnetization and magnetic “susceptibility”

Magnetic susceptibility Plays the same role in magnetics that density plays in gravity surveys Can be positive or negative, values from -.00001 to +19 are found in nature, strongest magnetic rocks are around +6 Magnetite (average k=6) is the major magnetic mineral Pyrrhotite (average k=1.5) and ilmenite (average k=1.8) also play an important role There is a very wide range in susceptibilities in rocks Generally sediments have the lowest (average) susceptibility, basic igneous rocks have the highest susceptibilities Soils and sands derived from igneous and metamorphic rocks can also be relatively rich in magnetite Magnetite is often deposited in high-energy depositional environments Iron or steel (manufactured) objects will also be strongly susceptible

Rock and mineral susceptibility: Note units!

Remanent magnetization Earlier we said The subscript i indicates the magnetization is induced by the external field Magnetization can also be permanently acquired – this is why paleomagnetic studies work In general rocks have both induced and remanent magnetization present: Note the vector sum! The relative size of the two terms is quantified by the “Königsberger ratio”:

Magnetic “permeability” Ignore the remanent magnetization (usually small) If this is zero, then this allows us to define the permeability so that: Note the vector sum!

Predicting magnetic field variations this is more difficult than it was for gravity orientation of the magnetization plays a role orientation of the sensor plays a role recall the results for a vertical dipole:

Predicting magnetic field variations the inducing field of the earth changes with latitude the target will usually not be directly below the maximum in the anomaly the resulting field anomaly sometimes opposes the earth’s field, and sometimes re-enforces it:

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.

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.