Question 6 of 9: Magnetic Anomaly Variation with Latitude and Reduction Methods

Question 6: Magnetic Anomaly Variation with Latitude and Reduction Methods (16.66% of paper)

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.

Why the anomaly changes with latitude. A body's total-field magnetic anomaly is the projection of its induced (and, if present, remanent) dipole field ONTO the direction of the ambient (inducing) field, and that ambient-field direction — its inclination $I$ — itself changes systematically with magnetic latitude, from nearly horizontal ($I\approx0^\circ$) at the magnetic equator to nearly vertical ($I\approx90^\circ$) at the magnetic poles. Since induced magnetization is (to first order) parallel to the ambient field, the SAME physical body, at the SAME depth, produces a total-field anomaly whose shape rotates from a simple symmetric positive peak directly over the source at high (polar) magnetic latitude, through an increasingly asymmetric, skewed shape with a prominent negative lobe on the equatorward side at mid-latitude, to a predominantly NEGATIVE anomaly straddling the source (with two small positive side lobes) at the magnetic equator itself, where the field is horizontal and the projection of a vertical dipole's field onto a horizontal ambient field is largely negative directly over the source.

How this complicates interpretation. At low-to-mid magnetic latitude the anomaly's PEAK is offset laterally from the true position of the source (typically displaced toward the pole from the body), so a naive interpreter who assumes "peak equals location," as is valid near the pole, will mis-locate the target; the skewed shape also makes simple half-width depth rules and visual pattern-matching against a library of polar model curves unreliable, and closely spaced sources produce a confusing, overlapping pattern of positive and negative lobes that is far harder to separate into individual anomalies than the simple, symmetric polar case.

Reduction-to-pole (RTP). RTP is a frequency-domain filter (using the known regional field inclination/declination) that mathematically transforms an anomaly measured at any latitude into the shape it WOULD have if measured at the pole — recentring the anomaly directly over the source and restoring the simple symmetric-peak interpretation rules. Strength: makes anomaly location and shape directly interpretable using the well-developed polar toolbox (half-width depth rules, Euler deconvolution structural indices, simple visual correlation with geology). Weakness: the RTP filter's amplitude response is proportional to $1/\sin^2I'$ (where $I'$ is the effective inclination), which blows up as $I'\to0$ near the magnetic equator, catastrophically amplifying noise there; RTP also strictly assumes purely INDUCED magnetization in a known direction, so it distorts anomalies from bodies with significant remanent magnetization in a different direction.

Reduction-to-equator (RTE). A companion transform designed specifically for LOW-latitude surveys, RTE recentres the anomaly assuming a horizontal ambient field. Strength: stable exactly where RTP is unstable (near the equator). Weakness: unstable near the poles (the opposite failure mode to RTP), and shares RTP's assumption of purely induced magnetization.

Analytic signal. Computed from the three orthogonal derivatives of the total field, $|A(x,y)|=\sqrt{(\partial T/\partial x)^2+(\partial T/\partial y)^2+(\partial T/\partial z)^2}$, the analytic signal's amplitude is MATHEMATICALLY INDEPENDENT of both the magnetization direction and the ambient field direction, so its peak sits directly over (or very close to) a simple source regardless of latitude. Strength: stable at all latitudes, including the equator where RTP fails, and does not require the magnetization direction to be known (useful when remanence is significant or unknown). Weakness: it only estimates source location/edges and an approximate depth, not the true reduced-to-pole anomaly shape, and its peaks broaden and can merge for deep or closely spaced sources, reducing resolution compared to a well-conditioned RTP.

Euler deconvolution. An automated technique that solves Euler's homogeneity equation using the measured field and its spatial gradients at a chosen structural index (a number encoding the assumed source geometry — sphere, cylinder, contact) to estimate source location and depth directly, without an explicit RTP step. Strength: latitude-independent, fast, automatable over a whole survey, and gives quantitative depth estimates. Weakness: results are sensitive to the (often not well known) choice of structural index and to noise in the numerically computed gradients, and it provides location/depth but not a reduced anomaly map for further qualitative interpretation.