Solution (source code)

= Solution

Assume the <greenstone belt> is more magnetically susceptible than the host rocks and <granite>, its <magnetization> is mainly <induced magnetization>, and the body is roughly east–west elongated so that the south–north line crosses it. At southern magnetic latitudes the main field has negative <magnetic inclination> in a north-and-down coordinate convention. The <total-field magnetic anomaly> is then generally asymmetric: \b[the principal negative lobe is on the southern side and the positive lobe is displaced northward] for the simple induced source illustrated here. The exact lobe sizes and peak positions depend on body geometry and the actual <magnetic inclination>.<Magnetic line profiles by UBC Geophysical Inversion Facility>[Examples 1–2: the low lies north at northern inclination and south at southern inclination]{ref}

An explicit sketching model is an induced <magnetic dipole> at depth $d$. With northward coordinate $x$, $\mathbf r=(x,-d)$ and unit field direction $\widehat{\mathbf F}=(\cos I,\sin I)$, its normalized <total-field magnetic anomaly> is
$$
\Delta T(x)\propto\frac{3(\widehat{\mathbf F}\cdot\mathbf r)^2/(x^2+d^2)-1}{(x^2+d^2)^{3/2}}.
$$
The plot uses $I=-36^\circ$ only as an illustrative dipole-field inclination for a latitude near $20^\circ$ south, not a measured modern field at the site. A wide <greenstone belt> would broaden the response and can produce prominent edge anomalies. <Remanent magnetization> or a magnetic <granite> could change the sketch substantially; <gravity> alone cannot identify the magnetic source.

\Image[/past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2023/paper-1-magnetic-profiles.png]
{title=Induced-source magnetic anomalies for opposite inclinations on a south–north profile}