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FowlerCh2 - Ilrtmimxnrmmp V‘ nflmvmt<dfinu:m 2...

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Unformatted text preview: Ilrtmimxnrmmp V‘- nflmvmt<dfinu :m 2 Tectonics on a Sphere The Geometry of Plate Tectonics 2.1 Plate Tectonics The earth has a cool and therefore mechanically strong outermost shell called the lithosphere (Greek lithos, ‘rock’). The lithosphere is of the order of 100 km thick and comprises the crust and uppermost mantle. It is thinnest in the oceanic regions and thicker in continental regions, where its base is poorly understood. The asthenosphere (Greek asthenia, ‘Weak’ or ‘sick’) is beneath the lithosphere. The high temperature and pressure which exist at the depth of the asthenosphere cause its viscosity to be low enough to allow viscous flow, on a geological time scale (millions of years, not seconds!) If the earth is viewed in purely mechanical terms, the mechan- ically strong lithosphere floats on the mechanically weak asthenosphere. Alternatively, if the earth is viewed as a heat engine, the lithosphere is an outer skin, through which heat is lost by conduction, and the astheno- sphere is an interior shell through which heat is transferred by convec- tion (Sect. 7.1). The basic concept of plate tectonics is that the lithosphere is divided into a small number of nearly rigid plates (like curved caps on a sphere), which are moving over the asthenosphere. Most of the deformation which results from the plate motion — such as stretching, folding or shearing —takes place at the edge, or boundary, of a plate. Deformation inside the boundary is not significant. A map of the seismicity (earthquake activity) of the earth (Fig. 2.1) outlines the plates very clearly because nearly all earthquakes as well as most of the earth’s volcanism occur along the plate boundaries. These seismic belts are the zones in which differential movements between the nearly rigid plates occur. There are seven main plates, of which the largest is the Pacific plate, and numerous smaller plates such as Nazca, Cocos, and Scotia plates (Fig. 2.2). ' The theory of plate tectonics, which describes the interactions of the plates and the consequences of these interactions, is based on several important assumptions: 1. The generation of new plate material occurs by seafloor spreading; that is, new oceanic lithosphere is generated along the active midocean ridges (see Chapters 3 and 8). 2. The new oceanic lithosphere, once created, forms part of a rigid plate; this plate may or may not include continental material. Plate Tectonics 3. The earth’s surface area remains constant; therefore, seafloor spreading must be balanced by consumption of plate elsewhere. 4. The lithospheric plates are capable of transmitting stresses over great horizontal distances without buckling; in other words, the relative motion between plates is taken up only along plate boundaries. Plate boundaries are of three types: 1. Along divergent boundaries, also called accreting or constructive, plates are moving away from each other. At such boundaries new plate material, derived from the mantle, is added to the lithosphere. The divergent plate boundary is represented by the midocean ridge system, along the axis of which new plate material is produced (Fig. 2.3a). 2. Along convergent boundaries, also called consuming or destructive, plates are approaching each other. Most such boundaries are represen- ted by the oceanic trench, island are systems of subduction zones where one of the colliding plates descends into the mantle and is destroyed (Fig. 2.3c). The downgoing plate often penetrates the mantle to depths of about 700 km. Some convergent boundaries occur on land. Japan, the Aleutians and the Himalayas are the surface expression of convergent plate boundaries. . Along conservative boundaries, lithosphere is neither created nor destroyed. The plates move laterally relative to each other (Fig. 2.3e). These plate boundaries are represented by transform faults, of which the San Andreas fault in California, USA. is a famous example. Transform faults can be grouped into six basic classes (Fig. 2.4). By far the most common type of transform fault is the ridge—ridge fault, which ranges from a few kilometres to hundreds of kilometres in length. Some very long ridge—ridge faults occur in the Pacific, equatorial Atlantic and southern oceans (Fig. 2.2, in which the modern distribution of types of plate boundary is also shown). Adjacent plates move relative to each other at rates up to about 15 cm yr‘ 1. The present-day rates for all the main plates are discussed in Section 2.4. Although the plates are made up of both oceanic and continental Figure 2.1. A computer plot of some 30,000 earthquakes which occurred between 1961 and 1967 at depths from 0 to 700 km. These earthquakes delineate the boundaries of the plates very well indeed. (From Barazangi and Dorman 1969.) .313 58:5: 25 3:25: dam? 58025 .8qu 2:28; SEE oak .m.m 2:3“. 111 figs mh<41 O_._.0m<hz< wh<._n_ Z<_QZ_ Z<O_mm_>_< O_n__0<n_ zfimmfifiw :uzflcw I M «95:... Hun. ny Z<O_mm=>_< EEOZ (b) (d) (f) 4 10 v AVB A B AVE 6 6 EVA 4 10 <— —> BVA BVA material, usually only the oceanic part of any plate is created or destroyed. Obviously, seafloor spreading at a midocean ridge produces only oceanic lithosphere, but it is hard to understand why continental material usually is not destroyed at convergent plate boundaries. At subduction zones, where continental and oceanic materials meet, it is the oceanic plate which is subducted (and thereby destroyed). It is probable that if the thick, relatively low-density continental material (approximate continental crustal density, 2.8 x 103 kgm"3) reaches a subduction zone, it may descend a short way, but because the mantle density is so much greater (approximate mantle density, 3.3 x 103 kg m"3), the downwards motion does not continue. Instead, the subduction zone ceases to operate at that place and moves to a more favourable location. Mountains are built (orogeny) above sub- duction zones as a result of continental collisions. In other words, the continents are rafts of lighter material which remain on the surface while the denser oceanic lithosphere is subducted beneath either oceanic or continental lithosphere. The discovery that plates can include both continental and oceanic parts, but that only the oceanic parts are created or destroyed, removed the main objection to the theory of continental ( l a (c) (bl <———> <—-—-> <— <—-—>-> A A -.—' -—> H <- <— (f) (d) (9) (—- 9 —> ._~. a A w.— v— wr- —> G— +- Figure 2.3. Three possible boundaries between plates A and B. (a) A constructive boundary (midocean ridge). The double line is the symbol for the ridge axis, and the arrows and numbers indicate the direction of spreading and relative rate of movement of the plates away from the ridge. In this example the half-spreading rate of the ridge (half-rate) is 20m yr" 1; that is, plates A and B are moving apart at 4cm yr" ‘, and each plate is growing at 2cm yr" ‘. (b) The relative velocities AvB and BvA for the ridge shown in (a). (c) A destructive boundary (subduction zone). The barbed line is the symbol for a subduction zone; the barbs are on the side of the overriding plate, pointing away from the subducting or downgoing plate. The arrow and number indicate the direction and rate of relative motion between the two plates. In this example, plate B is being subducted at 100m yr" ‘. (d) The relative velocities Avla and BvA for the subduction zone shown in (c). (e) A conservative boundary (transform fault). The single line is a symbol for a transform fault. The half-arrows and number indicate the direction and rate of relative motion between the plates: in this example, 6cm yr"‘. (f) The relative velocities,“B and EVA for the transform fault shown in (6). Figure 2.4. The six types of dextral (right-handed) transform faults. There also are six sinistral (left-handed) transform faults, mirror images of those shown here. (a) Ridge~ridge fault, (b) and (c) ridge—subduction-zone fault, (d), (e) and (f) subduction-zonefsubduction- zone fault. (After Wilson 1965.) i 1 i . t l Figure 2.5. (a) A two-plate model on a flat planet. Plate B is shaded. The western boundary of plate B is a ridge from which sea floor spreads at a half-rate of 2cm yr“. (b) Relative velocity vectors AV}; and I,vA for the plates in (a). (c) One solution to the model shown in (a): The northern and southern boundaries of plate B are transform faults, the eastern boundary is a subduction zone with plate B overriding plate A. (d) Alternative solution for the model in (a): The northern and southern boundaries of plate B are transform faults, the eastern boundary is a subduction zone with plate A overriding plate B. 8 2 Tectonics on a Sphere drift, which was the unlikely concept that continents somehow were ploughing through oceanic rocks. 2.2 A Flat Earth Before looking in detail at the motions of plates on the surface of the earth (which of necessity involves some spherical geometry), it is instructive to return briefly to the Middle Ages so that we can consider a flat planet. Figures 2.3a, c,e show the three types of plate boundary and the ways they are usually depicted on maps. To describe the relative motion between the two plates A and B, we must use a vector that expresses their relative rate of movement (relative velocity). The velocity of plate A with respect to plate B is written BVA (i.e., if you are an observer on plate B, then EVA is the velocity at which you see plate A moving). Conversely, the velocity of plate B with respect to plate A is AVE, and EVA (2-1) Figures 2.3b,d,f illustrate these vectors for the three types of plate boundary. To make our models more realistic, let us set up a two-plate system (Fig. 2.5a) and try to determine the more complex motions. The western boundary of plate B is a ridge which is spreading with 'a half-rate of 20m yr“. This information enables us to draw AVE and EVA (Fig. 2.5b). Since we know the shape of plate B, we can see that its northern and southern boundaries must be transform faults. The northern boundary is sinistral, or left-handed; rocks are offset to the left as you cross the fault. The southern boundary is dextral, or right-handed; rocks are offset to the right as you cross the fault. The eastern boundary is ambiguous: AvB indicates that plate B is approaching plate A at 4 cm yr‘1 along this boundary, which means that a subduction zone is operating there; but there is no indication as to which plate is being subducted. The two possible solutions for this AVE = (a) (b) (C) :m: < #1 mmme =17:mrqw-mxmemzmy .q a». .7... 2.2 A Flat Earth 9 OVA * AVE model are shown in Figure 2.50,d. Figure 2.50 shows plate A being subducted beneath plate B at 4cm yr'l. This means that plate B is increasing in length by 2cm yr‘ 1, this being the rate at which new plate is formed at the ridge axis. Figure 2.5d shows plate B being subducted beneath plate A at 4 cm yr‘ 1, faster than new plate is being created at its western boundary (2 cm yr‘ 1); so eventually plate B will cease to exist on the surface of the planet. If we introduce a third plate into the model, the motions become more complex still (Fig. 2.6a). In this example, plates A and B are spreading away from the ridge at a half—rate of 2 cm yr’l, just as in Fig. 2.5a. The eastern boundary of plates A and C is a subduction zone, with plate A being subducted beneath plate C at 6 cm yr‘ 1. The presence of plate C does not alter the relative motions across the northern and southern boundaries of plate B; these boundaries are transform faults just as in the previous example. To determine the relative rate of plate motion at the boundary between plates B and C, we must use vector addition: CV13 2 CVA + AVE (22) This is demonstrated in Figure 2.6d: Plate B is being subducted beneath plate C at 10 cm yr ‘ 1. This means that the net rate of destruction of plate B is 10 — 2 = 8 cm yr‘ 1; eventually, plate B will be totally subducted, and a simple two-plate subduction model will be in operation. So far the examples have been straightforward in that all relative motions have been in an east—west direction. (Vector addition was not really necessary; common sense would work equally well.) But now let us include motion in the north—south direction also. Figure 2.7a shows the model of three plates A, B and C: The western boundary of plate B is a ridge which is spreading at a half-rate of 2 cm yr ‘ 1, the northern boundary of plate B is a transform fault (just as in the other examples) and the boundary between plates A and C is a transform fault with relative motion of 3 cm yr‘ 1. The motion at the boundary between plates B and C is unknown and must be determined by using Eq. 2.2. For this example it is necessary to draw a vector triangle to determine CvB (Fig. 2.7d). A solution to the problem is shown in Figure 2.70: Plate B undergoes oblique subduction beneath plate C at 5 cm yr‘ 1. The other possible solution is for plate C to be subducth beneath plate B at 5 cm yr‘ 1. In that case, the boundary between plates B and C would not remain collinear with the boundary between plates A and C but would move to the east. (This is an example of the instability of a triple junction; see Sect. 2.6.) Figure 2.6. (a) A three-plate model on a flat planet. Plate A is unshaded. The western boundary of plate B is a ridge spreading at a half-rate of 2cm yr“. The boundary between plates A and C is a subduction zone with plate C overriding plate A at 6cm yr". (b) Relative velocity vectors for the plates shown in (a). (c) The solution to the model in (a): Both the northern and southern boundaries of plate B are transform faults, and the eastern boundary is a subduction zone with plate C overriding plate B at 10cm yr’l. (d) Vector addition to determine the velocity of plate B with respect to plate C, CvB. Figure 2.7. (a) A three-plate model on a flat planet. Plate A is unshaded. The western boundary of plate B is a ridge from which sea floor spreads at a half-rate of 20m yr" ‘. The boundary between plates A and C is a transform fault with relative motion of 3cm yr' 1. (b) Relative velocity vectors for the plates shown in (a). (c) The stable solution to the model in (a): The northern boundary of plate B is a transform fault with a 4cm yr"l slip rate, and the boundary between plates B and C is a subduction zone with an oblique subduction rate of 5cm yr‘ 1. (d) Vector addition to determine the velocity of plate B with respect to plate C, ch. 10 2 Tectonics on a Sphere These examples should give some idea of what can happen when plates move relative to each other and of the types of plate boundaries that occur in various situations. Some of the problems at the end of this chapter refer to a flat earth, such as we have assumed for these examples. The real earth, however, is spherical, so we need to understand some spherical geometry. 2.3 Rotation Vectors and Rotation Poles To describe motions on the surface of a sphere we use Euler's fixed point’ theorem, which states: ‘The most general displacement of a rigid body with a fixed point is equivalent to a rotation about an axis through that fixed point”. Taking a plate as a rigid body and the centre of the earth as a fixed point, we can restate this theorem: ‘Every displacement from one position to another on the surface of the earth can be regarded as a rotation about a suitably chosen axis passing through the centre of the earth’. This restated theorem was first applied by Bullard et a1. (1965) in their paper on continental drift, in which they describe the fitting of the coastlines of South America and Africa. The ‘suitably chosen axis’ which passes through the centre of the earth is called the rotation axis, and it cuts the surface of the earth at two points called the poles of rotation (Fig. 2.8a). These are purely mathematical points and have no physical reality, but their positions describe the directions of motion of all points along the plate boundary. The magnitude of the angular velocity about the axis then defines the magnitude of the relative motion between the two plates. Because angular velocities behave as vectors, the relative motion between two plates can be written as (0 = wk, where k is a unit vector along the rotation axis and a) is the angular velocity. The sign convention used is that a rotation which is clockwise (or right-handed) when viewed from the centre of the earth along the rotation axis is positive. Viewed from outside the earth, a positive rotation is anticlockwise. Thus, one rotation pole is positive and the other is negative (Fig. 2.8b). V Consider a point X on the surface of the earth (Fig. 2.8c). At X the value of the relative velocity v between the two plates is u = cuR sin 0 ' (2.3) where 6 is the angular distance between the rotation pole P and the point X, R is the radius of the earth. Thus, the relative velocity is zero at the rotation 2.4 Present-Day Plate Motions 11 (a) (b) Geographic longitudes of North Pole H mam)” Posrtive (great circles) Rotation pole rotation pole /" latitudes of N 7' rotation (small circles) Geographic South Pole poles, where 6 = 0° and 180°, and has a maximum value of (OR at 90° from the rotation poles. This factor of sint) means that the relative motion between two adjacent plates changes with position along the plate boundary, in contrast to the earlier examples for a flat earth. If by chance the plate boundary passes through the rotation pole, the nature of the boundary changes from divergent to convergent, or vice versa (Fig. 2.8b). Lines of constant velocity are small circles defined by 9 = constant about the rotation poles. 2.4 Present-Day Plate Motions 2.4.1 Determination of Rotation Poles and Rotation Vectors Several methods can be used to find the present-day instantaneous poles of rotation and relative angular velocities between pairs of plates. Instanta- neous refers to a geological instant; it means a value averaged over a period of time ranging from a few years to a few million years, depending on the method used. These methods include the following: 1.‘ A local determination of the direction of relative motion between two plates can be made from the strike of active transform faults. Methods of recognizing transform faults are discussed fully in Section 8.5. Since transform faults on ridges are much easier to recognize and more common than transform faults along destructive boundaries, this method is used primarily to find rotation poles for plates on either side of a midocean ridge. The relative motion at transform faults is parallel to the fault and is of constant value along the fault. This means that the faults themselves are arcs of small circles about the rotation pole. The rotation pole must therefore he somewhere on the great circle which is perpendicular to that small circle. So, if two or more transform faults can be used, the intersection of the great circles is the position of the rotation pole (Fig. 2.9). I Figure 2.8. The movement of plates on the surface of the earth. (a) The lines of latitude of rotation around the rotation poles are small circles (shown dashed), whereas the lines of longitude of rotation are great circles (i.e., circles with the same diameter as the earth). Note that these lines of latitude and longitude of rotation are not the geographical lines of latitude and longitude because the poles for the _ geographical coordinate system are the North and South poles, not the rotation poles. (b) Constructive, destructive and conservative boundaries between plates A and B. Plate B is assumed to be fixed so that the motion of plate A is relative to plate B. The visible rotation pole is positive (motion is anticlockwise when viewed from outside the earth). Note that the spreading and subduction rates increase with distance from the rotation pole. The transform fault is an arc of small circle (shown dashed) and thus is perpendicular to the ...
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