Teaching examples show how total-field magnetic anomalies depend on magnetic inclination, survey direction, geometry and remanent magnetization.
At low northern latitude, a simple induced total-field magnetic anomaly is generally asymmetric and bipolar, not a symmetric central positive peak. A compact body more magnetic than its surroundings, magnetized parallel to a northward, downward ambient field, gives its principal positive lobe on the southern side and a negative lobe toward the north. At exactly zero magnetic inclination its central anomaly reverses relative to the pole; latitude and survey orientation must therefore be included.[ref]
Magnetic line profiles by UBC Geophysical Inversion Facility. Line-profile examples 1–5: latitude, profile orientation and remanence effects
For an original explicit sketch, put a dipole at depth and let increase northward. In a north–south vertical section with inducing inclination , an induced magnetization parallel to the ambient field givesA geocentric-dipole approximation at latitude gives , only an illustrative field direction, not a measured local value.
Original induced-dipole profiles: a positive magnetic body and an excavated or weakly magnetized replacement give opposite signs at the same field inclination
. Details. For the actual crater, breccia, water and sediment may replace more magnetic basalt, giving negative magnetization contrast. In that case reverse the simple positive-body sketch: a dominant southern low and a northern high are possible even with purely induced contrasts. The magnetic sign cannot be inferred from density or from the word “crater” alone.
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: 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.[ref]
Magnetic line profiles by UBC Geophysical Inversion Facility. Examples 1–2: the low lies north at northern inclination and south at southern inclination
An explicit sketching model is an induced magnetic dipole at depth . With northward coordinate , and unit field direction , its normalized total-field magnetic anomaly isThe plot uses only as an illustrative dipole-field inclination for a latitude near 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.
Induced-source magnetic anomalies for opposite inclinations on a south–north profile
. Details. For the same geometry, field strength and induced magnetization model at the opposite magnetic inclination, replacing by gives . Thus the north–south asymmetry reverses: the principal low moves to the northern side and the high to the southern side. It is a horizontal reflection of the simple profile, rather than a necessary reversal of every anomaly's sign. At a magnetic pole the induced anomaly is symmetric; at the magnetic equator the symmetry is different again. If remanent magnetization dominates, a hemisphere change alone does not determine the new profile because that remanence direction also has to be specified.
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 northward and downward, as in this northern mid-latitude setting. Writewhere is the anomalous magnetic field and the last expression assumes . A total-field magnetic anomaly measures a field projection, so it need not have the same sign everywhere above a high-susceptibility body.[ref]
The 100 km east–west extent makes an approximately two-dimensional, east–west-striking body a useful model away from its ends. On a profile drawn north on the left, south on the right, the expected normally induced response has a subsidiary negative lobe on the northern side and a stronger 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.
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.


