1. The framing question

• Satellites (CHAMP, SWARM) and aircraft map the global lithospheric anomaly field at ~30-km resolution (EMAG2, Meyer et al. 2017 — NCEI public domain).
• The same physics — a magnetised body distorts the regional field — works at the continent, basin, and buried-fault scales.
• How do we go from a flight-line measurement back to the body that made it?

Read more → Lecture 25 §1

Learning objectives

By the end of today, students will be able to:

1. Decompose a total-field measurement into main, external, and lithospheric components.
2. Forward-model the magnetic anomaly of a buried dipole and predict its shape, sign, and skewness with latitude.
3. Apply the half-width depth rule to estimate source depth from an anomaly profile.
4. Use an ensemble forward model to bracket the non-uniqueness of magnetic inversion.
5. Read the Seattle Fault Zone aeromagnetic anomaly as an applied earthquake-hazard problem.

2. Decomposing a magnetic measurement

• — IGRF main-field model (core dynamo).
• — ionospheric & magnetospheric variations (corrected with base stations).
• → the lithospheric signal we want.

Read more → Lecture 25 §2

3. Forward model — a buried dipole

• A compact magnetised body acts (at distance ≳ 3 body-radii) as a dipole with moment .
• The total-field anomaly depends on (i) source geometry, (ii) magnetisation direction, and (iii) the regional field direction.
• Shape changes with latitude: a body at the equator yields a single negative lobe; at the pole, a single positive lobe; mid-latitudes show a dipolar pair.

Read more → Lecture 25 §3

3b. Reduction-to-the-pole

• RTP is an FFT operator that re-projects as if the source were under a vertical inducing field.
• Removes the latitude-dependent skew, so the anomaly sits directly over its source.
• Standard pre-processing step before interpretation at any scale.

Read more → Lecture 25 §3b

4. The half-width depth rule

For a buried sphere (or 2-D vertical line) of depth :

where is the anomaly half-width at half-maximum.

• A 50-km wide anomaly → source ~32 km deep — that puts it in the lower crust / Moho.
• A 2-km wide anomaly → source ~1.3 km deep — upper-crustal intrusion or fault block.

Read more → Lecture 25 §4

5. Ensemble forward modelling

• One observed profile is consistent with many combinations — the inversion is fundamentally non-unique.
• Strategy: forward-model an ensemble of plausible sources, keep those that match the data within noise, report the range of acceptable depths/moments.
• This is the same Bayesian logic we used for earthquake location (L14) and gravity (L20).

Read more → Lecture 25 §5

6. The induced/remanent ambiguity

• A high anomaly can be (a) an induced response of high- rock to today's field, OR (b) a strong remanent moment frozen in at an earlier epoch — possibly with reversed polarity.
• The Königsberger ratio (Lecture 24) decides which.
• Field discrimination tools: paired susceptibility map + anomaly map, or rock samples with both and measured.

Read more → Lecture 25 §6

7.1 Continent scale — North America

• USGS NAM compilation (Bankey et al. 2002) reveals:
  • Mid-continent rift (Lake Superior): a 1.1 Ga failed rift carrying ~600 nT highs.
  • Appalachian belt: long-wavelength low from Grenvillian basement.
  • Siletzia (PNW Coast Ranges): a strong positive anomaly from Eocene oceanic plateau basalts.

Read more → Lecture 25 §7-1

7.2 Basin/fault scale — Seattle Fault Zone

• Blakely et al. (2002) used low-altitude aeromagnetic flights to map the Seattle Fault Zone under the Puget Lowland.
• High-magnetisation Eocene Crescent Fm. (north block) abuts low-magnetisation Tertiary sediments (south) across the fault.
• The aeromagnetic gradient is the best map of an active fault that nowhere reaches the surface.

Read more → Lecture 25 §7-2

7.3 Three-scale summary

The same physics ties all three — only the resolving wavelength differs.

8. Research Horizon

• Magnetic gradiometry on UAVs — sub-meter resolution for archaeology, UXO, mineral exploration.
• Joint gravity-magnetic-seismic inversion with ML priors — pushing past the inherent non-uniqueness.
• Continuous monitoring of volcanic edifices: magnetisation drops sharply through , so a heating intrusion reduces over time.

Read more → Lecture 25 §8

9. AI Literacy — the latitude trap

• LLMs frequently quote the half-width rule without warning that it requires RTP first at mid-to-low latitudes.
• A skewed anomaly will give a biased depth estimate if naïvely fit.
• Always ask: "At what magnetic latitude was this measurement made, and has it been reduced to the pole?"

Read more → Lecture 25 §9

10. Concept check

1. An anomaly profile has km. Estimate the source depth.
2. You measure a +400 nT high near Bremerton. Could it be a remanent low-polarity body? How would you tell?
3. Why does the Mid-continent rift show up so strongly on a magnetic map but barely on topography?

Read more → Lecture 25 §10

11. Looking ahead

• Lecture 26 — Heat and geodynamics: from radiogenic heat production to mantle convection driving the plate motions we have just measured magnetically.
• The lithospheric blocks whose anomalies we mapped today are the plates that the next module sets in motion.

Read more → Lecture 26 — Heat and Geodynamics