V

Fig. 1.16. Master curves for declination and inclination for Great Britain. After Turner and Thompson (1981, 1982).

the sample. Therefore study of the paleosecular variation through scatter in paleomagnetic results is restricted to investigations of lava flows and is referred to as paleosecular variation from lavas (PSVL).

The scatter in paleomagnetic results from lavas is measured by the angular dispersion either of paleomagnetic directions or, more commonly, of the corresponding VGPs. Several models for the latitude variation of this angular dispersion have been suggested and are summarized in detail by Merrill et al. (1996). McFadden et al. (1988a) have shown that the concept of separation of the dynamo into two approximately independent families (symmetric and antisymmetric - see §1.1.3) can be useful in modeling PSVL. In this model, the total angular dispersion (S) of VGPs is given by

where SA is the angular dispersion due to the antisymmetric family and Ss is that due to the symmetric family. Although it is extremely unlikely that the two families are in fact independent at any given time, the effect in the time-averaged field may be approximately the same as if they were independent. By definition, the dispersion at the equator is caused entirely by the symmetric family. Analysis of the present geomagnetic field, which by chance has a latitudinal structure in

Latitude

Fig. 1.17. Least squares fit of Model G for PSVL to the VGP scatter from lavas for the past 5 Myr. After McElhinny and McFadden (1997).

Latitude

Fig. 1.17. Least squares fit of Model G for PSVL to the VGP scatter from lavas for the past 5 Myr. After McElhinny and McFadden (1997).

VGP scatter similar to that for the past 5 Myr, shows that the contribution from the symmetric family is effectively independent of latitude. The latitude variation comes from the antisymmetric family and up to latitude 70° the dispersion from this source is approximately proportional to latitude. Assuming a similar behavior for the paleomagnetic field, the model therefore predicts

where SA = ak and Ss = b, and a and b are constants to be determined. When this model is applied to paleomagnetic results from lavas for the past 5 Myr (McElhinny and McFadden, 1997), there is an excellent fit to the latitude variation of VGP scatter as shown in Fig. 1.17.

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Chapter Two

Rock Magnetism

2.1 Basic Principles of Magnetism

2.1.1 Magnetic Fields, Remanent and Induced Magnetism

The study of magnetism originated from observation of the behavior of natural permanent magnets, the earliest known of which were used as magnetic compass needles. A permanent magnet is usually described by its "north" and "south" magnetic "poles", imagined to reside at the opposite ends of the magnet. The concept of magnetic poles has been of considerable use in analyzing the behavior of magnets, but since the discovery by Oersted in 1820 that an electric current flowing in a wire deflected a compass needle placed near it, it has been recognized that all magnetic effects are appropriately described in terms of electric currents. An immediate consequence of this is that there are no isolated magnetic poles, so the "magnetic poles" at the end of a magnet are just convenient fictions for the purpose of simple analysis. An electron in orbit around a nucleus is, in essence, a current flowing in a loop and the magnetic effects of materials can all be described in terms of such elementary current loops.

Magnetic fields are specified in terms of the two vectors H, called the magnetic field, and B, the magnetic induction. B includes the effects of the macroscopic magnetization M, defined as the dipole moment per unit volume, according to the relation

where |i0 is the permeability of free space and has the value of An x 10"7 Hm"1 (Henry per metre). Outside any magnetic materials M = 0 and B and H are parallel and in this case B = |i0H. In geomagnetism and paleomagnetism the magnetic field of interest is almost always external to a magnetic medium, so that B and H are parallel and it is of no consequence which one is used. However, numerical conversion between the old cgs system and the current SI system of units is trivial for B but involves a factor of An (from (i0) in the case of H, so magnetic fields are generally specified in terms of the magnetic induction B rather than the magnetic field H. Furthermore, B is typically referred to in an informal manner as the magnetic field B, a usage that will often be followed in this book. Naturally, when considering magnetic fields inside a magnetic material M * 0, so it becomes important to distinguish between B and H because they will not be equivalent, will not always be parallel, and can even have opposite signs. Under such circumstances it becomes important to use the magnetic field H (see §4.1.2, in which such a situation occurs).

A permanent magnetic and electric current loop both have a magnetic dipole moment, m, associated with them. When placed in a magnetic field B (Fig. 2.1) each will experience a torque L = m xB (i.e., L = m/?sin0, where 9 is the angle between the long axis of the magnet and B or the angle between the axis drawn through the center of the current loop at right angles to the plane of the loop). Hence, the torque attempts to rotate the dipole moment into alignment with B. In the case of the current loop the dipole moment m = iA (current times the area of the loop), and in the case of the bar magnet it is m = pi, where p is the "pole strength" of the imaginary poles at each end of the magnet and I is the distance between the poles. Thus dipole moment is measured in units of Am2 and the magnetization M (dipole moment per unit volume) is measured in Am"1. Table 2.1 summarizes the basic magnetic quantities together with typical values that arise in geomagnetism and paleomagnetism.

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