Geomagnetism (I).

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Geomagnetism (I)

The Earth’s magnetic field
Magnetic field of the Earth measured at the surface comes from three sources: 97-99% represents main field generated by dynamo action in the outer core. Main field varies significantly with time (secular variation means variations along geological time) 1-2% represents external field generated in space in the magnetosphere. External field also varies on time scales of seconds to days. 1-2% represents crustal field from remnant magnetization above the Curie depth. Ali K. Abdel Fattah

The Earth’s magnetic field
The Earth’s magnetic field would be: vertical at the poles horizontal at the equator Today, the best-fit dipole is currently oriented 11.5° from the rotation axis of the geographic north pole, but this has varied with time. Ali K. Abdel Fattah

Describing the Earth’s magnetic field
Declination (D) Inclination (I) Horizontal Intensity (H) Vertical Intensity (Z) North-South Intensity (X) East-West Intensity (Y) Total Intensity (B) X Y Ali K. Abdel Fattah

Describing the Earth’s magnetic field
This first order simple model of the field allows to use the paleomagnetic observations to determine past plate motions Magnetic potential is given by The Earth’s best fit dipole moment (m) equals to 7.94x1022 Am2 in magnitude Magnetic field is determined by the differentiating the magnetic potential given the magnetic permeability of free space, μ0 = 4x10-7 kg m A-2 s-2 Ali K. Abdel Fattah

Spherical polar coordinates
Conversion from/spherical into Cartesian coordinates: Gradient operator Ali K. Abdel Fattah

Describing the Earth’s field
If the Earth’s magnetic dipole moment is aligned along the z-axis: At a latitude of θ and longitude , Magnetic field in spherical polar coordinates can show three components: Radial Component Br, Southerly Component B, and Easterly Components B Ali K. Abdel Fattah

Describing the Earth’s field
For the best fit dipole, Three components are given by Total field is given by Ali K. Abdel Fattah

Describing the Earth’s field
Then, the magmatic inclination (I) can be computed from the following equation At the North Pole, θ = 90° which gives I = 90° At the Equator, θ = 0° which gives I = 0° Ali K. Abdel Fattah

Describing the Earth’s field
Ali K. Abdel Fattah

Describing the Earth’s field
Ali K. Abdel Fattah

Describing the Earth’s field
The equation of the magnetic inclination is important because it allows use to use a measurement of inclination (I) to determine latitude (θ). This was once used by mariners, but is most important in paleomagnetism. A rock can record the magnetic field present when it crystallized (temperature fell below the Curie temperature). Thus we can find the latitude of a continent at some time in the past. This was the idea of Apparent Polar Wandering.

Diamagnetism and paramagnetism
The magnetic behaviour of minerals is due to atoms behaving as small magnetic dipoles. If a uniform magnetic field (H) is applied to a mineral, there are two possible responses. Diamagnetic behaviour Paramagnetic behaviour

Diamagnetic behaviour
This effect arises from the orbital motion of electrons in atoms. The atom develops a magnetic field that is opposite direction to the applied magnetic field Magnetic susceptibility is negative All minerals diamagnetic but will be masked by paramagnetism

Paramagnetic behaviour
This phenomena arises when the atoms have a net magnetic dipole moment due to unpaired electrons. The atoms align parallel to the applied magnetic field H and increase the local magnetic field. For paramagnetic materials Magnetic susceptibility is positive. Paramagnetic elements include iron, nickel and cobalt.

Rock magnetization and translation
Geomagnetism (II) Rock magnetization and translation

Magnetizing Igneous Rocks
Curie Temperature Temperature above which a mineral cannot be permanently magnetized spontaneous magnetization when temperature drops below Curie temperature Curie Depth Is the depth at which magnetic behaviour ceases since temperature exceeds curie temprature. Thermal vibrations of atoms prevents domain formation. Blocking Temperature Tens degrees less than the Curie point for most minerals Temperature below which the orientation of the rock’s magnetization cannot change magnetization cannot change once below blocking temperature Both temperatures are much lower than that at which lavas crystallize. The magnetization becomes permanent some time after lavas solidify. This type of permanent residual magnetization is called thermoremanent magnetization (TRM); atoms align when molten and freeze The magnetism of TRM is larger in magnitude than that induced in the basalt by the earth’s present field.

Magnetizing sedimentary rocks
Sedimentary rocks can acquire magnetization in through: Depositional or detrital remanent magnetization (DRM); acquiring during the deposition of sedimentary rocks. Chemical remanent magnetization (CRM); acquiring after deposition during the chemical growth of iron oxide grains as the case in sandstones. Strength of DRM and CRM fields typically 1-2 orders of magnitude smaller than TRM

Detrital remnant magnetization
Detrital magnetization can produce a weak remnant magnetization in sedimentary grains Grains being deposited contain some magnetite or other magnetic minerals Preferred orientation as they are deposited

Chemical remnant magnetization
Can occur during alteration Example from oil field in Gibson and Millegan (1988)

Induced magnetic field

Calculating palaeomagnetic latitude (use of TMR)

Example A rock sample was found at latitude of 34°N. Remnant magnetization in the sample was found to have an inclination I = 40 ° from the horizontal. Was the rock magnetized at the location where it was sampled?

Locating the palaeomagnetic pole (use of TMR)

Locating the palaeomagnetic pole (use of TMR)

Polar wander paths

Magnetic stripes (Dating the oceans)
Using magnetometer with overseas vessel Measure the total field intensity Subtract regional value Produce magnetic anomaly map

Magnetic stripes (Dating the oceans)
Raff and Mason, 1961 First magnetic field map Off the western coast of North America Magnetic anomaly map Take total magnetic field intensity and subtract regional average Black Stripes: positive intensity White Stripes: negative intensity Which is normal/reversed polarity? Coupled stripes with sea-floor spreading and magnetic pole reversals

Origin of Seafloor magnetic anomalies formed at mid-ocean ridges
Important evidence to support the hypothesis of continental drift came from observations of magnetic fields measured by survey ships on profiles that crossed the world’s oceans. Basalt erupted and when cools it is permanently magnetized in direction of Earth’s magnetic field at that time. Sea floor spreading moves rocks away from ridge. Magnetic field reverses direction

Magnetic stripes anomalies
Magnetic stripes anomalies are considered for two cases of magnetic stripes anomalies: High magnetic latitude Low magnetic latitude Magnetic stripes anomalies of high magnetic latitude are characterized by: Earth’s magnetic field is close to vertical. Remnant magnetization at the ridge is in the same direction as the Earth’s field. Positive magnetic anomaly at the ridge crest Magnetic stripes at High magnetic latitudes

Magnetic stripes anomalies