VẬT lý địa CHẤN magnetic

Magnetic SurveyingThe investigation of the subsurface ‘geology’ on the basis of anomalies in the Earth’s magnetic field resulting from the magnetic properties of the causative body.. •Th

Magnetic Surveying

The investigation of the subsurface ‘geology’ on the basis of anomalies in the

Earth’s magnetic field resulting from the magnetic properties of the causative body

•A broad range of applications

•Magnetic surveys can be performed on land, at sea, in the air, and on ice

•Very cheap to perform

Basic ConceptsWithin the vicinity of a bar magnet a magnetic flux is

developed which flows from one end of the magnet to

the other

•Mapped from the directions assumed by a small

compass needle, or bar magnet suspended within the

field

•Poles are where the flux lines converge

•The pole of the compass/magnet which points in the

direction of the Earth’s north pole is called the

north-seeking pole, or positive pole

•This is balanced by a south-seeking or negative pole

of identical strength at the opposite end of the

magnet

•The Earth’s magnetic field can be crudely

modeled as a bar magnet with it’s south pole at

the Earth’s north magnetic pole.

Basic Concepts

2 2 1 0

m m F

R

πµ

µ

=

The force F between two magnetic poles of strengths m 1 and m 2 separated by a

distance r is given by:

Where μ 0 and μ R are constants corresponding to the magnetic permeability of a

vacuum and the relative magnetic permeability of the medium separating the

poles The force is attractive if the poles are of different sign, and repulsive if they are of like sign

The magnetic field B due to a pole of strength m at a distance r from the pole is

defined as the force exerted on a unit positive pole at that point:

The magnetic field can be defined in terms of the magnetic potential in a similar

manner to gravitational fields For a single pole of strength m, the magnetic

potential V at a distance r from the pole is given by

r

m V

Basic Concepts

In the SI (what is this??) system of units, magnetic parameters are defined in terms

of the flow of electrical current

•If a current is passed through a coil consisting of several turns of wire, a magnetic flux flows through and around the coil annulus which arises from a magnetizing

force H.

•The magnitude of H is proportional to the number of turns in the coil and the

strength of the current, and inversely proportional to the length of the wire H is

expressed in A m -1

•The density of the magnetic flux, measured over an area perpendicular to the

direction of flow, is known as the magnetic induction, or magnetic field, B.

•B is proportional to H The constant of

proportionality μ is know as the magnetic

Basic Concepts

•Lenz’s law of induction relates the rate of change of magnetic flux in a circuit to the voltage developed within it, so B is expressed in V s m-2 (Weber (Wb) m-2)

•The unit of the Wb m-2 is designated the tesla (T)

•Permeability is expressed in Wb A-1 m-1 or Henry (H) m-1

•The tesla is too large to express the small magnetic anomalies on the Earth’s

surface Consequently, the nannotesla is used (1 nT = 10-9 T)

Basic Concepts

•Magnets exhibit a pair of pole – dipoles

•The magnetic moment of a dipole with poles of

strength m a distance l apart is:

•The magnetic moment of a current carrying coil is

proportional to the number of turns in the coil, its

cross sectional area, and the magnitude of the

current The magnetic moment is expressed in A m-2

•When a material is placed in a magnetic field it may

acquire a magnetization in the direction of the field

which is lost when it is removed

•This is called Induced Magnetization and results

from the alignment of elementary dipoles within the

material in the direction of the field

ml

M =

Basic Concepts

LA

M

J i =

•The intensity of induced magnetization J i of a material is

defined as the dipole moment per unit volume of material:

•Where M is the magnetic moment of a sample of length L

and cross-sectional area A J i is expressed in A m-1

•The induced intensity of magnetization is proportional to

the strength of the magnetizing force H of the inducing

B = µ0 + µ0

•In a vacuum the magnetic field strength B and magnetizing force H are related by:

Where μ 0 is the permeability of a vacuum (4π*10-7 H m-1)

•As air and water have very similar permeabilities to μ 0 the relationship can be

taken to represent the Earth’s magnetic field when it is undisturbed

•When a magnetic material is placed in the field, the resulting magnetization gives rise to an additional magnetic field in the region occupied by the material, whose strength is given by:

Within the body the total magnetic field, B, is given by:

Substituting the relationship with the magnetic susceptibility from the previous

slide gives:

H H

k kH

H

B = µ0 + µ0 = ( 1 + ) µ0 = µRµ0

Where μ R is a dimensionless constant known as the relative magnetic permeability The magnetic permeability is thus equal to the product of the relative permeability and the permeability of vacuum

Basic Concepts

•All substances are magnetic at an atomic scale

•Each atom acts as a dipole due to both the spin of its electrons and the orbital path of its electrons around the nucleus

•Diamagnetic materials: All electron shells are full and no unpaired electrons

exist When placed in a magnetic field the orbital paths of the electrons rotate so

as to produce an opposing magnetic field Magnetic susceptibility is weak and negative

•Paramagnetic materials: Electron shells are incomplete, creating a magnetic

field from the spin of the unpaired electrons When placed in a magnetic field the dipoles corresponding to the unpaired electron spins rotate to produce a field in the same sense as the applied field The susceptibility is positive, but still weak

•In small grains of certain paramagnetic substances whose atoms contain

several unpaired electrons, the dipoles associated with the spins of the unpaired electrons are magnetically couples between adjacent atoms Such a grain is said

to constitute a single magnetic domain This coupling may be either parallel or antiparallel

•Ferromagnetic: Dipoles are parallel Strong

spontaneous magnetization which can exist in the

absence of an external magnetic field Iron, cobalt,

nickel Rarely occur naturally in the Earth’s crust

•Antiferromagnetism: Dipole coupling is antiparallel,

with equal numbers of dipoles in each direction The

magnetic fields of the dipoles cancel out Defects may

give rise to a small positive magnetization (parasitic

antiferromagnetism) Haematite

•Ferrimagnetism: The dipole coupling is antiparallel,

but the strengths in each direction are unequal Strong

spontaneous magnetization, high susceptibility

Magnetite Virtually all minerals responsible for the

magnetic properties is common rock types fall into this

category

Basic Concepts

•Curie Temperature: Above this temperature ferromagnetic and ferrimagnetic

materials loose their magnetization Interatomic distances are increased to

separations which preclude electron coupling and the material behaves as if

paramagnetic

•Magnetite has a Curie temperature of 578oC

•Why might the curie temperature be important?

•Magnetic Domains: Grains may subdivide into domain, where all the dipoles are

aligned

•When a weak magnetic field is applied, domains magnetized in the direction

of the field grow at the expense of others When the field is removed, the

domains go back to their original configuration

•When a strong magnetic field is applied, domains can grow irreversibly

across small imperfections in the grain The domains are now permanently enlarged When the external field is removed, a remnant magnetization

remains

Remnant Magnetization

•Primary remnant magnetization:

•Acquired as an igneous rock cools through the Curie temperatures of its

constituent minerals (thermoremnant magnetization, TRM)

•Acquired as magnetic particles of a sediment align with the Earth’s magnetic field while settling (detrital remnant magnetization, DRM)

•Secondary remnant magnetization:

•Recrystallization of minerals during diagenesis of metamorphism (chemical remnant magnetization, CRM)

•Slow relaxation of domains in an ambient magnetic field (viscous remnant magnetization, VRM)

Remnant MagnetizationRock magnetization has two parts:

•Induced magnetization exists only while a magnetic field exists and is aligned

in the direction of the field The strength of magnetization is proportional to the strength of the field and to its magnetic susceptibility

•Remnant magnetization can exists largely irrespective of the direction of the magnetic field It may have a direction very different to the field of today

•Susceptibility is usually a function of

magnetite content

•Basic igneous rocks are usually

highly magnetic due to their high

Geomagnetic Field

At any point on the earth a freely suspended magnet will assume a position in

space in the direction of the ambient geomagnetic field

The total field vector, B, has a vertical component Z and a horizontal component

H in the direction of magnetic north

•Inclination = Dip of B

•Declination = angle between magnetic north and true north

B varies in strength from 25,000 nT in equatorial regions to 70,000 nT at the

Geomagnetic Field

•About 90% of the Earth’s magnetic field can be represented by a theoretical

magnetic dipole at the center of the Earth and inclined 11.5o to the axis of rotation

•The dipolar magnetic moments are far greater than is realistic.

•The prevailing temperatures are far in excess of the Curie temperatures of any magnetic material

•Dynamo – the magnetism is believed to be caused by the dynamo action

produced by the circulation of charged particles in coupled convective cells within the fluid outer core

•The exchange of dominance between convective cells is believed to produce the periodic changes in the polarity of the geomagnetic field

Secular Variation

•The circulation patterns within the outer core are not fixed and change slowly with time

•Slow, progressive, temporal change in all geomagnetic elements

•This has been recorded historically at observatories globally

•Accordingly, the correction to convert a compass reading to true north has to

be changed every few years (and according to location)

•Maps give both the declination and the rate of change

•If we look at the magnetism of old rocks

we see that the magnetic axis wobbles

about the rotation axis

•A full rotation takes ~2,000 years

•When averaged over >10,000 years, the

pole is close to axis of rotation

Diurnal VariationsMagnetic effects of external origin cause the geomagnetic field to vary on a daily basis What might these be??

•Under normal conditions the diurnal variation is smooth, regular, and has an

amplitude of 20-80 nT (maximum at the poles)

•Caused by magnetic field induced by the flow of charged particles within the ionosphere towards the magnetic poles as both the circulation patterns and diurnal variations vary in sympathy with the tidal effects of the Sun and Moon

•On disturbed days the diurnal variation is irregular, with short term disturbances

Magnetic Anomalies

2 2

A magnetic anomaly is now superimposed on the Earth’s field causing a change

ΔB in the strength of the total field vector B The anomaly produces a vertical component ΔZ and a horizontal component ΔH at an angle α to H.

Only that part of ΔH in the direction of H, namely ΔH’ will contribute to the

anomaly:

The product of the ambient geomagnetic field and the anomaly is thus:

2 2

)(B+∆B = H +∆H + Z +∆Z

Magnetic Anomalies

α

coscos

4

e

This previous equation, with a couple of other steps, can be rewritten as:

We can now calculate the anomaly caused by a small isolated magnetic pole of

strength m, defined as the effect of this pole on a unit positive pole at the

observation point This pole is at depth z, a horizontal distance x and radial

distance r from the observation point The force of repulsion ΔB r on the unit

positive pole in the direction r is given by:

If we assume that the profile lies in the direction of magnetic north so that the

horizontal component of the anomaly lies in this direction, the horizontal (ΔH)

and vertical (ΔZ) components can be computed by resolving in the different

directions:

3 2

3 2

sin

cos

r

Cmz r

Cm Z

r

Cmx r

Cm H

Magnetic Anomalies

3 2

3 2

sin

cos

r

Cmz r

Cm Z

r

Cmx r

Cm H

•The vertical field anomaly is negative as,

by convention, the z-axis is positive

downwards

•The horizontal field anomaly is a

positive/negative couplet and the vertical

field anomaly is centered over the pole

By substitution, we can now find the total field anomaly ΔB, where α = 0 If the profile is not in the direction of magnetic north, the angle α would represent the

angle between magnetic north and the profile direction

α

cos cos

sin I H I Z

Magnetic Anomalies

•A magnetic dipole produces a field

shown by the dashed lines, whose

directions and magnitudes at the

surface are shown by the arrows

•The actual field at the Earth’s

surface is found by vector addition

of the field due to the body and the

Earth’s field

•The anomaly is dependant on the

direction of magnetization of the

Flux-Gate Magnetometer

•Sensor has 2 identical bars of magnetic material.

•Primary coils are wound around each bar in opposite

directions Alternating current flows through the primary coils,

producing a changing magnetic field.

•This induces a current in the secondary coil, which is wound

around both bars.

•Because the primary coils are wound in opposite senses their

fields are opposite in direction and cancel Therefore the

induced current is zero.

•In the presence of an external field it will add to, then subtract

from, the field if the magnetizing coil as the current alternated.

•The fields experienced by the two bars are no longer equal –

the bar in which the field of the coil and the Earth add reaches

saturation sooner The induced voltages are now out of phase.

•The magnitude of the voltage induced in the secondary coil is

proportional to the amplitude of the external field.

Flux-Gate Magnetometer

•Can measure Z or H by aligning the coils in that direction

•Requires the orientation to be within 11 seconds of arc to achieve a reading

accuracy of 1 nT

•This accuracy is hard to maintain in a mobile instrument

•Instead, the total magnetic field is measured

•Can be measured to an accuracy of 1 nT with far less precise orientation as the field changes more slowly as a function of orientation about the total field direction

•Airborne versions employ orienting mechanisms of various types to maintain the axis of the instrument in the direction of the geomagnetic field

•Is not an absolute instrument, may require correction for drift and temperature effects

Proton Precession Magnetometer

•The most commonly used magnetometer

•Coil wrapped around a container filled with

a hydrogen atom rich liquid (water,

kerosene)

•The hydrogen nuclei (protons) act as small

dipoles and align with the ambient

geomagnetic field

•A current is passed through the coil,

generating a magnetic field 50-100 times

larger than the ambient field

•The protons align with the new field

direction

•When the current is switched off the

protons return to their original orientation by

spiraling, or precessing, in phase around the

direction of the Earth’s ambient field