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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 ridge axis. As the plate boundary passes the rotation pole, the boundary changes from ridge to subduction zone. (c) Cross section through the centre of the earth 0. P and N’are the positive and negative rotation poles, and X is a point on the plate boundary. 12 2 Tectonics on a Sphere —__—__—_.____—-———-———-—— 2. The spreading rate of an accreting plate boundary changes as the sine of the angular distance 0 from the rotation pole (Eq. 2.3). Thus, if the spreading rate at various locations along the ridge can be locally determined (from spacing of oceanic magnetic anomalies as discussed in Chapter 3), the rotation pole and angular velocity can then be estimated. 3. The analysis of data from an earthquake can give the direction of motion . and the plane of the fault on which the earthquake occurred. This is known as a fault plane solution or a focal mechanism. Fault plane solutions for earthquakes along a plate boundary can give the direction of relative motion between the two plates. For example, earthquakes which occur on the transform fault between plates A and B, as illustrated in Figure 2.8b, indicate that there is right lateral motion across the fault. The location of the pole and the direction, though not the magnitude, of Figure 2.9. On a spherical earth the x; motion of plate A relative to plate B must be a rotation about some pole. All the l . . . . . ti transform faults on the boundary the motion can thus be estimated. (Fault plane solutions are discussed in between plates A and B must be small Sect. 4.28.) :13 circles concentric about the Pole- 4. Where plate boundaries cross land, surveys of displacements can be used v.1. Transform faults can be used to locate the pole: It lies at the intersection of the great circles which are perpendicular to (over large distances and long periods of time) to determine the local relative motion. For example, stream channels and even roads, field requ‘refnem’ so " 1.5 not p9ss'blc to system to determine differences in distance between two sites on the determine the relative motion or locate the pole from the ridge use“ (After earth’s surface over a period of years. The other method, known as very- Morgan 1968.) long-baseline interferometry (VLBI), uses quasars for the signal source and terrestrial radio telescopes as the receivers. Again, the difference in 1 distance between two telescope sites is measured over a period of years. l. Figure 2.10 compares the velocity of the Pacific Plate relative to the I the transfrom faults, Although ridges are boundaries and buildings may be displaced. generally perpendicular to the direction 5. Satellites have made it possible to measure instantaneous plate motions l OfSPFCadmg: this IS 110‘ a geometrical with reasonable accuracy. One method uses a satellite laser-ranging . NORTH . . . . . . . . . AMERICAN PLATE PAClFlC _ PLATE Figure 2.10. Velocity of the Pacific Plate -120 . -115 relative to the North American Plate 4 cm/Yr along the San Andreas Fault system in velocity California. Solid arrows, velocities determined from VLBI data recorded uncertainty [. a _ over four years: dashed arrows, '-/ Ve’o‘my 0"“ 4 YBars geologically determined velocities. (After Kroger et al. 1987.] ““ velocity over 2.000.000 years i r i Figure 2.11. Diagram showing the relative positions of the positive rotation pole P and point X on the plate boundary. N is the North Pole. The sides of the spherical triangle N PX are all great circles, the sides N X and NP are lines of geographic longitude. The vector v is the relative velocity at point X on the plate boundary (note that it is perpendicular to PX). It is usual to quote the lengths of the sides of spherical triangles as angles (e.g., latitude and longitude when used as geographic coordinates). 2 Tectonics on a Sphere W . Table 2.2. Symbols used in calculations involving rotation poles / Symbol Meaning Sign convention A? Latitude of rotation pole P °N positive Ax Latitude of point X on plate boundary °S negative 4),; Longitude of rotation pole P °W negative 45x Longitude of point X on plate boundary °E positive v Velocity at point X on plate boundary v Amplitude of velocity (3 Azimuth of the velocity with respect to Clockwise north N positive R Radius of the earth to Angular velocity about rotation pole P M direction and magnitude of the relative {notion at any point along the plate boundary. The notation and sign conventions used in the following pages are given in Table 2.2. Figure 2.11 shows the relative positions of the North Pole N, positive rotation pole P and point X on the plate boungtq (comrfiri with Fig. In the spherical triangle N PX , let the angles X N P = A, N PX = B and PX N = C, and let the angular lengths of the sides of the triangle be PX = a, X N = b and NP = c. Thus, the angular lengths b and c are known, but a is not: b = 90 — AX (2.4) c = 90 —- AP (2.5) Angle A is known, but B and C are not: A = rip — qsx (2.6) Equation 2.3 is used to obtain the magnitude of the velocity at point X 2 v = wR sin a (2.7) The azimuth of the velocity B is given by l? = 90 + C (2.8) To find the angles a and C to substitute into Eqs. 2.7 and 2.8, we use spherical geometry. Just as there are cosine and sine rules which relate the angles and sides of plane triangles, there are cosine and sine rules for spherical triangles: cos a = cos b cos c + sin b sin 6 cos A (2-9) and sin a = sin c (2.10) srn A sm C Substituting Eqs. 2.4~2.6 into Eq. 2.9 gives 2.4 Present-Day Plate Motions cos a = cos (9O — Ax)cos (90 — zip) + sin (90 — xix) sin (90 — zip) cos (d)? — (bx) (2.11) This can then be simplified to ield th ' ' the velocfiy from Eq. 2.7. y e angle a,wh1chis needed to calculate a = cos‘ 1 [sin 2x sin 2,. + cos Ax cos [1,, cos (qSP — ¢x)] (2.12) Substituting Eqs. 2.5 and 2.6 into Eq. 2.10 gives sin a _ sin (90 — 2],) sin ((1),. — 4a,.) _ sinC (2'13) Upon rearrangement this becomes Czsin-I[W] (214) Sin a Therefore if the angle a is calculated from E , q. 2.12, angle C can then be calculated from Eq. 2.14, and finally, the relative velocity and its azimuth can be calculated from Eqs. 2.7 and 2.8. Note that the inverse sine function ofE.2.14'd b- * valugfor C.IS ou le valued. Always check that you have the correct Example: calculation of relative motion at a plate boundary Calculate the present-day relative motion at 28°S 71°W on the Peru—Chile Trench using the Nazca—South Amer" ' ' I ma rotation pole iven in T Assume the radius of the earth to be 6371 km. 9 abie 2.1- ,tx=—2s°, ¢x=—71° 1,. = 56°, 4),, = — 94° = —7 —1 n — a) 7.6 x 10 deg yr =@ x 7.6 x 10 7 radiansyr“1 These values are substituted into Eqs. 2.12, 2.14. 2.7 and 2.8 in that order giVing: a = cos‘1[sin(— 28) sin (56) + cos (— 28) cos (56) cos (— 94 + 71)] =86.26° (2.15) C=Sing1 [cos (56) sin (——94+71) sin (86.26) = —12.65° . g (2.16) V_._ —— . ,180 x 7.6 x10 7 x 6371 x105 x Sin (86.26) cmyr“‘ (2.17) ,An alt ‘ ' iggtrilgsllysetway to calculate motion along a plate boundary and to avoid the sign g I 0 use vector algebra (see Altman 1986 or Cox and Hart 1986, p. 154) 15 :5; as w 2.4 Present-Day Plate Motions 17 where xBA, yBA and 2M are the x, y and z coordinates of the vector BwA, and Suppose there are three rigid plates A, B and C and that the angular velocity of A relative to B, BaiA, and that of B relative to C, Cars, are known. The and the P016 POSitiOH i5 giVen by = 8.43 cm yr" h I; = 90 _ 12.65 (2.18) so on. Equations 2.21—2.23 become = 77.350 xCA : CwB ACE ¢CE + BwA ABA ¢BA Thus, the Nazca Plate is moving relative to the South American Plate at yCA = (3603005 lea Sin (bog + BwA cos ABA sin ¢BA (2'25) '2 8.4 cm yr‘1 with azimuth 77°; the South American Plate is moving relative z _. o - ; CA—Cw Slnlc + a) Sin}. s, to the Nazca Plate at 8.4 cm yr“. azimuth 257° (Fig. 2.2). ‘ B B B A 3" (226) » glen the three rotation vectors are expressed in their x, y, 2 components : e magnitude of the resultant rotation vect ' , ' i‘ 2.4.3 Combination of Rotation Vectors . or do" Is ll M = m (2.27) p re: re a ‘ A ch motion of plate A relative to plate C, CIDA, can be determined by vector i ’ addition just as for the flat earth: 11“ = sin‘ 1(ZC—A) (2 28) w = a) + w (2 19 Ca“ ' m \ c A c B B A r ) and B A w . . . . ‘3 C 3 (Remember that in this notation the first subscript refers to the ‘fixed’ plate.) _1 yCA Alternatively, Eq. 2.19 can be written as ¢CA = tan (2.29) CA Aces + ch + CwA = O (2.20) . Note that this expression for qSCA has an ambiguity of 180° (e.g. tan 30° = since BwA = - AwB. The resultant vector CwA of Eq. 219 must be in the Z “111.210 =0'5774’ tan 110° =tan 2900 = — 2-747). This is resolved b I _ t . . addin or subt t‘ 180° y same plane as the two original vectors BwA and C03. Imagine the great Circle g rac mg so that _ . . on which these two poles lie; the resultant pole must also lie on that same X“ > 0 When _900 < 4)“ < + 90° (2 30) Flgure 2-12. Relative rotation vectors great Circle (Fig. 2.12). Note that this relationship (Eqs. 2.19 and 2.20) should V ' Egghg‘giifé:izhfhglagifiiiingnc' be used only for infinitesimal movements or angular velocities and not for 2 xCA < 0 When I¢CA1 > goo (2 31) which the two was “cg The resultant finite rotations. The theory of finite rotations is cemplex. (For a treatment ' ' of the wh le theor of 'nstantaneous and finite rotations, the reader is . . 0 y ‘ Example: addition of relative rotation vectors rotation vector is can (Eq. 2.19). The resultant pole must also lie on the great referred to Le Pichon et al. 1973.) I circle because the resultant rotation Let the three vectors Ba,» Cwfl, CwA be written as Shown in Table 2.3_ It is Given the instantaneous rotation vectors in Table 2.1 for the Nazca Plate vector has to lie 1n the plane of the two Simplest to use a rectangular coordinate System through the centre of the relative to the Pacific Plate and the Pacific Plate relative to the Antarctic Ongma mam“ V6010“ Barth, whh the x_y plane being equatorial, the x axis passing through the Plate, calculate the instantaneous rotation vector for the Nazca Plate relative to the Antarctic Plate: - Greenwich meridian and the z axis passing through the North Pole, as shown in Figure 2.13. The sign convention of Table 2.2 continues to apply. Then Eq. 2.19 can be written xCA = XCB + xBA (2'21) Flotation Latitude Longitude Angular velocity 1 vector . of pole of pole (10‘7deg yr“) YCA = You + yBA (2.22) zca—Paciflc ., r ' PwN 55.6°N 90.1°W 14 2 elite—Antarctica a, c ' A P 64.3 S 96.0°E 9.1 ZCA = ZCB + ZBA and (2.23) calculate the rotation vector for the Nazca Plate relative to the Table 2.3. Notation used in addition of rotation vectors , . ,tl'CIIC Plate we apply Eq. 2.19; , I Rotation Latitude Longitude Figure 2.13. Rectangular coordinate vector i Magnitude of pole of pole AwN = AwP + PmN (2.32) system used in the addition of rotation ‘ ' 'étituti . vectors. The xfiy plane is equatorial with onemfig the tabulated values into the eQUations for the X. y and z the x-axis passing through 0° Greenwich BwA BwA ABA d)“ 8 Of AmN (Eqs' 224—226) yields and the z-axis through the North Pole. C6913 C6013 ACE $03 = 9 1 COS( 64 Notation and sign conventions are given CwA CwA )‘CA (pcn ' AN I — '3) 008 (960) + 14'2 COS (55's) C05 ( _ 901) = — 0.427 (2.33) in Table 2.3. 18 2 Tectonics on a Sphere ______________d____————————-’ 9.1 COS ( —64.3) sin (96.0) + 14.2 COS (55.6) sin(-—90.1) VAN = 4 098 (234) = ' — 64.3 + 14.2 sin (55.6) 2“ _ 9531;: ( ) (2.35) The magnitude of the rotation vector AwN can now be calculated from Eq. 2.27 and the pole position from Eqs. 2.28 and 2.29. a) = . /0 4272 + 4.0982 + 3.5172 = 5.417 (2.36) A N ' 3.517 o . 2'37 XAstin_1(5-4'1é7)=40.49 ( ) —4.098 O 2.38 ¢AN=tan"<_0427>=180+84.05 ( ) Therefore the rotation for the Nazca Plate relative to the Antarctic PldateI has a magnitude of 5.4 x 10’7deg yr”, and the rotation pole is locate a latitude 40.5°N. longitude 95.9”W. The problems at the end of this chapter enable the reader to usedthiees: methods to determine motions along real and imagined plate boun ar . 2.5 Plate Boundaries Can Change with Time The examples of plates moving upon a flat earth (Sect. 2.2) illltlistriltzd ' tay the same or a i . t s and late boundaries do not 5 ' SESéervationliemains true when we advance from plaLes fmovuig onoglnftlaa‘t ' herical earth. T e orma 1011 model earth to plates movmg on a sp b .Ous IObal ' f existing plates are the most 0 v1 g plates and destruction 0 ' l . h For example a lative motions c ange. , reasons why plate boundaries and re d hen most of bduction zone, such as happene w - plate may be lOSt down a su bd ted under the North American the Farallon and Kula plates were su uc . 1 two ' ' ' d in Sect. 3.3.3). Alternative y, Plate in the early Tertiary (discusse . t . bund- ' ‘ to one (With resultant moun ain continental plates may coalesce in 1 t. e mofions also ' ' ' tation pole changes, all the re a iv mg). If the posmon of a r0 . ' I 00 “1d of course, ' le posmon of 9 we , change. A drastic change in p0 b e rid es and 'Transform faults would ecom g completely alter the status quo. ' A d H ansform faults ' ‘ . Changes in the tren s o r subduction zones, and Vice versa 1 ' h d. Ction of sea- ‘ ' he PaCitic Plate imply that t e ire and magnetic anomalies on t ' . If _Faranon p016 ‘ d and indicate that the Pac11c floor spreading has change I I ' ' ‘ ' f times during the Tertiary. t on chan ed slightly a number 0 I p0i’lalrts of plite boundaries can change locally, however, \glthilué 2:1); major‘plate’ or‘pole’ event occurring. ConSider three plates A, an . lat ' be a convergent boundary between p _ n tsitireiife slip faults between plates A and C and plates B and C, as illustrated1 . Figure 2.14a b. From the point of View of an observer on plate C, t ‘ ' 't 's boundary of C (circled) will change with time beCIaus: the (plate tci)l lvvrtéfigiln 1a ' ' late B. T e oun ary w d ent Will change from plate A to . ’ Zejxaigl (right-handed) fault, but the slip rate Will change from 2 cm yt es A and B, and let there be, ‘to’ 2.6 Triple Junctions 19 (b) 6 cm yr" 1. Relative to plate C, the subduction zone is moving northwards at 6cm yr“ 1. Another example of this type of plate boundary change is illustrated in Figure 2.14c,d. In this case, the relative velocities are such that the boundary between plates A and C is a strike slip fault, that between plates A and B is a ridge and that between plates B and C is a subduction zone. The motions are such that the ridge migrates slowly to the south relative to plate C, so the circled portion of plate boundary will change with time from subduction zone to transform fault. These local changes in plate boundary are a geometric consequence of the motions of the three rigid plates and are not caused by any disturbing outside event. A complete study of all possible interactions of three plates is made in the next section. Such a study is very important because it enables us to apply the theory of rigid geometric plates to the earth and to deduce past plate motions from evidence in the local geological record. We can also predict details of future plate interactions. 2.6 Triple Junctions 2.6.1 Stable and Unstable Triple Junctions A triple junction is the name given to a point at which three plates meet, such the points Tin Figure 2.14. A triple junction is said to be ‘stable’ when the h that the configuration of the junction does not change with time. The 0 examples shown in Figure 2.14 are in these terms stable. In both cases triple junction moves along the boundary of plate C, locally changing tnuths and types of plate boundaries of the whole system do not change time. An ‘unstable’ triple junction exists only momentarily before ing to a different geometry. If four or more plates meet at one point, onfiguration is always unstable, and the system will evolve into two or triple junctions. ' further example, consider a triple junction where three subduction . 1 eet (Fig. 2.15): Plate A is overriding plates B and C, and plate C is ,iiéidmg plate B. The relative velocity triangle for the three plates at the 6 unction is shown in Figure 2.15b. Now consider how this triple ton evolves with time. Assume that plate A is fixed; then the positions plates at some later time are as shown in Figure 2.15c. The dashed (6) EVA Figure 2.14. Two examples of a plate boundary locally changing with time. (a) A three-plate model. Point T, where plates A, B and C meet, is the triple junction. The western boundary of plate C consists of transform faults. Plate B is overriding plate A at 4cm yr“. The circled part of the boundary of plate C changes with time. (b) Relative velocity vectors for the plates in (a). (c) A three-plate model. Point T, where plates A, B and C meet, is the triple junction. The boundary between plates A and B is a ridge, that between plates A and C is a transform fault and that between plates B and C is a subduction zone. The circled part of the boundary changes with time. (d) Relative velocity vectors for the plates in (c). In these examples, velocity vectors have been used rather than angular velocity vectors. This is justified, even for a spherical earth, because these examples are concerned only with small areas of the plates in the immediate vicinity of the triple junctions, over which the relative velocities are constant. .. f‘ir‘a'f’fl 20 2 Tectonics on a Sphere 2.6 Triple Junctions Figure 2.15. (a) A triple junction where Geometry Velocity triangle Stability Possible three subduction zones intersect. Plate A Examples overrides plates B and C, and plate C ; RRR |:ab All orientations East Pacific overrides plate B. AVB, CV3 and AvC are " A B Stable 25.23230, the relative velocities of the three plates acbc Rift Zone, 7 in the immediate vicinity of the triple /C\ / Sgfiflgggfiiy‘g junction. (b) Relative velocity triangle for C a. c Geometr of the three subduction (zdnfasLt some time later than in (a). The Hana) ‘ch lab Stable if ab, ac Central Japan dashed lines show where plates B and C flit: Ad}; my; would have been had they not been / B i/’ parénel to the subducted. The point X in (a) was \C ,/',A Slip Vecwr CA originally on the boundary between / C ' plates A and B; now it is on the boundary mlb} \ c Stab'e. “he between plates A and C. The original » B atb \ \PC ggfigg‘facffid, (‘23::13:12::Ziazlfgafiiizf {82;} been overridden by plate A The subduction zone between plates B and C A / 3 AK” Ecr_g)b_littécéil . has moved north along the north—south edge of plate A. Thus, the original \ C i 1;; 2233933! '5 triple junction (Fig. 2.15a) was unstable; however, the new triple junction k b (Fig. 2.15c) is stable (meaning that its geometry and the relative velocities of g, FFF \ia Uns‘ab'e the plates are unchanging), though the triple junction itself continues to H B :9 move northwards along the north—south edge of plate A. The point X is A B A C. 55> originally on the boundary of plates A and B As the triple junction passes V” C Q *1 X, an observer there Will see a sudden change in subduction rate and direction. Finally, X is a point on the boundary of plates A and C. Rm 3 la: ab mustgo In a real situation, the history of the northward passage of the triple A «\B be i tcrggiigiii of ABC junction along the boundary of plates A and C could be determined by J \/ l 5“ estimating the time at which the relative motion between the plates changed C C at a number of locations along the boundary. If such time estimates increase HF“: regularly with position along the plate boundary, it is probable that a triple B aci lab Unstable, junction migrated along the boundary and not that one of the plates had I A : __LH__.BCEC Sgfigggn changed its relative motion (that would happen only once). It can be seen 0 l l c ab and a}? are that although the original triple junction shown in Figure 2.15a is not I I perpend'cma' stable, it would be stable if AvC were parallel to the boundary between plates WW) \lc/ac Stable nab B and C. In this special case, the boundary between B and C would not A B /) \bc g‘r’fiztch'ggflfi move in a north—south direction relative to A, and so the geometry of the ‘/ \ a straight line triple junction would be unchanging in time. The other configuration in C A :ab B which the triple junction would be stable occurs when the edge of plate A, Tram) on both sides of the triple junction, is straight. This is, of course, the final \LC Stableifoom_ configuration illustrated in Figure 2.150. A \B QC ggfigtifigrfifgga‘ Altogether there are sixteen possible types of triple junction, all shown in / (2 ac I satisfied Figure 2.16. Of these sixteen triple junctions, one is always stable (the /A lab B ridge—ridge—ridge junction) if oblique spreading is not allowed, and two are always unstable (the fault—fault—fault and fault—ridge—ridge junctions). The other thirteen junctions are stable under certain. conditions. In the _ and so on, R dmotes fidge‘T trench and F transform fault. notation used to class1fy the types of triple junction, a ridge is written'as R, The dashed lines ab, be and ac in the velocity triangles represent transform fault as F and a subduction zone (or trench) as T. Thus, a ridge~ velocities which leave the geometry of the boundary between ridgC—ridge junCtion is RRR’ a fathfauu‘ridge lunCtion is FFR, and 50 plates A and B, B and C and A and C, respectively, unchanged. on. To examine the stability of any particular triple junction, it is easiest to A triple junction is- stable it ab, be and ac ineet at a point. Only draw a relative velocity triangle and include the azimuths of the plate “1 RRRtripleiuncmn(Wl‘h1‘13?Spfeadmfigizrfiggany boundaries. In Figure 2.16 the lengths of the lines AB, BC and AC are and perpendlcmar to the" St" cs) 15 aways S ‘ - . . . McKenzie and Morgan 1969.) proportional and parallel to the relatlve velocmes AVE, BvC and Avc. Thus, Figure 2.16. The geometry and stability of all possible triple junctions. In the categories represented by RRR, RTT, RTF 21 Geometry Velocity triangle Stability Possrbie Examples Ti'R c ( ) Io Stable if the A B be angles between \\ ,50 ab and ac, be / \ respectivlely C / I \\ are equa, or if A ‘ab B ac, bc form a ac straight line ITF(a) ab. \ \C,/ I I,/ \bc Stable it ac, be Intersection of A H B B" \ form a straight the Peru-Chile I line, or if C lies french and the / on ab West Chile C Al Ridge l ITF(b) H Stable if be, ab A 8 form a straigni / line, or if ac 0/ goes through B ‘lTF(c) A ll 3 Stable if ab, ac form a straignt line or if ab, bc (4 0/ do so FFR . \ | bc‘x' / Stable if C lies Owen fracture A B "0’ ac on ab, or if zone and the ,/ l ac, be form a geglsberg /’ \‘ I strai ht line i 99 C k //A lab B\ 9 West Chile ' Ridge and the East Pacific Rise \ iab A'a/C Stable if ab, be San Andreas \\' form a straight fault and BI line, or if ac, be Mendocmo : /’C\ e do so fracture zone X ‘ (Mendocmo I triple junction) RTF(a) I c C /’30 A B \i / lab Stable if ab goes Mouth of the \ / | B throu h C or Gulf of I 4 ‘t‘ c if ac, form a California ‘ C A I be? straight line (Rivera triple RTFM ' junction) \ c / A B c\ l/ac \x / l B Stable if ac, ab \(3 /A .ab ‘\ cross on be / i Figure 2.17. Determination of stability for a triple junction involving three subduction zones, TTT(a) of Fig. 2.16. (a) Geometry of the triple junction and relative velocities; this is the same example as Fig. 2.15a. (b) Relative velocity triangles. Sides BA, CB and AC represent BvA, CvB and Avc, respectively (i.e., the line from A to C is the velocity of plate C with respect to plate A, Avc; and the line from B to A is the velocity of plate A with respect to plate B, I,vA). The upper triangle in the parallelogram is the relative velocity triangle of Figure 2.15. In the lower, dashed triangle the corner A represents the velocity of plate A; thus, for example, relative to plate A, plate C is moving with velocity of AC, Avc. (c) The dashed lines ab, be and ac drawn onto the velocity triangle ABC represent possible velocities of the boundary between plates A and B, plates B and C and plates A and C, respectively, which leave the geometry of that boundary unchanged. The triple junction is stable if these three dashed lines intersect at a point. In this case that would occur if ab were parallel to ac or if the velocity Avc were parallel to be. If the geometry of the plate boundaries and relative velocities at the triple junction do not meet either of these conditions, then the triple junction is unstable and can only exist momentarily in geological time. 22 2 Tectonics on a Sphere the triangles are merely velocity triangles such as that shown in Figure 2.15b. The triple junction of Figure 2.15, type TTT(a) in Figure 2.16, is shown in Figure 2.17. The subduction zone between plates A and B does not move relative to plate A because plate A is overriding plate B. However, because all parts of the subduction zone look alike, any motion of the subduction zone parallel to itself would also satisfy this condition. Therefore, we can draw onto the velocity triangle a dashed line ab, which passes through point A and has the strike of the boundary between plates A and B (Fig. 2.17c). This line represents the possible velocities of the boundary between plates A and B which leave the geometry of these two plates unchanged. Similarly, we can draw a line bc which has the strike of the boundary between plates B and C and passes through point C (since the subduction zone is fixed on plate C) and a line ac which passes through A and has the strike of the boundary between plates A and C. The point at which the three dashed lines ab, ac and be meet represents the velocity of a stable triple junction. Clearly, in Figure 2.170, these three lines do not meet at a point; therefore, this particular plate boundary configuration is unstable. However, the three dashed lines would meet at a point (and the triple junction would be stable) if bc were parallel to AC or if ab and ac were parallel. This would mean that either the relative velocity between A and C, Avc, was parallel to the boundary between plates B and C or the entire boundary of plate A was straight. These are the only two possible situations in which such a TTT triple junction is stable. By plotting the lines ab, be and ac onto the relative velocity triangle, we can obtain the stability conditions more easily than we did in Figure 2.15. (a) (b) . . . . _. C EVA , PlateA I CV3 v V . ‘ . I . V . V . ' . ' . ' .' C B'. AVG . . . . . . .. I / ..... [__.—>;” A . . . . .. 3 BA 2.6 Triple Junctions 23 Figure 2.18 illustrates the procedure for a triple junction involving a ridge and two transform faults (type FFR). In this case, ab, the line representing motion along the ridge, must be the perpendicular bisector of AB, and be and ac, representing motion along the faults, are collinear with BC and AC. This type of triple junction is stable only if line ab goes through C (both transform faults have the same slip rate) or if ac and be are collinear (the boundary of plate C is straight). Choosing ab to be the perpendicular bisector of AB assumes that the ridge is spreading symmetrically and at right angles to its strike. This is usually the case. However, if the ridge does not spread symmetrically and/or at right angles to its strike, then ab must be drawn accordingly, and the stability conditions are different. Figure 2.16 gives the conditions for stability of the various types of triple junction and also gives examples of some of the triple junctions occurring around the earth at present. Many research papers discuss the stability or instability of the Mendocino and Queen Charlotte triple junctions that lie off western North America. These are the junctions (at the south and north ends, respectively) of the Juan de Fuca Plate with the Pacific and North American plates and so are subjects of particular interest to North Americans because they involve the San Andreas Fault in California and the Queen Charlotte Fault in British Columbia. Another triple junction in that part of the Pacific is the Galapagos triple junction, where the Pacific, Cocos and Nazca plates meet; it is an RRR junction and thus is stable. 2.6.2 Significance of Triple Junctions Work on the Mendocino triple junction, at which the Juan de Fuca, Pacific and North American plates meet at the northern end of the San Andreas Fault, shows why the stability of triple junctions is important for continental geology. The Mendocino triple junction is an FFT junction involving the San Andreas Fault, the Mendocino transform fault and the Cascade subduction zone. It is stable, as seen in Figure 2.16, provided that the San Andreas Fault and the Cascade subduction zone are collinear. It has, however, been suggested that the Cascade subduction zone is after all not exactly collinear with the San Andreas Fault and, thus, that the Mendocino triple junction is unstable. This instability would result in the northwards migration of the triple junction and the internal deformation of the continental crust of the western United States along preexisting zones of weakness. It would also explain many features such as the clockwise rotation of major blocks, such as the Sierra Nevada, and the regional extension and eastward stepping of the San Andreas transform. The details of the geometry of this triple junction are obviously of great importance to the regional evolution of the entire western United States. Much of the geological history of the area over approximately the past 30 million years may be related to the migration of the triple junction, and so a detailed knowledge of the plate motions is essential background for any explanation of the origin of Tertiary structures in this region. This subject is discussed further in Section 3.3.3. The motions of offshore plates can thus produce major structural changes even in the continent. Figure 2.18. Determination of stability for a triplejunction involving a ridge and two transform faults, FFR. (a) Geometry of the triple junction and relative velocities. (b) Relative velocity triangles (notation as for Fig. 2.17b). (c) Dashed lines drawn onto relative velocity triangle as for Figure 2.17c. This triple junction is stable if point C lies on the line ab or if ac and be are collinear. The first condition is satisfied if the triangle ABC is isosceles (i.e., the two transform faults are mirror images of each other). The second condition is satisfied if the boundary of plate C with plates A and B is straight. 24 2 Tectonics 0“ a Sphere 2.7 Absolute Plate Motions 2.7 Absolute Plate Motions , ‘ Gulfof Although most of the volcanism on the earth’s surface is associated with the - Rig“- ‘3‘“ boundaries of plates, along the midocean ridges and subduction zones, v ‘, 15““ ° 3.. some isolated volcanic island chains occur in the oceans. These chains of oceanic islands are unusual in several respects: They occur well away from the plate boundaries (i.e., they are intraplate volcanoes); the chemistry of the '1 53,532? erupted lavas is significantly different from both midocean ridge and subduction zone lavas; the active volcano‘may be at one end of the island chain, with the islands aging with distance from that active volcano; the island chains appear to be arcs of small circles. These features, taken together, are consistent with the volcanic islands having formed as the plate moved over what is colloquially called a hot spot, a place where melt rises from deep in the mantle. Figure 2.19 shows four volcanic island and seamount chains in the Pacific Ocean. There is an active volcano at the southeastern end of each of the island chains. The Emperor—Hawaiian seamount chain is the best defined and most studied. The ages of the seamounts increase steadily from Loihi, the youngest and presently active, a submarine volcano which lies off the southeast coast of the main island of Hawaii, northwest through the Hawaiian chain. There is a pronounced change in strike where the volcanic rocks reach 43 million years old (Ma). The northern end of the Emperor seamount chain near the Kamchatka peninsula of the USSR is 78 Ma old. The change in strike at 43 Ma can most simply be explained by a change in the direction of movement of the ,0. ram Pacific Plate over the hot spot at that time. The chemistry of oceanic island lavas is discussed in Section 7.8.3 and the structure of the islands themselves in Section 8.7. All the plate motions described so far in this chapter have been relative motions, that is, motions of the Pacific Plate relative to the North American Plate, the African Plate relative to the Eurasian Plate and so on. There is no ‘ ' ‘ ’ ’ ’ fixed point on the earth’s surface. Absolute plate motions are motions of the I I r I 1 plates relative to some imaginary fixed point. One way of determining r absolute motions is to suppose that the earth’s mantle moves much more \ \ \ slowly than the plates so that it can be regarded as nearly fixed. Such __ ,,.,\v\ \ \ \ \’ absolute motions can be calculated from the traces of the oceanic island chains or the traces of continental volcanism, which are assumed to have formed as the plate passed over a hot spot with its source in the mantle. The absolute motion of a plate, the Pacific, for example, can be calculated from the traces of the oceanic island and seamount chains on it. The absolute motions of all the other plates can then be calculated from their motion relative to the Pacific Plate. Repeating the procedure, using hot spot traces from other plates, gives some idea of the validity of the assumption that hot spots are fixed. Figure 2.20 shows a determination of the present absolute plate motions. They are not fixed; the mantle is moving. Nevertheless, a framework of motion can be developed. The Pacific and Indian plates are moving fast and the North American Plate more slowly, while the Eurasian and African plates are hardly moving at all. Figure 2.21 is a plot of the orientation of horizontal stress measured in the interior of the plates. The pattern of these intraplate stresses in the crust (stress is force per unit area) can be used to assess the forces acting on the \‘\‘\‘\\‘\f\‘\ °'\(\\\‘\‘\\f\ 75° l l 160' I20' 30' 40‘ an 25 Figure 2.19. Four volcanic island chains in the Pacific Ocean. The youngest active volcano is at the southeast end of each chain. (From Dalrymple et al. 1973.) Easter . . Island Figure 2.20. Absolute motions of the plates as determined from hot spot traces. (Courtesy M. L. Zoback, after Minster and Jordan 1978.) 80° 120' 160" 75” 160° 120° 80" L L 160” 120“ 80" Figure 2.21. World stress map. Lines Show orientation of the maximum horizontal compressive stress. (From Zoback et a]. 1989) Figure 2.22. Map of part of a flat planet. 26 2 Tectonics on a Sphere 40° 0° 40° 810° 120° 160° 40° 0° W 230° 120° 160° 75 plates. The direction of the stresses is correlated with the direction of the absolute plate motions (Fig. 2.20). This implies that the forces moving the plates around, which act along the edges of the plates (Sect. 7.10), are also partly responsible for the stresses in the lithosphere. PROBLEMS 1. All plates A—D shown in Figure 2.22 move rigidly without rotation. All ridges add at equal rates to the plates on either side of them; the rates given on the diagram are half the plate separation rates. The trench forming the boundary of plate A does not consume A. Use the plate velocities and directions to determine by graphical means or otherwise (a) the relative motion between plates B and D and (b) the relative motion between the triple junction .l and plate A. Where and when will J reach the trench? Draw a sketch of the geometry after this collision showing the relative velocity vectors and discuss the subsequent evolution. (From Cambridge University Natural Sciences Tripos 1B, 1982.) 2. Long ago and far away on a distant galaxy lived two tribes on a flat Problems 27 planet known as Emit-on (Fig. 2.23). The tribe of the dark forces lived on the islands in the cold parts of the planet near A, and a happy light- hearted people lived on the sunny beaches near B. Both required a constant supply of fresh andesite to survive and collected the shrimp- like animals that prospered near young magnetic-anomaly patterns, for their food. Using the map and your knowledge of any other galaxy, predict the future of these tribes. (From Cambridge University Natural Sciences Tripos 1B, 1980.) . Use the map in Fig. 2.2 to do the following: (a) Calculate the relative present-day motions at the tabulated lo- cations, using or calculating the appropriate poles from those given in Table 2.1. Latitude Longitude Location 54°N 169°E W. Aleutian Trench 52°N 169°W E. Aleutian Trench 38°N 122°W San Francisco—San Andreas Fault 26°N 110°W Gulf of California 13°S 112°W East Pacific Rise 36°S 110°W East Pacific Rise 59°S 150°W Antarctic—Pacific Ridge 45°S 169°E S. New Zealand 55°S 159°E Macquarrie Island 52°S 140°E Southeast Indian Ridge 28°S 74°E Southeast Indian Ridge 7°N . 60°E Carlsberg Ridge 22°N 38°E Red Sea 55°S 5°E Southwest Indian Ridge 52°S 5°E Mid—Atlantic Ridge 9°N 40°W Mid-Atlantic Ridge 35°N 35°W Mid-Atlantic Ridge 66°N 18°W Iceland 36°N 8°N Gorringe Bank 35"N 25°E E. Mediterranean 12°S 120°E Java Trench 35°N 72°E Himalayas 35°S 74°W S. Chile Trench 4°S 82°W N. Peru Trench Middle America Trench 20°N 106°W (b) Plot the azimuth and magnitude of these relative motions on the map. (0) Plot the pole positions. Note how the relative motions change along plate boundaries as distance from the pole changes. (d) Discuss the nature of the plate boundary between the Indian/ Australian and Pacific plates. AMNESIA PLATE Figure 2.23. Map of part of Emit-on. ...
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