GLE 594: An introduction to applied geophysics

Magnetic Methods

Fall 2004

Magnetic Methods: Concepts and rock properties

Readings from textbook Today : pages 65-75Next Lecture: pages 75-86

History of the magnetic method

• Oldest Branch of Geophysics– Chinese first to use north-seeking properties of lodestone– 1600 William Gilbert publishes De Magnete: ‘…the whole

earth is a magnet’

• Prospecting– Began in Sweden for iron ore in 1640’s – Thalen and Tiberg (1870) measured Earth’s magnetic fields – A. Schmidt (1915) developed a balance magnetometer– During WWII instruments became smaller and easier to use

• Now, magnetic tools are one of the most cheaply and easiest to acquire geophysical data sets

Applications• Shallow (Engineering and Environmental):

contaminants, toxic waste, pipes, cables and metal inclusions

• Military: location of UXO’s• Archeology: buried walls, old fire pits• Mining: iron sulfide deposits• Oil and groundwater: depth to magnetic basement in

basins, detection of faults• Geotectonics: major player in discovery of, and current

analysis of tectonic processes.

Definitions: Magnetic potential• Remember that the ‘potential’ is defined as the

‘potential to do work’.• Magnetic Potential:

where µo=4π 10-7 [H/m] is the magnetic permeability of free space and p [A/m] is magnetic pole strength

• Gravitational Potential: µo/4π is equivalent to G p is equivalent to m

⎥⎦⎤

⎢⎣⎡=

πµ

=m

Wbrpc

rp

4W o

rmGU =

• Definition: Vector quantity defining the magnetic flux/unit area; i.e., the density of the magnetic field lines. Thus often called Flux Density

• Mathematical Definitions:

– Air:

– Magnetic materials:

µ is the magnetic permeability of the materialµr is the relative magnetic permeability of the materialř is a unit vector pointing from the magnetic pole to the measurement point.

Definitions: Magnetic field or flux density

⎥⎦⎤

⎢⎣⎡ ==

πµ

=−∇= TeslamWbr̂

rpcr̂

rp

4WB 222

o

r̂rpcr̂

rp

4

r̂rp

4WB

2r20r

2

µ=πµµ

=

πµ

=−∇=

Definitions: Magnetic field strength or intensity

• Biot-Savart’s law definition: for a loop of wire of radius r that is carrying a current I, H at center is given as:

H=nI/2r [A/m]

where n is a unit vector normal to the plane of the loop.

• The magnetic field strength H is related to the magnetic field B as:

B = µH = µο µr H[A/m]

IH n

Dipole nature of magnetic materialsBar Magnet

N+

S-

• Although, no magnetic monopoles exist in nature, they are useful for theory: magnetic monopoles of same sign repel, opposite signs attract. • Dipole created by two poles of opposite sign and separated by distance l. • If you are close to one of the poles, the field can be though of as originating from a monopole. • Magnetic body can be though of as composed of a bunch of little magnets, or dipoles.

• A measure of the pole strength/unit area along one of the ‘ends’ of magnetic material:

J=(p/A) n [A/m]

Magnetization or magnetic polarization

Magnetic moment

• Strength of a magnetic field ‘generator’M=J V = p l [A m2]

For a loop of current: M=(Iπr2) n

Units

Quantity Symbol SI Units cgs units Magnetic Pole Strength p A m -

Permeability µo, µ H/m - Relative permeability µr unitless unitless Magnetic Flux Density B Wb/m2=Tesla Gauss/gamma

Magnetic Intensity H A/m oersteds Magnetic Polarization J A/m

Magnetic Moment M A/m2

Basic comparison of magnetic and gravitational potential

• A gravity perturbation can always be thought of as being caused by one or a series of ‘monopoles’. That is field lines either point toward or away from the perturbation.

• A magnetic perturbation, or magnetic field in general, is always produced by a dipole. Thus direction of field depends on relative position to one or the other ends of the magnetized body.

Earth dipolar fieldGravitational Potential:

rmGPU =)(

Magnetic Potential and Fields:

[Wb/m]

[T=Wb/m2]

[T=Wb/m2]

Total force, inclination and declinationEarth’s ‘Dipole’ not aligned perfectly with rotational axis.

Earth dipolar fieldDipole that best fits earth’s field (origin outer core):

─ Moment of 8·1022 [A m2]

─ Axis inclined 11.5o to the geographical pole.

Not a perfect dipole.

60,000 nT

25,000 nT

Geomagnetic reference field

• What we want is the magnetic anomaly: ∆T=Bobs-Bref.

• Thus need to define ‘Reference’.

Inclination

Declination

Geomagnetic reference field (cont.)

Secular variation: Slow changes in polar location

Southern Pole ‘Wandering’

Northern Pole ‘Wandering’

Induced magnetization (JI) and magnetic susceptibility

• A magnetizable body acquires magnetization when H field is applied– Disappears when field is removed

– Field ‘induces’ magnetization in material

• The induced magnetization is parallel and proportional to H: JI=κH (due to the earth: JI=κF/µo)– k = susceptibility – k = µr-1– Dimensionless, however, kSI=4πkcgs

Cause of magnetic susceptibility

• At the atomic level, materials have a net magnetic moment due to:– Rotation of electrons in various shells around nucleus– The spin of the electrons– Number of electrons in each shell– i.e., it’s a quantum effect

• All of above result that each atomic nucleus can be though of as a small magnetic dipole with its own moment

Classifications of magnetic materials

• Diamagnetic• All electron shells are full, thus there is no net moment.• In the presence of an external field, the net moment opposes

the external field, i.e., slightly negative susceptibility.

• Paramagnetic• Materials contain unpaired electrons in incomplete electron

shells.• However magnetic moment of each atom is uncoupled from

others so they all behave independently. • Results in weakly magnetic materials, i.e. small susceptibility

Classifications of magnetic materials

• Ferromagnetic• Materials contain unpaired electrons in incomplete

electron shells.• Magnetic moment of each atom is coupled to others

in surrounding ‘domain” such they all become parallel.

• Caused by overlapping electron orbits.• Gives rise to a spontaneous magnetization even in

absence of an external field.• Magnets are ferromagnetic.

• Examples: Cobalt, iron and nickel.

Classifications of magnetic materials

• Anti-ferromagnetic• Almost identical to ferromagnetic except that the

moments of neighboring sublattices are aligned opposite to each other and cancel out

• Thus no net magnetization is measured • Example: Hematite

• Ferrimagnetic• Sublattices exhibit ferromagnetically but then

couple antiferromagnetically between each other • Example: Magnetite and ilmenite

Magnetic properties

Concept of hysteresis

• Complex relationship between B and H that occurs in ferromagnetic materials.– B flattens off with increasing H

at ‘saturation’– When H is decreased, B does not

follow same curve– Will have ‘remanent’ B value at

zero H

Remanent magnetization (RM)

• Permanent magnetization of rock installed during its formation (JR).• Ferromagnetic materials exhibit this creating spontaneous magnetization.• Direction of remnant may differ radically from induced field.

Total magnetization

• Total magnetization:J=Ji+Jr

• Effective or apparent k:ke or ka=(Ji+Jr)/(F/µ0)

• Note: a J that is not fully aligned with the natural H field at a site will cause a perturbation in H, and thus H local will have a slightly different direction and strength then the natural field.

Magnetic properties of materials of interest

• Basement: tends to be igneous or metamorphic, thus greater magnetic properties.

• Soils and other weathered products: because magnetic minerals tend to weather rather rapidly compared to quartz, will get reduction of magnetic materials with weathering.

• Man-made objects: iron and steel• Ore deposits: many economic ores are either

magnetic, or associated with magnetic minerals.