Geomagnetics. Magnetic Surveying

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1 Geomagnetics ieso 2010 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 name some Magnetic surveys can be performed on land, at sea, in the air, and on ice. Very cheap to perform. 1

2 Basic Concepts 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 Earth s north pole is called the northseeking 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. From Mussett and Khan, 2000 Basic Concepts The force F between two magnetic poles of strengths m 1 and m 2 separated by a distance r is given by: μ0m1m2 F = 2 4πμ R r 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: μ0m B = 2 4πμ R r 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 μ0m V = 4πμ R r The magnetic field component in any direction is then given by the partial derivative of the potential in that direction. 2

3 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 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). 3

4 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: M = ml 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. Basic Concepts The intensity of induced magnetization J i of a material is defined as the dipole moment per unit volume of material: M J i = LA 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 field: J i = kh Where k is the magnetic susceptibility of the material. As J i and H are both measured in A m -1, k is dimensionless. 4

5 Basic Concepts In a vacuum the magnetic field strength B and magnetizing force H are related by: B = μ0h 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: μ 0 J i Within the body the total magnetic field, B, is given by: B = μ 0H + μ0j i Substituting the relationship with the magnetic susceptibility from the previous slide gives: = μ H + μ kh = ( 1+ k μ H = μ μ H B 0 0 ) 0 R 0 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. 5

6 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 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 578 o C. 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. 6

Remnant Magnetization Primary remnant magnetization: Acquired as an igneous rock cools through the Curie temperatures of its constituent minerals (thermoremnant magnetization, TRM).

7 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 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,

Susceptibility Susceptibility is usually a function of magnetite content. Basic igneous rocks are usually highly magnetic due to their high magnetite content.

8 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. 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 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. 8

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 11.5 o to the axis of rotation.

9 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 11.5 o to the axis of rotation. 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. From Mussett and Khan, 2000 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 Earth s 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. 9

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.

10 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. From Mussett and Khan, 2000 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 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. 10

11 Magnetic Anomalies The normal geomagnetic field can be described by a vector with vertical and horizontal components: B = H + Z 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: ΔH ' = ΔH cosα The product of the ambient geomagnetic field and the anomaly is thus: 2 2 ( B + ΔB) = ( H + ΔH ') + ( Z + ΔZ ) 2 Magnetic Anomalies This previous equation, with a couple of other steps, can be rewritten as: ΔB = ΔZ sin I + ΔH cos I cosα 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: Cm μ0 ΔBr = where C = (assuming μ = 1) 2 R r 4π 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: Cm Cmx ΔH = cosθ = 2 3 r r Cm Cmz ΔZ = sinθ = 2 3 r r 11

Magnetic Anomalies Cm Cmx ΔH = cosθ = 2 3 r r Cm Cmz ΔZ = sinθ = 2 3 r r The vertical field anomaly is negative as, by convention, the z-axis is positive downwards.

12 Magnetic Anomalies Cm Cmx ΔH = cosθ = 2 3 r r Cm Cmz ΔZ = sinθ = 2 3 r r 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. ΔB = ΔZ sin I + ΔH cos I cosα 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 body. From Mussett and Khan,

13 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. 13

14 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 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. Proton Precession Magnetometer The frequency of precession is given by: γ B p e f = 2π Where γ p is the gyromagnetic ratio of the proton, x 10 4 T -1 s -1. Therefore: B e = f 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. 14

Magnetic Surveys Magnetic gradiometers: Typically two instruments separated by a short distance. Measures the gradient of the magnetic field. Not prone to diurnal variation.

15 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 Data Reduction Diurnal variation correction: During quiet times, the diurnal variation changes smoothly. Periodically returning to a base station and recording the Earth s 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. 15

16 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. Forward Modeling Forward modeling: Many similarities to gravity modeling. Many differences: Anomaly varies depending on location on the Earth s surface Remnant magnetization will almost certainly be in a different direction to the ambient field. 16

17 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. 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. 17

18 Anomaly of a Vertical Sheet From Mussett and Khan, 2000 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. 18

19 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 Poisson s 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. 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. 19

20 References Used 1. Mussett, A.E. and M.A. Khan, Looking into the Earth: An introduction to geological geophysics, Kearey, P., M. Brooks, and I. Hill, An Introduction to Geophysical Exploration,

Geophysics 223 January Geophysics 223 C1: Basics of Geomagnetism. C1.1 Introduction

Geophysics 223 January Geophysics 223 C1: Basics of Geomagnetism. C1.1 Introduction Geophysics 223 C1: Basics of Geomagnetism C1.1 Introduction Lodestone was known to the Greeks (800 BC) and Chinese (300 BC) First compass (200 BC) made by Chinese, but not clear why it worked Europeans