## Relative Plate Motions

The present day motion of plates can now be measured using the techniques of space geodesy (Section 5.8). However, these techniques were only developed in the 1980s, and, ideally, measurements are required over a period of 10-20 years (Gordon & Stein, 1992). Prior to this relative plate motions, averaged over the past few million years, were determined using geologic and geophysical data.

The motion of plates over the Earth's surface can be described by making use of Euler's theorem (Section 3.2.1), which says that the relative motion between two plates is uniquely defined by an angular separation about a pole of relative motion known as an Euler pole. The pole and its antipole are the two unique points on the surface of the Earth that do not move relative to either of the two plates. An important aspect of relative plate motion is that the pole of any two plates tends to remain fixed relative to them for long periods of time. Plate velocities are similarly constant for periods of several million years (Wilson, 1993).

There are three methods by which the pole of relative motion for two plates can be determined. The first, and most accurate, is based on the fact that for true tangential motion to occur during the relative movement of two plates, the transform faults along their common boundary must follow the traces of small circles centered upon the pole of relative motion (McKenzie & Parker, 1967; Morgan, 1968). The pole of rotation of two plates can thus be determined by constructing great circles at right angles to the trends to transform faults affecting their common margin and noting their point of intersection. The most convenient type of plate margin to which to apply this technique is the accretive type (Fig. 5.3), as ocean ridges

Figure 5.3 Determination of the Euler pole for a spreading ridge from its offsetting transform faults that describe small circles with respect to the pole.

are frequently offset laterally by transform faults (Section 4.2.1). Because of inaccuracies involved in mapping oceanic fracture zones, the great circles rarely intersect at a single point. Consequently, statistical methods are applied which are able to predict a circle within which it is most probable that the relative rotation pole lies.

A second method is based on the variation of spreading rate with angular distance from the pole of rotation. Spreading rates are determined from magnetic lineations (Section 4.1.6) by identifying anomalies of the same age (usually number 3 or less so that the movement represents a geologically instantaneous rotation) on either side of an ocean ridge and measuring the distance between them. The velocity of spreading is at a maximum at the equator corresponding to the Euler pole and thence decreases according to the cosine of the Euler pole's latitude (Fig. 5.4). The determination of the spreading rate at a number of points along the ridge then allows the pole of relative rotation to be found.

The final, and least reliable, method of determining the directions of relative motion between two plates makes use of focal mechanism solutions of earthquakes (Section 2.1.6) on their common margins. If the inclination and direction of slip along the fault plane are known, then the horizontal component of the slip vector is the direction of relative motion. The data are less accurate than the other two methods described above because, except in very well determined cases, the nodal planes could be drawn in a range of possible orientations and the detailed geometry of fault systems at plate boundaries is often more complex than implied here (Section 8.2 and below).

Divergent plate boundaries can be studied using spreading rates and transform faults. Convergent boundaries, however, present more of a problem, and it is often necessary to use indirect means to determine relative velocities. This is possible by making use of information from adjoining plates and treating the rotations between plate pairs as vectors (Morgan, 1968). Thus, if the relative movements between plates A and B and between plates B and C are known, the relative movement between plates A and C can be found by vector algebra.

This approach can be extended so that relative motions can be determined for any number of interlocking plates. Indeed, the method can be applied to the complete mosaic of plates that make up the Earth's surface, provided that there are sufficient divergent

Velocity as a percentage of Wmax 20 40 60 80 100%

Velocity as a percentage of Wmax 20 40 60 80 100%

Figure 5.4 Variation of spreading rate with latitudinal distance from the Euler pole of rotation.

plate margins to be able to compute relative velocities at convergent margins.

The first study of this type was undertaken by Le Pichon (1968). He made use of globally distributed estimates of relative plate velocities derived from transform faults and spreading rates, but not of information obtained from focal mechanism solutions. Le Pichon used a subdivision of the Earth's surface based on only six large plates: the Eurasian, African, Indo-Australian, American, Pacific, and Antarctic plates. In spite of this simplification his model provided estimates of spreading rates that agreed well with those derived from magnetic anomalies (Section 4.1.6).

Subsequently, more detailed analyses of global plate motions were performed by Chase (1978), Minster & Jordan (1978), and DeMets et al. (1990). These studies recognized a number of additional plate boundaries and hence additional plates. The latter included the Caribbean and Philippine Sea plates, the Arabian plate, the Cocos and Nazca plates of the east Central Pacific, and the small Juan de Fuca plate, east of the Juan de Fuca ridge, off western North America (Fig. 5.5). The American plate was divided into two, the North American and South American plates, and the Indo-Australian plate similarly, into the Indian and Australian plates. The new boundaries identified within the American and

Figure 5.5 Map showing the relative motion between the major plates, and regions of diffuse deformation within plates (shaded areas). Solid arrowheads indicate plate convergence, with the arrow on the underthrusting plate; open arrowheads indicate plate divergence at mid ocean ridges. The length of the arrows represents the amount of plate accretion or subduction that would occur if the plates were to maintain their present relative velocities for 25 Ma. Note that, because of the Mercator projection, arrows at high latitudes are disproportionately long compared to those at low latitudes. AN, Antarctica; AR, Arabia; AU, Australia; CA, Caribbean; CO, Cocos; EU, Eurasia; IN, India; JF, Juan de Fuca; NA, North America; NB, Nubia; NZ, Nazca; PA, Pacific; PH, Philippine; SA, South America; SC, Scotia Sea; SM, Somalia (modified from Gordon, 1995, by permission of the American Geophysical Union. Copyright © 1995 American Geophysical Union).

Figure 5.5 Map showing the relative motion between the major plates, and regions of diffuse deformation within plates (shaded areas). Solid arrowheads indicate plate convergence, with the arrow on the underthrusting plate; open arrowheads indicate plate divergence at mid ocean ridges. The length of the arrows represents the amount of plate accretion or subduction that would occur if the plates were to maintain their present relative velocities for 25 Ma. Note that, because of the Mercator projection, arrows at high latitudes are disproportionately long compared to those at low latitudes. AN, Antarctica; AR, Arabia; AU, Australia; CA, Caribbean; CO, Cocos; EU, Eurasia; IN, India; JF, Juan de Fuca; NA, North America; NB, Nubia; NZ, Nazca; PA, Pacific; PH, Philippine; SA, South America; SC, Scotia Sea; SM, Somalia (modified from Gordon, 1995, by permission of the American Geophysical Union. Copyright © 1995 American Geophysical Union).

Indo-Australian plates are rather indistinct and characterized by diffuse zones of deformation and seismicity (Gordon, 2000) (Fig. 5.5). Thus, the analysis of DeMets et al. (1990) involved 14 plates. Other plates have been recognized, but the relative movement across one or more of their boundaries is difficult to quantify. Examples include the Scotia Sea plate, and the diffuse boundary through the African plate, associated with the East African Rift system, that divides the African plate into the Nubian and Somali plates (Fig. 5.5). The only well-defined plate boundaries invariably omitted from these analyses are the spreading ridges in certain backarc basins (Section 9.10), for example, those in the east Scotia Sea, the east Philippine Sea and the South Fiji basin.

These analyses of relative plate motions all used large datasets of relative motion vectors derived from transform faults, spreading rates and focal mechanism solutions; that of DeMets et al. (1990) employing a dataset three times larger than those used in the earlier models. In all cases so many data were available that the problem became over-determined, and in inverting the data set to provide the global distribution of plate motions, they used a technique whereby the sum of the squares of residual motions was minimized. Errors in determining spreading rates were generally less than 3 mm a-1, in transform fault orientation between 3° and 10°, and in earthquake slip vector direction no more than 15°.

Figure 5.5 illustrates the directions and rates of spreading and subduction predicted by the model of DeMets et al. (1990), at specific points on the respective plate boundaries. The rates have been corrected for a subsequent revision of the geomagnetic reversal times-cale (DeMets et al., 1994). In Table 4.1, predicted rates of spreading, at various points on the mid-ocean ridge system, are compared with observed rates derived from the magnetic anomalies observed over these ridge crests. Along the length of the East Pacific Rise accretion rates per ridge flank vary from 25 to 75 mm a-1. By contrast, subduction rates around the margins of the Pacific are typically between 60 and 95 mm a-1. Thus the oceanic plates of the Pacific are steadily reducing in size as they are being consumed at subduction zones at a higher rate than they are being created at the East Pacific Rise. By contrast, plates containing parts of the Atlantic and Indian oceans are increasing in size. A corollary of this is that the Mid-Atlantic Ridge and Carlsberg Ridge of the northwestern Indian Ocean must be moving apart. This has important implications for the nature of the driving mechanism of plate tectonics discussed in Chapter 12. Not all ocean ridges spread in a direction perpendicular to the strike of their magnetic lineations. It may be significant that the major obliquities of this type are found in the more slowly spreading areas, in particular the North Atlantic, Gulf of Aden, Red Sea, and southwestern Indian Ocean (Plate 4.1 between pp. 244 and 245).

In contrast to accretionary plate margins, where the spreading boundary is typically perpendicular to the direction of relative motion, convergent margins are not constrained in this way and the relative motion vector typically makes an oblique angle with the plate boundary. Extreme examples, with very high obliquity, occur at the western end of the Aleutian arc and the northern end of the Indonesian arc (Fig. 5.5). In subduction zones therefore, in addition to the component of motion perpendicular to the plate boundary, that produces underthrusting, there will be a component of relative motion parallel to the plate boundary. This "trench parallel" component often gives rise to strike-slip faulting within the overriding plate immediately landward of the forearc region. As a consequence, focal mechanism solutions, for earthquakes occurring on the interface between the two plates beneath the forearc region, do not yield the true direction of motion between the plates. They tend to underestimate the trench parallel component of motion because part of this is taken up by the strike-slip faulting (DeMets et al., 1990). Classic examples of such trench parallel strike-slip faults include the Philippine Fault, the Median Tectonic Line of southwest Japan (Section 9.9), and the Atacama Fault and the Liquine-Ofqui Fault (Section 10.2.3) in Chile.

As indicated in Fig. 5.5, approximately 15% of the Earth's surface is covered by regions of deforming lithosphere; for example in the Alpine-Himalayan belt, southeast Asia, and western North America. Within these areas it is now possible to identify additional small plates, albeit often with diffuse boundar ies, using GPS (Global Positioning System) data (Section 5.8). GPS measurements also make it possible to determine the motion of these plates relative to adjacent plates, whereas this is not possible using the techniques based on geologic and geophysical data described above. Most of the poorly defined zones of deformation surrounding these plates occur within continental lithosphere, reflecting the profound difference between oceanic and continental lithosphere and the ways in which they deform (Sections 2.10, 8.5.1).

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### Responses

• patrick
How can we determine the pole of rotation of plates using variation in spreading rates?
2 years ago
• IMOGEN
What relative motion of the plates Divergent?
2 years ago
• gabriela
What type(s) of plate boundaries indicate(s) the direction of relative plate motions?
1 year ago