Introduction to Geophysics

Basic Theory Geomagnetism & Rock Magnetism

Coulomb’s Law

•  Force between two magnetic point poles is expressed by Coulomb’s Law

•  Force is proportional to product of pole strengths F α p1 p2

•  Force is proportional to inverse square of the separation distance

F α 1/r2

•  F = (1/µ) x p1 p2 / r2 where µ is the magnetic permeability

µ = 1 for vacuum

•  Since p1 and p2 can be positive (north seeking) or negative (south seeking), the force F can be either attractive or repulsive

r

p 1

p 2

Point Poles (magnetic monopoles)

F = [ (1/µ) p1 p2 r / r2]

F may be positive or negative F α p1p2

F α 1/r2

µ=1 for a vacuum (not in a conductor)

Force F is a vector quantity

Basic Concepts

•  Magnetic moment is the product of the pole strength and distance separating the poles

•  Magnetization (magnetic strength of a substance) is commonly defined in terms of magnetic moment per unit volume

•  Magnetic susceptibility of a material is a measure of the ease with which it will become magnetized when exposed to a magnetic field

•  Magnetic Field Intensity is the force acting on a unit (north) pole and has units of Oersted or Tesla

Geomagnetism •  The Earth has a magnetic field that varies with both

time and position

•  The Earth’s magnetic field has contributions from internal and external sources

•  Ftot = Fc + Fl + Fe (Fc = core field, Fl = lithospheric field, Fe = external field)

•  Internal sources are dominantly located in either the liquid outer core or in the crust

•  External sources include atmospheric electrical currents

Earth’s Magnetic Field

•  The geomagnetic field is dominantly dipolar with a north and south magnetic pole

•  A small fraction (~10%) of the magnetic field is due to non-dipole contributions

•  Earth’s magnetic poles do NOT currently coincide with the geographic poles

•  The direction of the geomagnetic field is defined by the angles of inclination and of declination

Dipole Field N N

S S

F = Intensity Magnetic coordinates are a RH system, but with vertical positive downward

Intensity of Geomagnetic Field •  The intensity of the Earth’s

magnetic field varies with latitude and longitude on the Earth’s surface

•  A dipole field has a strength at the poles 2x that at the equator

•  Field is strongest at the magnetic poles ( intensities of ~61,000 nT (N pole) and ~67,000 nT (S pole)

•  The field is weakest at the magnetic equator with intensities of ~25,000 nT

Hulot (2007)

Earth’s Magnetic Field

•  The geomagnetic field is dominantly dipolar with a north and south magnetic pole

•  A small fraction (~10%) of the magnetic field is due to non-dipole contributions

•  Earth’s magnetic poles do NOT currently coincide with the geographic poles

•  The direction of the geomagnetic field is defined by the inclination and declination

Geographic North

Declination and Inclination

Magnetic Inclination – Variation with Latitude

•  Inclination varies regularly with latitude •  Points outward in southern hemisphere •  Points inward in northern hemisphere •  Geocentric Axial Dipole (left) relates

inclination (I) to latitude (λ)

Magnetic Declination •  Declination is angle between N-S

direction and magnetic field direction

•  Measured clockwise from N

•  So 0° ≤ D ≤ 360°

Declination of the Geomagnetic Field

Parkinson (1983)

External Sources •  The major external sources are

electrical currents in the ionosphere produced as a result of solar activity

•  These currents cause magnetic fields that interfere with magnetic surveys but also provide sources for electrical surveys

•  Enhanced solar activity produces magnetic storms that can severely impact magnetic surveys

1- bow shock 2 – magnetosheath 3 – magnetopause 4 - magnetosphere 5 – northern tail lobe 6 – southern tail lobe 7 - plasmasphere

The magnetic field in space (NASA)

Internal Sources •  Internal sources of the geomagnetic field can be divided into 2

parts: a regular part from the outer core responsible for the main field and an irregular part from the crust and upper mantle

•  Magnetized bodies in the crust and mantle perturb the regular or main magnetic field producing magnetic anomalies that are usually small with respect to the main field (<1-3%)

Origin of Earth’s Magnetic Field •  Successful explanations for the origin of the Earth’s magnetic

field must satisfy several constraints including:

–  observed intensity –  secular variation –  polarity transitions –  long term nature –  dominantly dipolar character –  minor non-dipole components

Mussett and Khan (2009)

Secular Variation in Europe

Secular Variation Dipole Strength

McElhinney et al. (1983)

Valet et al. (2005)

(top) Dipole strength from rock samples (right) Dipole strength from sediment cores

•  The dipole varies in strength by ~50% over timescale of thousands of years

•  Can become very weak during geomagnetic reversal transition

Merrill et al. (1996) Merrill & McElhinny (1983)

Secular Variation in Direction •  (left) SV in declination and inclination recovered in lake cores

•  (right) SV in position of the geomagnetic pole (dipole wobble)

•  Note that average dipole position close to the spin axis

Secular Variation •  Average magnetic field over >104-105 years is geocentric axial dipole (GAD) •  Plots show VGP for last 5 Myr •  Average to geographic pole (left) •  Average to GAD (right) •  Maybe a small amount of non-dipole field (quadrupole – dashed line)

Virtual Geomagnetic Pole (VGP)

•  Using measured paleomagnetic inclination and declination, we can determine the location of the paleomagnetic pole for the age of the sampled formation

•  Using the GAD hypothesis, we interpret this as location of spin axis in plate reference frame

•  tanI=2tanl=2cotθ so inclination determines distance to pole

•  Declination determines pole azimuth

•  Apparent polar wander path is defined by poles of different ages

•  APWP  used  for  tectonic  interpreta2ons  

Irving & Irving (1982)

Models for Geomagnetic Field •  The different explanations that have been proposed for the

origin of the Earth’s magnetic field include:

–  Permanent magnetization

–  Rotation of earth (and all celestial bodies)

–  Electrically charges inside the Earth

–  Electrical currents produced by geochemical potentials

•  As new observations have been gathered most of these explanations have been rejected

•  Dynamo models involving the electrically conducting, liquid outer core are currently the accepted explanation

Simple Disk Dynamo •  Although the geometry of any dynamo inside the Earth is believed to be

quite complex, an overall idea of how such a dynamo might work can be obtained by considering simpler dynamos

•  One of the simplest dynamo geometries is that of a circular disk rotating in a magnetic field

•  The disk is a conductor which cuts lines of magnetic force creating a difference in electrical potential between its center and its periphery

Robinson and Coruh (1988)

Simple Disk Dynamo •  Charge separation on the disk takes place because the electrical

particles ( i.e., electrons) are subject to Lorentz forces that act perpendicular to both the magnetic field, B, and the tangential velocity, v, of the disk:

•  If a connection is made between the center of the disk and its edge then a current will flow. If the connection has no organized geometry then the magnetic field associated with the current flow will be randomly oriented and neither add to nor subtract from the initial field

F = B x v

Robinson and Coruh (1988)

Current Flow in Disk Dynamo

Simple Disk Dynamo •  If connection has an organized geometry then it is possible for

the resulting field to either oppose or re-inforce the original magnetic field

•  Re-inforcement of the original field will increase B which will increase the Lorentz force which in turn will produce a greater charge separation

•  Increased charge separation will result in a stronger electrical current thereby further re-inforcing the field

•  In this way a small initial field can be greatly amplified by the dynamo action

Simple Disk Dynamo •  Note that although the disk dynamo is self-exciting and

regenerative it still needs a small initial field to begin the process

•  The field once produced by the dynamo will persist for a considerable time

•  Note that for a single sense of rotation the simple disk dynamo will produce a steady dipolar field in the either direction depending on the direction of this initial field

•  Although the simple single disk dynamo will sustain a field in either direction it will not produce a reversal of the magnetic field

•  Obviously, there is no disk dynamo in the core and the process is more complex than this simple model

Internal Sources

•  Internal sources of the geomagnetic field can be divided into 2 parts: a regular part from the outer core responsible for the main field and an irregular part from the crust

•  Magnetized bodies in the crust perturb the regular or main magnetic field producing magnetic anomalies that are usually small with respect to the main field (<1-3%)

Rock Magnetism •  Rocks display both induced magnetization and remanent

magnetization

•  Rocks magnetized by induction acquire magnetizations in the direction of the Earth’s present field

•  The intensity of the induced magnetization depends on the rock magnetic susceptibility and the intensity of geomagnetic field

•  Rocks can also acquire a remanent magnetization in which the direction of an earlier (ancient) field is captured and retained for a considerable time (~106 - 109 years)

Induced Magnetization •  Induced magnetization occurs when a magnetizable body is placed

in an external magnetic field

•  The induced magnetization, Mi , depends on the magnetic susceptibility, χ, of the rock and the Earth’s field strength, H, at the rock’s location

Mi = χ H •  Such magnetizations disappear when the body is placed in a zero

field (field free) space

•  Such magnetizations also change to a new orientation when removed from one field and placed in another

•  For example for a rock moved from Africa to North America the induced magnetization will change in both intensity and direction

Magnetic Susceptibility §  The magnetic susceptibility, χ , is a measure of the ease with

which a material becomes magnetized when placed in a magnetic field

§  To a large extent the magnetic susceptibility of a rock depends on the concentration of magnetic minerals (mainly magnetite)

§  A magnetization, Mi , occurs by induction in the ambient external field, H, such that the magnetization is either parallel or anti-parallel to the external field

Mi = χ H

§  This linear relationship between Mi and H is valid for small values of H. However, as H is increased, the value of Mi will reach a saturation value and the linear relationship is no longer valid

§  Few, if any, natural earth materials saturate in the small field of the Earth

Mag

netiz

atio

n |M

i|

Magnetic Field |H|

Saturation

Linear for low H Mi = χ H

Induced Magnetization

Mussett & Khan (2009)

There is a progressive increase in magnetic susceptibility from sedimentary to meta-morphic to igneous rocks Basic igneous rocks have the highest magnetic susceptibility

Susceptibility of Rocks

Robinson & Coruh (1988)

[Conversion Volume Susceptibility: cgs units = SI units x (1/4π)]

More Magnetic Susceptibility

Remanent Magnetization

•  Remanent magnetization Mr is a magnetization acquired in an external magnetic field that is retained by a body for considerable time period (i.e., millions to possibly billions of years) after the external, applied field is removed or changed

•  The magnetization characterizes the ambient field at the time the magnetization was acquired

•  The intensity and direction of a remanent magnetization is controlled by the initial field at the time of remanence acquisition

•  Physical and chemical changes, however, may remove the magnetization over time

•  Several mechanisms for remanence acquisition are known

Types of Magnetism

•  There are basically 3 types of magnetism acquired by earth materials

•  Two of these produce an induced magnetization, Diamagnetism, Paramagnetism

•  The third type of magnetism is Ferromagnetism which results in a remanent magnetization

•  Paramagnetism is a form of induced magnetization found in only certain materials

•  It is produced by the alignment of the spin magnetic moments of unpaired electrons

•  Paramagnetism is acquired in a direction parallel to the applied field and consequently the susceptibility is positive

Paramagnetism

Mussett and Khan (2009)

Ferromagnetism •  Ferromagnetism is also produced by the alignment of spin

magnetic moment of electrons

•  In paramagnetic and diamagnetic materials, the individual magnetic moments from adjacent atoms do not interact with one another in any strong or meaningful way

•  In ferromagnetic materials, the lattice positions of the atoms are such that electrons interact and can be shared between adjacent atoms. This is especially prevalent in some metals (e.g., iron, nickel, cobalt)

•  As a result of this sharing or exchange, the electron spin moments become coupled and are able to create a strong local molecular magnetic field within the material

•  The spins lock into a lattice with parallel magnetic moments

Lowrie (2007)

Spins all aligned - occurs in metals

Types of Ferromagnetism – Spin Alignments

Two anti-parallel lattices of equal strength

Two anti-parallel lattices of equal strength – but slightly tilted - hematite

Two anti-parallel lattices of unequal strength – magnetite

Remanent Magnetization Types •  Remanent magnetization is a magnetization acquired in an

earlier (ancient) field and retained for a considerable time (~106 - 109 years)

•  Various types of remanent magnetization have been documented. Three of the more important from a geologic point of view are:

- Thermal remanent magnetization (TRM)

- Depositional remanent magnetization (DRM)

- Chemical remanent magnetization (CRM)

Thermal Remanent Magnetization

•  When rocks cool down through the Curie temperature of constituent magnetic minerals a magnetization is acquired in the direction of the ambient magnetic field

•  Rocks may continue to acquire this magnetization at temperatures below the Curie point

•  The Curie temperature is different for different minerals e.g. magnetite - 580°C; hematite - 675°C

Thermal Remanent Magnetization Lille (1999)

Thermal Remanent Magnetization

•  Curie temperatures of basalts ~150-450°C •  Curie temperatures of most rocks = 250-600°C so rocks cool from molten

state before aquiring TRM

Mussett and Khan (2009)

Resetting of Magnetization at Baked Contact

Remanent Magnetization •  Remanent magnetization is a magnetization acquired in an

earlier (ancient) field and retained for a considerable time (~106 - 109 years)

•  Various types of remanent magnetization have been documented. Three of the more important from a geologic point of view are:

- Thermal remanent magnetization

- Depositional remanent magnetization

- Chemical remanent magnetization

Cox & Hart (1986)

Small magnetized particles become oriented in the ambient magnetic field as they accumulate in sedimentary environments (oceans, rivers, lakes ) Particles will continue to re-orient themselves in response to changing field directions until locked into position by lithification Alignment of magnetized particles is a statistical process that results in a preferred direction of magnetization.

Depositional Remanent Magnetization

Remanent Magnetization •  Remanent magnetization is a magnetization acquired in an

earlier (ancient) field and retained for a considerable time (~106 - 109 years)

•  Various types of remanent magnetization have been documented. Three of the more important from a geologic point of view are:

- Thermal remanent magnetization

- Depositional remanent magnetization

- Chemical remanent magnetization

Chemical Remanent Magnetization

•  Most rocks undergo alteration as a result of physical and chemical processes - e.g. abrasion, oxidation, etc.

•  Where a chemical process is accompanied by a change in the magnetic minerals present, a new remanence can be acquired

•  The formation of new magnetic minerals will result in a remanence that corresponds to the field at the time of the chemical change

Mussett and Khan (2009)

Mineral Remanent Magnetization

Sources

Whole Earth Geophysics, 1999 R. J. Lillie

Fundamentals of Geophysics, 2007 William Lowrie

Basic Exploration Geophysics, 1988 E.S. Robinson & C. Coruh

Plate Tectonics: How it Works, 1986 A. Cox and R. Hart

Looking into the Earth, 2009 A. E. Mussett & M. A. Khan

Introduction to Geomagnetism, 1983 W. D. Parkinson

The Earth’s Magnetic Field, 1983 R. T. Merrill & M. W. McElinny

The Magnetic Field of the Earth, 1996 R. T. Merrill et al.

Geomagnetic dipole strength and reversal rate over the past 2 million years, J. P. Valet, L. Meynadier, & Y. Guyodo, Nature, 435, 802-805, 2005.

Apparent polar wander paths Carboniferous through Cenozoic and the assembly of Gondwana, E. Irving & G. A. Irving, Geophys. Surv., 5, 141-188, 1982