Stacey F.D., Davis P.M. Physics of the Earth

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explanation of global geological processes, but

many of the ideas have long histories. The

concept of mantle convection can be traced

back to the early nineteenth century when it

was supposed that the deep interior is largely

fluid. Even with the mantle recognized to be

solid, sea floor spreading and subduction were

advocated by A. Holmes and a figure showing

these processes in a form very similar to our

present understanding appeared in the 1944

edition of his textbook Principles of Physical

Geology and is reproduced in Cox (1973, p. 20).

These ideas were brought into focus by echo-

sounding across the Pacific, especially by

H. Hess, a submarine commander during World

War II, who subsequently used his observa-

tions to link continental drift with sea floor

spreading. Plate tectonics was generally accep-

ted only when the structure of the ocean floor

had become clear.

Although comprehension of global geology

was very incomplete before it incorporated the

ocean floors, it is also true that their restricted age

range would present a very limited view of

Earth history without evidence from the conti-

nents. The permanence of the continents is due

to their buoyancy, which prevents subduction.

The continental crust has an average thickness

z ¼37 km and an average density contrast rela-

tive to the underlying mantle D 500 kg m

3

giving a mass deficiency (relative to an equal vol-

ume of mantle material) zD 1.85 10

kg m

This is greater than the negative buoyancy

of thermally contracted lithosphere, which has

shrunk by Dz 2.1 km; taking the mantle den-

sity to be  ¼3350 kg m

3

, the mass excess is

Dz ¼7.0 10

kg m

. The negative buoyancy of

cooled lithosphere fails by a factor exceeding

two to overcome the positive buoyancy of con-

tinental crust. Only oceanic sections of plates

subduct and when they bring continental blocks

together, collision zones appear, most impres-

sively the Himalaya. Even for oceanic plates

there is some crustal buoyancy, but it is not

clear that it seriously inhibits subduction of

young oceanic lithosphere. At depth, basalt con-

verts to eclogite and loses its buoyancy, so that

the resistance to subduction is probably a shal-

low effect.

12.2 Wadati–Benioff zones

and subduction

Deep earthquakes were first clearly identified in

1928 from Japanese records studied by K. Wadati.

They are now recognized to occur down to

700 km along the zones of strong subduction,

shown in Fig. 12.2, and to mark inclined planes

extending into the mantle from the zones

of convergence of the lithospheric plates. Deep

ocean trenches mark the lines where the sub-

ducting plates turn down. The contribution

of H. Benioff to the identification of planes of

deep seismicity is acknowledged by referring to

them as Wadati–Benioff zones. By convention

earthquakes are classified into three groups,

with shallow (0 to 60 km), intermediate (60 to

300 km) and deep (>300 km) foci, although it is

sometimes convenient simply to refer to all

earthquakes with foci below 60 km as deep.

Shallow earthquakes are the most numerous.

The largest earthquakes occur at shallow depths

in subduction zones.

The detailed geometries of the Wadati–Benioff

zones are variable and depend on factors such as

plate speed, age of the subducting lithosphere

and its geology, especially the distribution of oce-

anic and continental crust. The deep seismicity of

Japan has been studied in particularly close detail

and gives valuable insight on the subduction pro-

cess. Figure 12.4 shows the distribution of deep

earthquakes in this area, where there are inter-

sections of several subduction arcs. Figure 12.5

shows an east–west cross-section of a subset of

the data in Fig 12.4, between latitudes 398Nand

408N. In this case, precise location of foci by a

close network of seismic stations has delineated

a pair of parallel planes. Focal mechanisms for

earthquakes show that the upper plane is in

down-dip compression and the lower one is in

down-dip extension. These observations are natu-

rally explained by identifying the upper plane

as the upper boundary of the subducting litho-

spheric slab, and the lower plane as the middle of

the slab, which fails in tension due to the negative

buoyancy that is carrying the plate down. In other

subduction zones, down-dip extension dominates

12.2 WADATI–BENIOFF ZONES AND SUBDUCTION 167

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FIGURE 12.4 The pattern of earthquake foci down the Wadati–Benioff zones of Japan and neighbouring arcs.

Reproduced, by permission, from a drawing by Sasatani (1989) of an original plot by T. Utsu. Several inclined planes

of foci intersect in this area, indicating complicated plate geometry.

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at intermediate depths, but the deepest shocks

give down-dip compression, indicating increasing

resistance by mantle viscosity.

An intriguing feature of subduction zones is

the wide range of angles of subduction. At one

extreme it appears to be almost horizontal for

some distance, for example under central Peru

(Fig. 12.6). Steep subduction is slightly more com-

mon, with an average angle of about 508. There

have been several attempts to explain this varia-

bility, and the fact that the subducting slabs are

not vertical, although they are driven by gravity.

None of the explanations is yet convincing.

There is considerable variability in the seis-

mic activity in subducting material, due to dif-

ferences in local conditions that appear to be

reflected in volcanic activity. Deep earthquakes

are much rarer than shallow ones everywhere,

and in some places they do not occur at all. There

is a similar variability in the volcanic activity

along subducting arcs. As indicated in the car-

toon of tectonic processes in Fig. 12.3, subducted

material generates andesitic lava (named after

the Andes Mountains in South America), produc-

ing lines of volcanos which appear where the

slabs have penetrated to about 100 km depth.

But along some sections of the subduction

zones volcanos are completely absent, including

central Peru (Fig. 12.6). Either the chemistry or

the mode of subduction is unsuitable for magma

generation in these areas. It may be that one

important factor is the availability of water

in subducted sediments. The section of the

Nazca plate that is subducting under central

FIGURE 12.5 Cross-section of the Wadati–Benioff zone under northern Honshu, Japan, showing two parallel planes

of earthquake foci. VF indicates the volcanic front, at the centre of the land area. Reproduced, by permission, from

Hasegawa (1989). For a colour plot with greater detail see Hasegawa et al. (1991).

12.2 WADATI–BENIOFF ZONES AND SUBDUCTION 169

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Peru includes an atypical crustal component,

that may be a continental fragment, the Nazca

ridge. Being more elevated than most of the

ocean floor, it has accumulated less wet sedi-

ment. Another possibility is that, if subduction

is slow or delayed, as in the central Peru case, the

volcanic heat is too diffuse for magma genera-

tion and slower, broader scale upwelling occurs,

with granitic intrusions.

The incorporation of subducted material in

the lava produced by subduction zone volcanos

was proved beyond all doubt by the discovery of

the isotope

Be in andesitic lavas (see especially

Morris et al., 1990). This is a radioactive isotope

produced in the atmosphere by cosmic ray bom-

bardment, washed into the sea and deposited in

marine sediments. Its half-life, 1.5 10

years

(Table H.2, Appendix H), is short enough to

ensure that it could not have a long residence

time in the Earth. The lava incorporates marine

sediment that cannot be more than 10

years old.

Subduction, to 100 km at least, must proceed at

the full speed of the surface plates and, in some

areas, all the sediment must be subducted.

Morris et al. (1990) pointed out also that the

abundance of boron in andesitic lavas requires

the incorporation of sea water as an important

component. There is no other plausible source of

boron. Thus we arrive at the conclusion that ande-

sitic volcanism is a consequence of the subduc-

tion of sea water. Melting of dry material would

not occur and it is the availability of water that

leads to magma generation. Since the Earth’s free

ocean water is unique in the Solar System, it

follows that its acid volcanism is also unique,

at least at the present time. As far as we know,

all lavas on the other terrestrial planets (and the

Moon) are basaltic. In Sections 1.1 and 2.9 it is

pointed out that acid rocks are the essential ingre-

dients of continents, which remain as rafts on the

surface as the mantle convects. The subduction of

sea water is responsible for the development of

continental crust and therefore for the bimodal

surface elevation shown in Fig. 9.4.

The ultimate fate of subducted material has

been a subject of conjecture. Since earthquakes

do not occur below 700 km the evidence for the

penetration of slabs beyond that is less direct.

This is approximately the depth of a major phase

transition, accepted as the boundary between

the upper and lower mantles. Viscosity increases

with depth and the lower mantle is almost cer-

tainly more viscous than the upper mantle, but

the thermal argument in Section 22.4 requires

FIGURE 12.6 A cross section of the Wadati–Benioff zone under central Peru, showing evidence of 300 km of

‘horizontal subduction’. Solid circles are earthquake foci plotted by M. Barazangi and B. Isacks for a 100 km wide

section. Schneider and Sacks (1992) added the open circles, representing foci determined by a local network for a

more restricted area. Arrows indicate extensional stress deduced from focal mechanisms.

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convection to be a whole-mantle process. Much

of the Earth’s heat originates in the lower mantle

so the coolness carried downwards by subducted

slabs must be distributed through the lower man-

tle. The problem of the mechanism is addressed

in Section 12.6. Although the 660 km transition

presents an obstacle to convection, in the absence

of a strong mid-mantle thermal boundary whole

mantle convection must prevail, perhaps with a

delay or complication at 660 km, and this is empha-

sized by a consideration of lower mantle cooling

(Section 12.6). In the upper mantle there can be

little doubt that subducting slabs are continuous;

observed breaks in seismic activity must be inter-

preted in terms of material properties and not dis-

continuities in the slabs themselves (Okal, 2001).

12.3 Spreading centres and

magnetic lineations

The buoyancy of the continents is indicated by

their 5 km elevation above the ocean floors

(Fig. 9.4) and, as explained in Section 12.2, they

resist subduction, so that where converging

plates bring continents into collision, as at the

Himalayan boundary between India and the main

Asian mass, they form a crumpled pile of abnor-

mally thick continental crust. Continents break up

and reform in different ways, but they do not dis-

appear. They gradually increase in total volume as

acid volcanism adds to them, with the loss of

minor fragments too small to escape subduction

and sediments washed into the sea and subducted

from there. Continents just grow older and they

havecoresofages3.510

years or more, but

there is a continuous recycling via erosion and

sedimentation, as discussed in Section 5.3.

The ocean floors are, by comparison, youth-

ful. Nowhere is there ocean floor of age exceed-

ing about 2 10

years and the average age

at subduction is about 9 10

years. Since the

ocean floors occupy 60% of the Earth’s surface

(3 10

), their limited age-range is a mea-

sure of the rate at which oceanic crust is both

forming and disappearing: 3 10

/9 10

years 3.4 km

/year. The ocean floors are a ther-

mal boundary layer, transferring to the ocean

the heat that is convectively transported from

the deep mantle.

The ocean ridges, which mark the crustal

spreading centres, are less active seismically

than the subduction zones, but still show clearly

in Fig. 12.1. However, they have no deep earth-

quakes and many of the shallow ones occur on

transform faults, offsets between sections of

ridge, rather than on the ridge axes where the

spreading occurs (Fig. 12.7). In Section 13.2 it is

argued that the spreading is a more-or-less pas-

sive consequence of subduction-driven conven-

tion and that mantle viscosity estimates can be

rationalized only by accepting that plate motion

is accommodated by shear in a relatively thin

low-viscosity layer (the asthenosphere) and not

by bulk mantle motions. Thus, most of the fresh

crustal material appearing at the spreading

centres probably flows from the adjacent asthe-

nosphere. It is unlikely to be derived from

more than modest depths, except for a possible

asthenospheric connection between spreading

centres and the deep mantle plumes that bring

up core heat. Beneath spreading centres there is,

therefore, nothing comparable to the Wadati–

Benioff zones. Moreover, since there is no large,

cool mass at a spreading centre, there is rather

little material in which earthquakes are readily

generated. This means that we do not have

such a clear or detailed picture of the geometry

of spreading as we do of subduction.

FIGURE 12.7 Transform faults. These are planes of

horizontal shear between sections of a spreading centre,

marked by double lines. The ocean ridges, where spreading

occurs, are broken up by transform faults, which leave

their signatures on the ocean floors as seismically

inactive ‘fracture zones’, indicated by broken lines.

12.3 SPREADING CENTRES AND MAGNETIC LINEATIONS 171

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Figure 12.8 shows the increase with distance

from the centre of the mid-Atlantic ridge of the

age of the ocean floor in the South Atlantic.

Originally plotted by Maxwell et al. (1970), these

data are probably still the most convincing evi-

dence that the mid-Atlantic ridge is a spreading

centre. The data points are mostly to the west

of the ridge, but span it and demonstrate that

the spreading is symmetrical, at 1.9 cm/year

each way. More comprehensive evidence of the

spreading speeds along all of the active ridges,

shown in Fig. 12.2, has been obtained by compar-

ing the spacing of the sequences of linear mag-

netic anomalies that they have produced. The

ridge axes are generally marked by rifts, along

which fresh lava appears, as the sides of rifts

slowly move apart, with a ‘tape recording’ of

the field polarity (Fig. 12.9). The linear magnetic

anomalies were first recognized in the Pacific by

A. D. Raff and R. G. Mason and their interpreta-

tion was given by Vine and Matthews (1963).

The symmetrical pattern of anomalies across a

part of the mid-Atlantic ridge is reproduced in

Fig. 12.10.

The tectonic pattern of ridges and trenches is

not fixed. They move and old ones are extin-

guished as new ones form. Perhaps the most

obvious new ridge runs down the Red Sea, and

a new subduction zone appears to be forming in

the Indian Ocean, separating the Australian and

Indian plates (Fig. 12.2). Another feature indica-

tive of the transient nature of the tectonic pat-

tern is the formation of back-arc basins. Volcanic

800400

1200

1600

Distance from rid

e axis (km)

Age (10

years)

FIGURE 12.8 Paleontologically

determined ages of the lowest ocean

floor sediments, immediately above

the basalt basement, which they

date, as a function of distance from

the mid-Atlantic ridge at 30 8S.

Replotted from data by Maxwell

et al. (1970).

FIGURE 12.9 Alternating normal and reversely

magnetized basalt in the ocean floor adjacent to a

spreading centre. Rock magnetized in a direction opposite

to the present field is shown shaded. The sea floor cools as

it moves away from the ridge axis and the boundary

marked a is the isotherm at the blocking temperature of

the magnetic minerals, at which remanent magnetism is

established. Basalt below this level is too hot to have

acquired remanence. Boundaries between the normal and

reversely magnetized rock mark the blocking temperature

isotherms at times when the geomagnetic field reversed.

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island arcs arise where subducted slabs have

penetrated to about 100 km depth and are sepa-

rated from the corresponding trenches by zones

referred to as fore-arc basins. As the trenches roll

back, tensions develop in the over riding plates

on the opposite sides of the arcs causing spread-

ing and the formation of back-arc basins. They

are spreading centres that may initiate new

ocean ridges and develop into major basins.

The Atlantic Ocean is regarded as fully developed

back-arc basin. Sea floor topography (Fig. 12.11)

shows that in the case of the Mariana back-arc

basin a ridge formed right at the arc and split

it into two, leaving two fossil arcs. Another appa-

rent example of the same phenomenon is the

separation of Baja California from mainland

North America.

The ocean rises are elevated because they are

hot. As the fresh lithosphere moves away from

the ridges it cools and so contracts thermally.

Isostatic balance is maintained (Section 20.2),

with constant mass in any vertical column, so

that the ocean floor deepens systematically

away from the ridges (Fig. 20.2). The depth data

give valuable evidence of the cooling, because

reliable measurements of heat flow are notori-

ously difficult to make. The principal disturbance

is sea water circulation in the crust, especially

near the ridge axes. The total contraction between

formation of fresh lithosphere at a ridge and

subduction is typically 2.1 km. This provides the

negative buoyancy that drives subduction and is

related to the convective heat transport by the

ratio of expansion coefficient to the heat capacity

per unit volume, as in Eq. (20.8). Thus, study of the

ocean floors has provided the observations that

are the basis of the quantitative theory of mantle

convection in Chapter 22.

12.4 Plate motions and hot

spot traces

The rates of separation of pairs of plates at

spreading centres are estimated by the spacing

of magnetic anomalies adjacent to the ridges.

Directions of motion are not everywhere pre-

cisely perpendicular to the ridge axes but are

revealed by the orientations of transform faults

which separate sections of ridge (Fig. 12.7). Thus,

the relative motions of pairs of plates that

have common boundaries at spreading centres

are reliably determined. Rates of subduction

are not as directly observable, although the mag-

nitudes and repetition rates of earthquake

displacements appear to give a reasonable indi-

cation along at least some zones of rapid conver-

gence (Section 14.7). Further constraint is

provided by the condition that spreading and

convergence must match along any circular

path around the Earth. DeMets et al. (1990, 1994)

used all the information of this kind to produce a

coherent set of plate motions, averaged over a few

FIGURE 12.10 Linear magnetic anomalies flanking the

mid-Atlantic ridge south-west of Iceland, where it is

known as the Reykjanes ridge. This shows the surface

variation in total field strength, with positive anomalies

black. Lighter shading over Iceland shows the area of

Quaternary volcanism and dots are earthquake epicentres.

Reproduced, by permission, from Heirtzler et al. (1966).

12.4 PLATE MOTIONS AND HOT SPOT TRACES 173

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million years, and Kreemer et al. (2003) used an

extensive set of data from GPS observations to

present a similar set of present day plate motions.

Differences between the two solutions are slight

enough to be attributable to data uncertainties,

demonstrating that plate motion is steady on the

time scale of a few million years.

The motion of a rigid plate across the Earth’s

surface is quantitatively represented as a rotation

about an axis through the Earth’s centre. The

points where the axis cuts the surface are the

poles of rotation. The poles are generally remote

from the plates, but this is not a necessary con-

dition as rotation of a plate about an axis through

itself is conceivable. It is important to note that

this gives a complete and general representation

of the motion. It is valid for the well-determined

relative motions between plates, as well as their

less-certain absolute motions. The sign conven-

tion established in the pioneering work on

rotational mechanics by L. Euler is followed.

The pole of rotation is the one about which a

plate is moving anticlockwise (either absolutely

or relative to another plate) when viewed from

above the pole of the motion. The Euler vector is

a line from the centre of the Earth to this pole and

the magnitude of the vector is the angular speed,

!, of the plate about this axis. Euler rotation

vectors add and subtract by the normal vector

rules, so that if we write the vector for motion

of plate A relative to plate B as

,then

: (12:1)

The local speed of the motion, or relative

motion, at a point at angular distance  from

the pole of the motion is

v ¼ !R sin ; (12:2)

where R is the Earth’s radius. If the coordinates

(latitude, longitude) of the rotational pole (p)

FIGURE 12.11 Sea floor topography in the area of the Mariana island arc. This shows two fossil remnants of an arc

which was split by a ridge and a new, active arc parallel to them. Courtesy of David Sandwell.

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and the point in question (x ) are (

) and

(

) then

cos  ¼ cos 

cos 

cosðl

 l

þ sin 

sin 

: (12:3)

A comprehensive treatment of the geometry of

plate motions and how to calculate them is given

by Cox and Hart (1986).

Kreemer et al. (2003) converted the numerous

GPS observations of relative motions between

plates to tables of the motions of the individual

plates relative to the Pacific plate and relative to

a ‘no-net-rotation frame’, that is, assuming the

surface area average to be stationary. They gave

some emphasis to the fact that plate boundaries

are not sharp but that many of them involve

deformation spread over hundreds of kilometers,

especially at convergent margins. Nevertheless,

most of the surface can be considered divided

into plates that are effectively rigid and between

which relative motion is unambiguous. An inter-

esting result from this analysis is that the global

rms plate velocity is 3.8 cm/year in the no-net-

rotation frame. Comprehensive details of plate

boundaries and relative motions are presented

by Bird (2003).

If the viscous interaction between the plates

and the underlying mantle were the same every-

where then the no-net-rotation frame would coin-

cide with the average mantle frame. However,

this is not quite true. The asthenosphere appears

to be somewhat cooler (or thinner) and more

viscous under continents than under oceans and

continents tend to ‘drag their feet’. The zero net

torque condition is not the same as no net rota-

tion, although they may not be very different.

There is also a possibility that GPS measurements

over a decade or so may not average over suffi-

cient time the relative motions across plate boun-

daries where displacements occur erratically with

major earthquakes at intervals of tens or hun-

dreds of years. Although these are minor quib-

bles, we consider motion of the plates relative to

the underlying mantle to be more fundamental

than motion relative to a plate average. In

Table 12.1 the geologically derived plate motions

from the NUVEL-1 model of DeMets et al. (1990)

are referred to the position of the Hawaii volcanos

as a nominal fixed marker.

The motion of the India plate relative to the

Reunion Island hot spot can be used as a check

on the results in Table 12.1. The values in the

table for the India plate give its motion relative

to the Hawaii hot spot as 4.6 cm/year at 698 east

of north. This would also be the motion relative

to the Reunion Island hot spot if hot spots were

fixed with respect to one another. Reunion

Island is on the Africa plate, but the hot spot

that produced it began 65 million years ago on

the India plate as a massive outpouring of flood

basalts in what is now the Deccan area of central

India. For about 20 million years the India plate

moved northwards across it, leaving the Maldive

Islands as the hot spot trace, but there was a

change of direction about 40 million years ago

when the trace turned north-east. The mid-

Indian ridge spreading centre then intervened,

so that most of the subsequent trace appears as a

somewhat irregular ridge on the Africa plate,

extending to the Seychelles. But this does not

interfere with our estimate of the motion of

Table 12.1 Parameters of the Euler vectors

for plate motions relative to the Hawaii hot

spot, obtained from motions relative to the

Pacific plate by DeMets et al. (1990),

assuming motion of the Pacific plate given

as the first entry. The plates are identified

in Fig. 12.2

Plate

Pole

latitude

(N)

Pole

longitude

l(E)

Angular

speed ! (10

6

deg/year)

Pacific 55 144 0.75

Africa 36 132 0.37

Antarctica 31 156 0.39

Arabia 68 26 0.42

Australia 46 52 0.50

Caribbean 12 138 0.37

Cocos 22 124 1.72

Eurasia 25 150 0.40

India 69 14 0.42

Nazca 41 122 0.86

N. America 4 134 0.35

S. America 11 158 0.35

Juan de Fuca 35 85 0.54

Philippine 46 55 0.85

12.4 PLATE MOTIONS AND HOT SPOT TRACES 175

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the India plate relative to the hot spot since the

direction change, which is seen to be close to 508

east of north at a speed of about 6 cm/year. Thus,

the observed motion of the India plate relative to

the Reunion Island hot spot differs from its

motion relative to the Hawaii hot spot, but

the difference is small. Molnar and Atwater

(1973) reported a more extensive check on hot

spot relative motions, concluding that they had

speeds in the range 0.8 to 2.0 cm/year.

The calculation of plate motions relative to

the Hawaii hot spot assumes that we know the

motion of the Pacific plate. This is obtained from

the dated sequence of islands, which give a speed

of 8.3 cm/year past the hot spot. For this purpose

the island trace, shown in Fig. 12.12, is assumed

to follow a great circle, putting the pole of the

motion 908 away from the hot spot, at (558 S

148 E), and giving an angular speed of 0.758/

year (the first entry in Table 12.1). An interesting

feature of the island chain is the change in direc-

tion in the mid-Pacific, apparent in Fig. 12.11.

The ages increase linearly from zero at Hawaii

Island (198 N 1558 W) to 43 million years at (328 N

1728 E). At that point there is an abrupt change in

the direction of the chain, which continues

north as the Emperor Seamounts. The Pacific

plate is a major one and a dramatic change in

its motion could not have occurred without a

reorganization of its boundaries and perhaps

other boundaries. Norton (1995) argued that evi-

dence for such reorganization is lacking and

attributed the direction change to hot spot

motion. This would be incompatible with con-

ventional ideas about plumes, and we have men-

tioned evidence for a change in the motion of the

FIGURE 12.12 Trace of the Hawaii hot spot along the chain of the Hawaii Islands and Emperor Seamounts. This is a

computer plot of ocean floor topography of the north-central Pacific, with the Japan, Kurile and Aleutian trenches

marking the subduction zones at the top of the figure. Courtesy of David Sandwell.

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