SME
Geophysics · Problem type
Paleolatitude from magnetic inclination
Use this for “A lava flow’s remanent magnetism dips 49.1° below the horizontal. At what latitude did the lava cool?”
Diagram
A dipole on the spin axis dips the field by I at latitude φ: tan I = 2 tan φ.
tan 49.1° = 1.15 = 2 × tan 30°, so φ = 30° (down in the north).
This is an example. Type your own values to start a new problem.
tan(
I
°)
=
2
tan(
φ
°)
Formulas
tan(
I
°)
=
2
×
tan(
φ
°)
tan(49.1°) = 2 × tan(29.9942°)
Assumptions
•
Earth’s field averaged over thousands of years is a dipole on the spin axis.
•
A dipole’s field dips more steeply than the latitude: tan I = 2 tan φ.
•
I is measured from the horizontal, down (positive) in the north and up (negative) in the south.
Step-by-step
WE KNOW
I = 49.1°
FIND
latitude (φ)
Step 1 · Find latitude (φ)
Use tan(I°) = 2 × tan(φ°)
Halve
tan
I
,
then
take
tan⁻¹
for
the
latitude
where
the
rock
formed.
φ
=
tan⁻¹(
tan(
I
°)
2
)
φ
=
tan⁻¹(
tan(49.1°)
2
)
tan(49.1°) = 1.154
1.154
2
=
0.5772
φ
=
29.9942°
Check
Put the numbers back in. Both sides should match.
tan(49.1°) = 2 × tan(29.9942°) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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