= Solution
Assume that the intrusion has a positive <magnetic susceptibility> contrast, that <induced magnetization> dominates its <remanent magnetization>, and that the local present-day <geomagnetic field> points roughly \b[northward and downward], as in this northern mid-latitude setting. Write
$$
\Delta\mathbf M\simeq\Delta\chi\,\mathbf H_0,\qquad \Delta T=|\mathbf B_0+\mathbf b|-|\mathbf B_0|\simeq\widehat{\mathbf B}_0\cdot\mathbf b,
$$
where $\mathbf b$ is the anomalous <magnetic field> and the last expression assumes $|\mathbf b|\ll|\mathbf B_0|$. A <total-field magnetic anomaly> measures a field projection, so it need not have the same sign everywhere above a high-susceptibility body.<Magnetic surveying: induced magnetization by UBC Geophysical Inversion Facility>[The buried-dipole construction obtains total-field response by projecting the anomalous field along the inducing field and shows how the pattern changes with field orientation.]{ref}
The 100 km east–west extent makes an approximately \b[two-dimensional, east–west-striking body] a useful model away from its ends. On a profile drawn \b[north on the left, south on the right], the expected normally induced response has a subsidiary \b[negative lobe on the northern side] and a stronger \b[positive lobe over the body, displaced towards the south]. The northward horizontal field component makes the anomaly asymmetric; its downward component produces the dominant positive response. The field falls back towards the regional value away from the intrusion. Broad bodies can have edge shoulders or a broad central high, so the sketch represents a qualitative shape rather than one uniquely specified curve.
\Image[/past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2024/paper-3-q2-magnetic-profile.png]
{title=North–south total-field anomaly of a normally induced long east–west magnetic body}
{description=An original infinite-strike line-dipole calculation illustrates the northern low and southward-displaced main high. The 65-degree downward inclination is illustrative; the geometry underneath is schematic and is not a quantitative model of the source intrusion.}
An exactly vertical inducing field would remove this north–south skew for a symmetric induced body. Real <magnetic inclination> and <magnetic declination> should be taken from a suitable <geomagnetic field> model for the survey date and location; no exact local value is supplied here. Strong oblique or reversed <remanent magnetization> can shift or reverse the lobes, and heterogeneous <magnetic susceptibility>, body dip and three-dimensional end effects can alter the profile. Higher <magnetic susceptibility> alone does not determine a unique amplitude or polarity pattern without these qualifications.
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