Question 3 of 8: Sphere Anomaly Components and Rock Magnetism

Question 3: Sphere Anomaly Components and Rock Magnetism (equal value)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(i) Sphere anomaly components. With the magnetization induced by, and therefore parallel to, the Earth's field $B$, the sphere acts as a dipole pointing along $B$. On the printed figure the field lines carry arrowheads pointing UP and to the RIGHT, so $B$ comes up out of the ground with its horizontal component toward the right; the lines are drawn at about $55^\circ$ to the surface, so the inclination is about $I\approx-55^\circ$. The sketch below reproduces the figure and plots the anomalies computed for an induced dipole with that inclination, along a profile running south (left) to north (right), with the sphere's centre at depth $z$:

• Vertical component $\Delta Z$ (positive downward): one dominant NEGATIVE extremum almost directly over the sphere. The induced dipole points upward, so its field just above the body also points upward and adds to the upward vertical component of the Earth's field. The extremum sits slightly north of the centre (about $0.16z$), and there is only a small positive flank on the south side, about $1.2z$ from the centre and roughly one tenth the size.
• Horizontal component $\Delta H$ (positive toward north): antisymmetric, negative on the south side (extreme about $0.3z$ south of the centre) and positive on the north side (about $0.7z$ north), crossing zero slightly north of the centre (about $0.2z$).
• Total field $\Delta T$ (the component along $B$, which a total-field magnetometer records): a positive peak displaced slightly north of the body (about $0.3z$), with a negative lobe on the SOUTH side (about $0.8z$ from the centre, roughly a quarter of the peak). The low always lies on the side toward the nearer magnetic pole: north of the body in the Northern Hemisphere, south of it in the Southern Hemisphere.

Geographic north and hemisphere. The horizontal component of the geomagnetic field always points toward (magnetic) north, so north is toward the RIGHT of the figure, the direction in which the arrowheads lean; mark N on the right-hand side. The field vector points UPWARD out of the ground (negative inclination), which happens only in the Southern Hemisphere; in the Northern Hemisphere the field points down into the ground as it heads north. The survey is therefore in the Southern Hemisphere, at an inclination of about $-55^\circ$ (a mid southern magnetic latitude, about $36^\circ$S from $\tan I=2\tan\lambda$).

(ii) Rock magnetism classes and magnetic domains. The most important class of magnetism in an exploration context is ferrimagnetism (with true ferromagnetism, in the strict sense of iron/nickel/cobalt metal, essentially absent in natural rocks) — overwhelmingly carried by magnetite (Fe$_3$O$_4$) and, to a lesser extent, its oxidized/titanium-bearing relatives titanomagnetite, maghemite ($\gamma$-Fe$_2$O$_3$) and pyrrhotite (Fe$_{1-x}$S, which is actually ferrimagnetic in its monoclinic form). These minerals have susceptibilities orders of magnitude larger than the weak paramagnetic (e.g. biotite, pyroxene) or diamagnetic (e.g. quartz, calcite) minerals that make up the bulk of most rocks, so it is almost always the trace magnetite content that a magnetic survey is actually detecting, whether the target is the magnetite itself (e.g. banded iron formation, some skarns) or magnetite acting as an indirect tracer of a host rock type or alteration halo.

Ferrimagnetism arises because the crystal lattice contains TWO magnetic sublattices whose moments are aligned ANTI-parallel by a strong quantum-mechanical superexchange interaction (the same coupling that produces true antiferromagnetism), but the two sublattices are UNEQUAL in magnitude (different numbers of ions, or different ionic moments, on each sublattice site), so their opposing moments do not fully cancel and a net spontaneous magnetization remains. Below the Curie temperature ($T_C\approx580^\circ$C for magnetite), the mineral spontaneously divides into small volumes called magnetic domains, each fully magnetized to saturation but with different domains pointing in different crystallographically-preferred directions so that, overall, an unmagnetized grain shows near-zero net moment; domain walls (Bloch walls) separate regions of differing orientation. An applied field (the Earth's own field, during cooling through $T_C$ or during later exposure) causes the domain walls to migrate, growing domains favourably aligned with the field at the expense of others, and can rotate the magnetization within domains resistant to wall motion — the NET result, summed over all domains, is the bulk induced (and, once the field is removed, partly remanent) magnetization measured at the sample or outcrop scale.