## Plate Motions and Paleomagnetic Poles

7.1.1 Combining Euler and Paleomagnetic Poles

In plate tectonic theory the relative motion between two plates is simply described by means of a rotation about an Euler pole as was shown in §5.1.1. The Euler pole defining the relative rotation between two plates is fixed to these two plates and describes only the instantaneous motion that takes place (McKenzie and Parker, 1967). For three contiguous plates, A, B, and C, it is not possible for all three to rotate simultaneously about their instantaneous relative rotation axes (McKenzie and Morgan, 1969). However, it is possible for two of the relative rotations (e.g., A-B and A-C) to remain simple and for each to be described by rotation about a single Euler pole, whereas the relative motion B-C is changing continuously in a complex manner (Le Pichon, 1968). Bullard et al. (1965) have shown how to reconstruct the original relative positions of two continents by finite rotations about suitably chosen Euler poles, but no physical significance can be attached to these rotations; they are nothing more than construction entities. They do, however, provide an important constraint because they represent an integral of the motion over some time. If there is no sea floor or magnetic record between two plates A and B, the understanding of the relative motion between them would require that the timing of the motion between, for example, A and C and B and C be accurately known because the order of the rotations is important. For an excellent text on how to perform such reconstructions, see Cox and Hart (1986).

The above concepts relate to the relative motions between plates and demand full information about the relative movements. A record of the relative movements is typically available from the sea floor for movements younger than about 160 Ma. In paleomagnetism, however, the available datum is the position of a paleomagnetic pole relative to a continental block. For ease of description "continental block" here implies the associated plate as well. A sequence of paleomagnetic poles provides an APWP as discussed in §6.4. A paleomagnetic pole provides information about the latitude and the azimuthal orientation of a continental block but provides no longitudinal information. This is reasonably obvious because if a continent moves along a line of latitude and maintains its azimuthal orientation, an observer on the continent will not perceive any apparent motion of the pole. The problem then is how to use a paleomagnetic pole to determine the location of the continental block and how to assess the relative motion between continental blocks.

First it must be recognized that a large amount of apparent polar wander does not necessarily equate to large movement of the continental block. Furthermore, the absence of apparent polar motion does not necessarily mean that the continental block was stationary. For example, if a continental block remains at the same location on the equator but rotates, an observer on the block would perceive a large amount of apparent polar wander along a circle 90° away. Conversely, for the same rotation but with the continent located at the north pole, there would be no apparent polar wander. As already noted, a continental block can move a long way along a line of latitude and, provided it retains its azimuthal orientation, there will be no apparent polar movement.

The obvious way to restore a paleomagnetic pole at latitude A,p and longitude <t>p, P(\, <|>p), to the north pole, G, is simply to move it along the great circle joining P and G. This is equivalent to rotating through an angle -(90-X) about a pole C on the equator at longitude (<j)+90) as shown in Fig. 7.1. Note that the rotation here is clockwise when viewed from outside the Earth and the rotation angle is therefore negative (see §5.1.1). It is unlikely that this was the actual motion of the paleomagnetic pole so C is merely a construction pole that represents the integrated motion. The continental block is restored to its appropriate longitude and azimuthal orientation by rotating it through the same angle about the construction pole C. As shown in Fig. 7.1, if the paleomagnetic pole was at an angular distance p from the continental block a, then after the rotation to a' the continental block is at the correct colatitude p and has the correct azimuthal orientation. Note, however, that the longitude remains indeterminable and can only be defined by reference to some arbitrarily chosen point on the plate.

North Pole, (J

Fig. 7.1. The paleomagnetic north pole, P, is at latitude /.p and east longitude <|>p. The construction pole C is on the equator at longitude (<t>+90). Rotation of the pole P and its associated continental block a through an angle -(90-X) about C will rotate P to the geographic pole and will restore the continental block to its previous latitude and azimuthal orientation at a'.

North Pole, (J

Fig. 7.1. The paleomagnetic north pole, P, is at latitude /.p and east longitude <|>p. The construction pole C is on the equator at longitude (<t>+90). Rotation of the pole P and its associated continental block a through an angle -(90-X) about C will rotate P to the geographic pole and will restore the continental block to its previous latitude and azimuthal orientation at a'.

Let Ge>A be the angular velocity vector describing the real motion of plate A relative to the geographic pole G and let z be a unit vector along the rotational axis. As with any vector, Ge>A can be split into two components, one along the rotational axis and the other, oilA, passing through the equator (Fig. 7.1). The component along the rotational axis, (G<aA-z)z, contains the longitudinal information and is indeterminable. Thus, in paleomagnetism the only available information is in oilA, given formally by