Class Projects

1
Class Projects

• Poster or paper.
• Undergraduates can do joint projects.
• Graduates must do their own.
• Determine project title by 7 Oct.
• Think up your own title
• Ask me for help
• I can also suggest a project title and supply
  data.
• Project is due 9 Dec.
• Some ideas
• A history of geophysics
• Mapping from space the shuttle SRTM mission
• Mapping from space satellite altimetry
• The seismicity of ??
• Gravity and/or magnetic modeling of ??
• Seismic reflection data collection equipment and
  methods
• Seismic interpretation of ???
• Seismic processing of ???

2
Library Open House

• Rodgers Library for Science and Engineering
• Thursday, September 30, 2004, 900 a.m. to 1100
  a.m
• Free cookies and drinks.

3
Magnetic data can be used in a number of ways
can you think of any??
4
Magnetic Surveying

• The investigation of the subsurface geology on
  the basis of anomalies in the Earths magnetic
  field resulting from the magnetic properties of
  the causative body.
• A broad range of applications name some
• Magnetic surveys can be performed on land, at
  sea, in the air, and on ice.
• Very cheap to perform.

5
Basic Concepts
From Kearey, Brooks, and Hill, 2002

• Within 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 Earths 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 Earths magnetic field can be crudely modeled
  as a bar magnet with its south pole at the
  Earths north magnetic pole.

From Mussett and Khan, 2000
6
Basic Concepts
The force F between two magnetic poles of
strengths m1 and m2 separated by a distance r is
given by
Where µ0 and µR 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
The magnetic field component in any direction is
then given by the partial derivative of the
potential in that direction.
7
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
  permeability.

From Mussett and Khan, 2000
8
Basic Concepts

• Lenzs 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 Earths surface.
  Consequently, the nannotesla is used (1 nT 10-9
  T).

9
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

From Kearey, Brooks, and Hill, 2002

• 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.

10
Basic Concepts

• The intensity of induced magnetization Ji of a
  material is defined as the dipole moment per unit
  volume of material

From Kearey, Brooks, and Hill, 2002

• Where M is the magnetic moment of a sample of
  length L and cross-sectional area A. Ji is
  expressed in A m-1.
• The induced intensity of magnetization is
  proportional to the strength of the magnetizing
  force H of the inducing field

Where k is the magnetic susceptibility of the
material. As Ji and H are both measured in A m-1,
k is dimensionless.
11
Basic Concepts

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

• Where µ0 is the permeability of a vacuum (4p10-7
  H m-1).
• As air and water have very similar permeabilities
  to µ0 the relationship can be taken to represent
  the Earths 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
Where µR 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.
12
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.

13
Basic Concepts

• 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
  Earths 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.

From Kearey, Brooks, and Hill, 2002
14
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.

15
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 Earths 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).

16
Remnant Magnetization

• Rock 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. Why??
• Total magnetization is the addition of the
  induced and remnant magnetization taking into
  account their directions.
• Ratio of remnance to induced magnetizations is
  the Könisberger ratio, Q. To further complicate
  matters, Q may vary through a body.

From Mussett and Khan, 2000
17
Susceptibility

• Susceptibility is usually a function of magnetite
  content.
• Basic igneous rocks are usually highly magnetic
  due to their high magnetite content.
• Magnetite content decreases with increasing
  acidity.
• Granite is generally less magnetic than basalt.
• Lots of overlap, impossible to interpret
  lithology.

18
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.
From Mussett and Khan, 2000
From Kearey, Brooks, and Hill, 2002

• 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 poles.

19
Geomagnetic Field

• About 90 of the Earths 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.

From Mussett and Khan, 2000

• If this dipole field is subtracted from the
  observed magnetic field, the residual can be
  modeled by the effects of a second, smaller,
  dipole.
• This can be repeated again and again until the
  magnetic field of the Earth has been modeled with
  sufficient accuracy.
• The effects of each fictitious dipole contribute
  to a function known as a harmonic.
• The technique of successive approximations of the
  observed field is known as spherical harmonic
  analysis.

20
Geomagnetic Field

• Spherical harmonic analysis is used to compute
  the formula of the International Geomagnetic
  Reference Field (IGRF).
• The IGRF defines the theoretical undisturbed
  magnetic field at any point on the Earths
  surface.
• The geomagnetic field cannot in fact result from
  a series of superimposed bar magnets. Why?
• 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.

21
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 gt10,000 years, the pole is
  close to axis of rotation.

From Mussett and Khan, 2000
22
Diurnal Variations

• Magnetic 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 of up to
  1000 nT.
• Magnetic storms resulting from intense solar
  activity and the arrival in the ionosphere of
  charge solar particles.
• Makes magnetic surveying difficult if not
  impossible.

23
Magnetic Anomalies
From Kearey, Brooks, and Hill, 2002
The normal geomagnetic field can be described by
a vector with vertical and horizontal components
A magnetic anomaly is now superimposed on the
Earths field causing a change ?B in the strength
of the total field vector B. The anomaly produces
a vertical component ?Z and a horizontal
component ?H at an angle a to H. Only that part
of ?H in the direction of H, namely ?H will
contribute to the anomaly
The product of the ambient geomagnetic field and
the anomaly is thus
24
Magnetic Anomalies
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 ?Br on the unit positive pole in the
direction r is given by
From Kearey, Brooks, and Hill, 2002
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 (?H) and vertical (?Z)
components can be computed by resolving in the
different directions
25
Magnetic Anomalies

• 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.

From Kearey, Brooks, and Hill, 2002
By substitution, we can now find the total field
anomaly ?B, where a 0. If the profile is not in
the direction of magnetic north, the angle a
would represent the angle between magnetic north
and the profile direction.
26
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 Earths surface is found
  by vector addition of the field due to the body
  and the Earths field.
• The anomaly is dependant on the direction of
  magnetization of the body.

From Mussett and Khan, 2000
27
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.

From Kearey, Brooks, and Hill, 2002
28
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.

29
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 Earths ambient field.

From Kearey, Brooks, and Hill, 2002
30
Proton Precession Magnetometer

• The frequency of precession is given by

Where ?p is the gyromagnetic ratio of the proton,
26752.2 x 104 T-1 s-1. Therefore

• Consequently, measurement of f provides a very
  accurate measurement of the total magnetic field.
  f is determined by measurement of the alternating
  voltage of the same frequency induced in the coli
  by the precessing protons.
• Accuracy of 0.1 nT
• Sensor does not have to be oriented.
• Can be towed behind a ship or aircraft.

31
Magnetic Surveys

• Magnetic gradiometers Typically two instruments
  separated by a short distance.
• Measures the gradient of the magnetic field.
• Not prone to diurnal variation.
• Shallower magnetic bodies produce steeper
  gradients.
• May reveal boundaries not seen in a total field
  survey.
• Ground magnetic surveys Small station spacing.
• Do not take readings near magnetic objects.
• Aeromagnetic and marine surveys
• In the air a sensor known as a bird can be
  towed, isolating it from the magnetic field of
  the aircraft.
• Can be installed in a stinger in the tail of an
  aircraft. Coil installations compensate for the
  aircrafts magnetic field.
• At sea the sensor, or fish is towed at least
  two ships lengths behind the vessel to remove
  its magnetic effect.

From Mussett and Khan, 2000
32
Data Reduction

• Diurnal variation correction
• During quiet times, the diurnal variation changes
  smoothly. Periodically returning to a base
  station and recording the Earths magnetic field
  allows corrections in a manner similar to drift
  correction in gravity surveys.
• Preferably, a magnetometer is set to continuously
  record at a base station while the survey is
  carried out. The variations in the field at that
  location (where the field would ideally be fixed)
  can then be removed from the mobile
  magnetometer.
• Use the records from a magnetic observatory
  should be no more than 100 km away as the diurnal
  variations vary with location.
• Diurnal variation in land and airborne surveys
  can be removed with cross-over corrections.

From Kearey, Brooks, and Hill, 2002
33
Data Reduction

• Geomagnetic Correction
• Magnetic equivalent of the latitude correction in
  gravity data reduction.
• Remove the IGRF (spherical harmonics) from the
  recorded field. Very complex, must be done by
  computer.
• The magnetic field may also be approximated by a
  gradient for example in the British Isles the
  gradient is approximately 2.13 nT km-1 N 0.26 nT
  km-1 W.
• All these corrections vary with time.
• Alternatively a regional gradient can be removed
  by fitting a trend surface through the data.
• Terrain correction
• Fourier methods exist to removed the effects of
  terrain.

From Kearey, Brooks, and Hill, 2002
34
Forward Modeling

• Forward modeling
• Many similarities to gravity modeling.
• Many differences
• Anomaly varies depending on location on the
  Earths surface
• Remnant magnetization will almost certainly be in
  a different direction to the ambient field.

From Kearey, Brooks, and Hill, 2002
35
Forward Modeling

• Simple anomalies can be simulated by a single
  dipole.
• The magnetic anomaly of most regularly-shaped
  bodies can be calculated by building up the
  bodies from a series of dipoles parallel to the
  magnetixation direction.
• The poles of the magnets are negative on the
  surface of the body where the magnetization
  vector enters the body, and positive where it
  leaves the body.

From Kearey, Brooks, and Hill, 2002
36
Forward Modeling

• In the example below, building a sill out of
  dipoles results in negatives along the top, and
  positives along the bottom.
• These cancel out in a sill or lava flow the
  anomaly will only be present where the horizontal
  structure is truncated.

From Kearey, Brooks, and Hill, 2002
37
Anomaly of a Vertical Sheet
From Mussett and Khan, 2000
38
Direct Interpretation

• Magnetic anomalies caused by shallow bodies have
  a higher frequency nature.
• The log-power spectrum of the anomaly has a
  linear gradient whose magnitude is dependant upon
  the depth of the source.

From Kearey, Brooks, and Hill, 2002
39
Potential Field Transformations

• A consequence of the similar laws of attraction
  governing gravitating and magnetic bodies is that
  the two main equations have the variable of
  inverse distance (1/r) in common.
• Elimination of this term between the two formulae
  provides a relationship between the gravitational
  and magnetic potentials know as Poissons
  equation.
• Magnetic fields can be transformed into gravity
  fields and vice versa, for bodies in which the
  ratio of intensity of magnetization to density
  remains constant.
• Pseudogravity anomalies
• Transforming a magnetic anomaly to a gravity
  anomaly simplifies interpretation.
• If the pseudogravity and gravity anomalies are
  the same, then the body responsible for the
  magnetic anomaly is the same as that responsible
  for the gravity anomaly.

From Kearey, Brooks, and Hill, 2002
40
Applications

• Finding metalliferous deposits iron ore (must
  have high abundance of magnetite).
• Delineate fault zones.
• Finding man made objects pipelines, aircraft,
  etc.
• Volcanic studies delineating volcanic vents.
• Large-scale crustal studies.
• Seafloor age.
• Sediment age.
• Etc.

41
References Used

• Mussett, A.E. and M.A. Khan, Looking into the
  Earth An introduction to geological geophysics,
  2000.
• Kearey, P., M. Brooks, and I. Hill, An
  Introduction to Geophysical Exploration, 2002.