Geomagnetism

Question 1

What is the equation for the magnetic potential?

Answer 1

V(r) = m*r/4πr^3, where m is the magnetic dipole moment from S->N

Question 2

What is the equation for the magnetic field?

Answer 2

-μ0*∇V(r), where ∇ is in spherical polar coordinates

Question 3

What are the equations for the 3 components of spherical polar coordinates for the magnetic field?

Answer 3

B(r) = 2*μ0*m*cosθ/4πr^3
B(θ) = μ0*m*sinθ/4πr^3
B(Ф) = 0

Question 4

What are meridians?

Answer 4

Arcs of constant Ф in spherical polar coordinates

Question 5

What is geomagnetic field strength measured with?

Answer 5

A magnetometer.

Question 6

What does the magnetic field strength vary between at earths surface?

Answer 6

25 μT to 65 μT

Question 7

What is the geomagnetic latitude?

Answer 7

Latitude analogues to geographical latitude, but defined relative to the magnetic poles.

Question 8

What is the declination angle for geomagnetism?

Answer 8

Angle between the magnetic and geographical meridians.

Question 9

What is the inclination angle for geomagnetism?

Answer 9

Angle between magnetic field and a horizontal on the surface.

Question 10

What are 2 equations for the inclination angle?

Answer 10

tan(I) = B(r)/B(θ) = 2*cos(θ)/sin(θ)

tan(I) = 2sin(λ)/cos(λ) = 2tan(λ), where λ = 90 - θ

Question 11

What are 3 important types of magnetism? How do they differ?

Answer 11

• Ferromagnetism (All spins aligned, generating strong B-field up to curie temp)
• Ferrimagnetism (spins on multiple sublattices of a crysta, some spins antialigned)
• Antiferromagnet (spins are all antialigned, so no net B-field)

Question 12

What are the locations of the magnetic poles right now?

Answer 12

North: 193.710 degrees W, 86.395 degrees N

South: 136.419 degrees E, 64.245 degrees S

Question 13

What type of magnet is the solid iron core of the Earth?

Answer 13

A giant ferromagnet, or geodynamo.

Question 14

What is the curie temperature of iron, and what is the temperature of Earths core?

Answer 14

T(c) of iron = 1043 K

T(core) = 6000 K +/- 500 K

Question 15

What does the temperature of Earths core mean for its magnetism?

Answer 15

• Far above curie temp
• Is not a permanent magnet
• Field strengths are very low

Question 16

Why does the Earth create a magnetic field?

Answer 16

Fluid flow between inner core and outer core means movement of molten iron, which results in currents and generates magnetic fields.

Question 17

What is thermoremanent magnetism?

Answer 17

• Ferrimagnet cools through Tc in the presence of external geomagnetic field
• Internal magnetisation will align with that field
• Ferrimagnetic material can permanently record the geomagnetic field strength and direction at the time it was cooled below Tc

Question 18

What is a mid ocean ridge?

Answer 18

A constructive plate boundary where new oceanic crust is created from upwelling magma.

Question 19

What can we use a combination of to study mid ocean ridges?

Answer 19

Radiometric dating, plate tectonics and magnetism.

Question 20

What can the magnetic survey record information about for things like magnetite?

Answer 20

Past field strength, orientation, inclination and polarity

Question 21

What is palaeomagnetism?

Answer 21

Can traverse the ridge axis and measure the local B-field, and subtract what we expect to find from the geomagnetic field - gives us a reference field.

Question 22

What does palaeomagnetism do for us?

Answer 22

Gives a local field due to magnetic materials in the crust e.g. magnetite. Records field as material cooled through Tc.

Question 23

How can we look at the polarity of the B-field? What do we observe?

Answer 23

Look at rocks away from mid ocean ridge and obtain an accurate timeline of polarity reversals. Observe a stripe pattern away from the ridge in both directions.

Question 24

What is the equation for x, the stripe widths when looking at polarity?

Answer 24

x(i) = v0/2 * Δt(i), where v is the spreading rate of the ith ridge and Δti is the time since geomagnetic reversal.

Question 25

How can we infer the latitude at which point the rock cooled below Tc?

Answer 25

Use tan(I) = 2*tan(λ)

Question 26

What were polarity reversals and inclination significant evidence for historically?

Answer 26

Continental drift.

Question 27

What is topography?

Answer 27

• Low density material below ridge axis where hot, less dense, material upwells from mantle
• Gentle rise of sea bed up to ridge axis
• Trench on ridge axis due to spreading of plates

Question 28

What is a gravity survey?

Answer 28

Survey done by ship at sea level so that the free air correction dg(r) = 0

Question 29

What is the equation for the Bouguer Correction?

Answer 29

dg(B) = 2πGh*(ρ(rock)-ρ(water))

Question 30

What is the equation for the Bouguer anomaly?

Answer 30

g(B) = g(0) - g(λ) - dg(F) - dg(B)

Question 31

Why does the Bouguer anomaly become less positive near the centre of ridge?

Answer 31

Due to increased amount of low density material (buried low density magma chamber below ridge)

Question 32

What are 2 models of magma upwelling?

Answer 32

• Slow extrusions under water form pillow shaped structures.

- Violent volcanoes and island formation near fast extrusion e.g. Iceland

Question 33

How can we use seismology with tomography?

Answer 33

Seismic wave tomography of P- and S- waves with large arrays of seismometers on the ocean floor.

Question 34

What does seismic tomography give us?

Answer 34

Wave speed map in 3D, and therefore k(r), μ(r), ρ(r)

Question 35

What can we conclude from seismic tomography?

Answer 35

• Plates move apart at constructive boundary
• Mid-ocean ridges are fed by upwelling magma
• Gravity surveys and seismic tomography to confirm low density buried magma chamber