Fowler A. Mathematical Geoscience

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590 9 Magma Transport

positional Rayleigh number

Rs =

βρ

gc d

ηκ

, (9.181)

where c is the prescribed compositional excess. This is the conventional deﬁni-

tion, although one might be tempted to replace κ in the denominator with D,the

compositional diffusivity.

With these deﬁnitions, positive Ra is destabilising, while positive Rs is stabil-

ising. In particular, when Ra > 0 and Rs < 0 are numerically large enough, then

convection will occur in the usual way. There are two interesting variants which

can occur even when the ﬂuid is statically stable (i.e., its density increases with

depth, Ra +Rs > 0). The ﬁrst occurs for Rs < 0, Ra < 0: temperature is stabilis-

ing but composition is destabilising. In this case the static state may be unstable to

very narrow convection cells, known as ﬁngers (often, in practice, salt ﬁngers). This

style of convection is readily demonstrated in the laboratory, and has been observed

to occur in the oceans.

In the opposite quadrant, a destabilising temperature ﬁeld can render a stable

compositional ﬁeld oscillatorily unstable, but this linear stability result is not of-

ten seen in practice, partly because the boundary conditions relevant to the result

are difﬁcult to obtain, and partly because in nature, double-diffusive convection is

wildly nonlinear, and leads to other dramatic phenomena.

Perhaps the principal behavioural feature of double-diffusive convection is the

readiness with which the ﬂuid forms separately convecting layers. Two examples

will illustrate this predilection. Suppose a stable compositional gradient has been

set up in a ﬂuid, and it is then suddenly heated (strongly) from below. What is found

is that a layer of ﬂuid at the base begins to convect turbulently, but not throughout the

ﬂuid depth. In fact, the convecting ﬂuid homogenises the density, but the convecting

layer can only extend to its level of neutral buoyancy: above this, the ﬂuid is static.

Nevertheless, there are turbulent thermal and compositional ﬂuxes across the in-

terfacial boundary layer at the top of the convecting layer, and the thermal ﬂux gen-

erates a growing thermal boundary layer which eventually becomes unstable, caus-

ing a second convecting layer to form. In this manner, a series of convecting layers

is set up, due to the fact that the thermally unstable boundary layers win because

the diffusivities satisfy κ>D(so there is no compensating buoyancy generated by

the compositional ﬂuxes). In the laboratory, these layers appear long-lived, being

roughly associated with the thermal diffusive time d

/κ of the chamber. On an even

longer time scale, the convective layers merge from the base up, and the eventual

state will be one of well-mixed thermal convection, with the compositional gradi-

ents eradicated. In practice, the long transient is more interesting than the eventual

steady state.

It is tempting to suppose that the large hexagonal basalt columns seen, for example, at the Giant’s

Causeway in Northern Ireland might represent a similar phenomenon, but this appears not to be the

case; such columnar basalts are thought to arise through an instability associated with contraction-

induced fracturing.

9.6 Crystallisation in Magma Chambers 591

The basic motto in this and other double-diffusive settings is simply that light

ﬂuid rises where it can. Another instance of layering exempliﬁes this. Again we

start with a stably compositionally stratiﬁed ﬂuid in a chamber whose walls slope

inwards at the base. If the walls are cooled, a convection current (essentially like a

katabatic wind) is generated which ﬂows down the walls. Again, the ﬂow stops when

it reaches its level of neutral buoyancy, and then turns sideways into the interior ﬂuid

of the chamber. In this way, a series of (transient) horizontal convective layers are

set up.

Convection in Magma Chambers We can now paint a plausible sequence of

events in a cooling magma chamber, bearing in mind that many other things are also

dynamically feasible. A typical sort of shape for a magma chamber may be like a

tadpole, or a balloon, with the blunt upper surface formed by doming of the overly-

ing country rock, and the lower tail being connected to the umbilical feeder dyke.

In such a chamber, the emplacement of hot magma is followed ﬁrst by chilling and

quenching at the margin. The cooling of the magma at the walls leads to thermal

convection where cold rafts of magma detach from the sides and roof of the cham-

ber and descend to the ﬂoor. If we suppose the feeder dyke is sealed, then there is no

warming from below, and the cool magma will pond at the ﬂoor, forming a stably

stratiﬁed layer, which thickens with time. The same thermal stratiﬁcation is a com-

mon (and inefﬁcient) feature of heated rooms, for example by use of a fan heater in

a bathroom (although there, it is caused by ponding of hot air at the ceiling).

At a rate controlled by heat conduction (since the Stefan number is O(1)), crys-

tals grow from the walls, ﬂoor and roof. In general (but not always), we may suppose

that the crystals are denser than the melt, and also that light ﬂuid is released on crys-

tallisation. Because we may expect the crystals to grow in a slurry, it is then natural

to expect sloughing off of mats of crystals from the walls and the roof, which then

rain down to the ﬂoor, forming a crystal pile at the ﬂoor. Compositional convec-

tion from this pile will occur if light ﬂuid is released, causing ﬁnger-like plumes

in the overlying ﬂuid. This compositional convection will then lead to a compo-

sitional stratiﬁcation of the chamber. Evidence for such zonation can be found in

relict magma chambers which are now exposed at the Earth’s surface, and is in-

directly evidenced by the (inversely) stratiﬁed deposits which are formed in some

volcanic eruptions.

9.6.4 Layered Igneous Intrusions

An intriguing phenomenon in some fossil magma chambers is the presence of

widespread layering in the rocks, at a scale from centimetres to metres. This lay-

ering can be seen through bands of differently-coloured rocks (Fig. 9.20), and there

can also be layering in crystal size. The type example, for historical reasons, is the

Skaergaard intrusion of East Greenland, one of a swarm of igneous intrusions asso-

ciated with Tertiary volcanism and the opening of the Atlantic Ocean. It was here

592 9 Magma Transport

Fig. 9.20 Graded layering in the Skaergaard intrusion. Photo courtesy of Kurt Hollocher

that Wager, Brown and Deer undertook their voluminous studies from the 1930s

onwards which mapped the intrusion, and they also provided a tentative explanation

for the observations.

It must be said (and any petrologist will do so) that the Skaergaard exhibits ev-

idence of a bewildering variety of different dynamic features, and to attempt an

explanation of all of them would be somewhat like endeavouring to explain every

last eddy in a turbulent ﬂow. This we will not (and cannot) do.

Instead we focus on some features of the large scale behaviour of the magma

chamber. The chamber is divided into different zones. There is the marginal border

series, associated with initial quenching and subsequent crystallisation at the sides.

The main part of the chamber is divided into a number of different horizontal zones

(lower zone a: LZa; lower zone b: LZb; etc.) which are distinguished by the min-

erals present. The same sequence of minerallisation occurs upwards as downwards,

suggesting that fractional crystallisation proceeded both upwards from the ﬂoor and

downwards from the roof.

The sequence of minerals present as we rise from the ﬂoor is ﬁrstly olivine and

plagioclase; then augite is added; then magnetite; then pigeonite replaces olivine;

and so on. These zones represent the natural process of fractional crystallisation as

the residual melt alters its composition. Within the zones, we ﬁnd modally graded

layers. For example, a layer of LZa would have olivine at the base grading into

plagioclase at the top. Sometimes these layers alternate continuously, sometimes

they are intercalated by uniform gabbro layers. In thickness, they range from a scale

of centimetres to metres.

9.6 Crystallisation in Magma Chambers 593

The other very noticeable feature about the Skaergaard is the presence of huge

blocks of anorthosite (i.e., plagioclase) within the chamber. These are thought to

represent caved in (stoped) fragments of the crystallising roof of the chamber (now

long eroded) which collapsed and fell to the crystal pile growing on the ﬂoor. These

blocks show evidence of impact on the growing layered series. Layers have been

bent, cut and warped by the blocks, and have then resumed growth about them.

Armed with the discussion of double diffusion in Sect. 9.6.3, there is an obvious

possible explanation for the layering which is observed. Since there is inevitably

convection, and since magmas are multi-component mixtures, double-diffusive con-

vection must occur, and the ubiquity of layering in such convective systems then

suggests itself as a cause of the layering in the rocks.

However, this idea instantly runs into problems. The situations where convective

layers occur are those where there is pre-existing compositional stratiﬁcation, and

the layers form by a superimposed thermal convection. This is the opposite to what

we expect in a magma chamber, where we suppose ponding will produce a thermal

stratiﬁcation, which is then subjected to compositional convection. Moreover, the

layering in the Skaergaard is compositionally oscillatory. One sees, for example,

olivine grading into plagioclase, then back to olivine, and so on. This is not what

convective layering exhibits.

The original explanation favoured by Wager and Brown in their pioneering work

was that crystal-rich turbidity currents would sweep down from the walls of the

chamber, and then gravitational settling would separate the heavier olivine from the

lighter plagioclase crystals. This old idea may seem implausible, but it is not with-

out merit. While it seems unlikely that olivine and plagioclase could separate in a

fairly crystal-rich slurry, it is by now well-known that differently sized particles will

spontaneously separate in a granular ﬂow, so it is at least plausible that separation

could occur this way. Nor is the regular occurrence of crystal avalanches of this type

so unlikely. As a crystal slurry grows and thickens, it may become gravitationally

unstable, and initiate an avalanche. The resultant turbidity current can then sweep

up the crystals in its path, cleaning the wall and depositing its load at the ﬂoor. Es-

sentially the same thing happens in snow avalanches, and in submarine turbidity

currents, which carve out submarine canyons in regular avalanche-induced runout

events.

One of the apparent difﬁculties with this scenario is the question of how the

growing layer can reach ﬁnite size before failing, since we envisage growth of a

slurry with little intergranular contact. The apparent answer to this problem lies

in the fact that silicate melts are polymerised (by chains of silica molecules), and

consequently they have a yield stress, which increases with silica content. Typical

sorts of values for yield stress are in the range 10

–10

Pa, and these values increase

with increasing crystal content. A slurry of crystals a metre thick having an excess

density of, say, 500 kg m

−3

over the bulk liquid, will exert a differential stress of

0.5 ×10

Pa. So it is entirely possible that a stationary slurry will grow and then

detach at some critical thickness, and that this will happen periodically.

The yield stress of silicate magmas can also explain what has been called the

plagioclase ﬂotation problem. At least in some magmas, precipitated plagioclase

594 9 Magma Transport

crystals are lighter than their parent magma, and should thus ﬂoat. It is then difﬁcult

to understand the occurrence of plagioclase crystals in the lower zone (and olivine

crystals in the upper zone). But if the crystals grow in a slurry, they should remain

immobile within it if ρg d

<τ

, where ρ is the density difference between crys-

tal and melt, d

is the grain size, and τ

is the yield stress. For a millimetre sized

crystal, the buoyant stress is only 10 Pa, even if the density excess is 10

kg m

−3

This seems a plausible way of locking crystals in a slurry, although it will also have

the effect of preventing compositional convection within the slurry.

An altogether simpler mechanism to obtain successive layers is to ascribe the

cause to periodic inputs of fresh magma to the base of the chamber. This is probably

not feasible for the Skaergaard, but it is a likely thing to occur, since the formation

of igneous provinces and volcanic eruptions is essentially a periodic phenomenon

(input of magma lowers source pressure, which lowers ﬂow rate and causes even-

tual blockage of the vent, which is then subsequently re-opened by the build-up of

pressure at the source).

One possible scenario is the following. Suppose a two component magma con-

taining liquids A and B is injected into a chamber of more evolved magma. We

suppose that B is heavier (more basic) and crystallises out ﬁrst. When the magma is

injected, it is hotter than the evolved magma, but ponds at the bottom because of its

greater content of B. Being hotter, it cools by convective heat transfer to the upper

layer, and as it does so, crystals of B form and will eventually sink to the ﬂoor (they

may be kept in suspension for a time by the turbulent convection). The residual liq-

uid becomes progressively enriched in A, and when its density reaches that of the

liquid above, rollover occurs, and the magmas mix. If the composition reaches the

eutectic point, then a different rock precipitates, containing also B. In this way, we

can generate a layer of A followed by a layer of A–B. Subsequent injection of B-

rich magma will lead to the same sequence of events, and the build-up of a periodic

sequence of layers.

It is thought that this process can explain the alternating layered rocks on the

Isle of Rum in the Hebrides.

The Rum intrusion consists of alternating layers of

peridotite (essentially olivine) and allivalite (olivine-plagioclase). So in our simple

model, A would be plagioclase, and B would be olivine.

Another suggested mechanism to explain the Skaergaard layering is that of oscil-

latory nucleation. In essence, the idea is indicated in Fig. 9.21, which shows a phase

diagram (more or less the same as Fig. 9.5) of a binary mixture of two components

A and B which form a eutectic (at E in the ﬁgure). Nucleation, and subsequent

crystallisation, of either phase requires a ﬁnite undercooling, and so the two dashed

curves below the equilibrium liquidus curves represent the meta-liquidus curves

where nucleation and thence growth is initiated. Note that these, and the liquidus

curves themselves, continue past the eutectic point. If the parental liquid tempera-

ture and composition starts out to the left of E, then cooling will cause nucleation

The former spelling was Rhum; apparently the ‘h’ was added in the 1900s by the owner George

Bullough, who disliked the alcoholic connotation. ‘Rum’ is an anglicisation of the Scots Gaelic

‘Rùm’, of uncertain meaning.

9.6 Crystallisation in Magma Chambers 595

Fig. 9.21 Maaløe’s

mechanism for rhythmic

layering. The liquid

composition oscillates as

indicated by the arrowed line,

alternately nucleating A

and B. The eutectic point is

denoted by E

Fig. 9.22 A putative temperature-composition path for the liquid in the crystal layer. The tem-

perature cools (slowly) until nucleation (and growth) of A begin at a. The liquid is then enriched

in B until the A liquidus is reached at b, at which point growth ceases, and the liquid cools until

nucleation of A recommences at c. Again enrichment of the liquid in B occurs, but this time when

the A liquidus is reached at d, nucleation and growth of B has already begun, so that enrichment of

A begins. Potentially, the liquid will be thus diluted of B until it reaches the B liquidus, at which

point A enrichment begins again

when the temperature reaches the A meta-liquidus. The resulting growth of A moves

the liquid composition to the right. Unlike the equilibrium situation, where the tem-

perature would be constrained to move gradually down the liquidus, and would stop

when it reached the eutectic point, here the temperature can move horizontally to the

right through the non-equilibrium ﬁeld until B starts to nucleate and grow. Then the

liquid composition moves towards A and, depending on the rates, the temperature

may reach the (continuation of the) B liquidus. Repeating the process leads to the

oscillation shown in Fig. 9.21, and one approach to this is shown in Fig. 9.22.

While this may seem to provide a plausible oscillation mechanism, it is by no

means clear that it will work in practice, when the diffusion of heat is taken into

account. It appears that the necessary numerical simulation of an appropriate space-

dependent crystallisation model has not yet been done, although the model is some

thirty years old!

596 9 Magma Transport

An intriguing variation on this idea uses the fact that the rate coefﬁcients K



and



in (9.149) and (9.154) represent diffusion rates of the various chemical species

to the crystal–liquid interface, and of course they must depend on the concentrations

of these species (after all, crystallisation is simply a reaction). Thus the concentra-

tions of chemical species in the liquid will satisfy a sequence of reaction–diffusion

equations, with the kinetics of the reaction described by the dependence of the crys-

tal growth rates on the concentrations. It is not difﬁcult to organise the kinetics

to provide oscillations, and the addition of diffusion would then naturally lead to

travelling waves: layers! But it is not clear whether chemical concentrations can in

practice be rate-limiting in this way (one would expect not).

9.7 Volcanic Eruptions

Not all magma chambers emplaced in the crust simply freeze. The emplacement de-

pletes the source region, the asthenosphere, of some fraction of its partial melt, and

this causes excess compaction which induces a lower melt pressure. The upwelling

dyke runs out of gas, so to speak, and the chamber is inﬂated. But the source re-

gion will in time be replenished, and the melt pressure will build again. Thus we

can expect magma chambers to be subject to the contrary inﬂuences of cooling and

reinﬂation. When reinﬂation wins, further fractures are generated, and the resulting

magma ﬂow to the surface becomes a volcanic eruption.

9.7.1 Types of Eruption

There are many different types of eruption, and they differ in style because of the

different types of magma which are erupted. The simplest kind of eruption is the

effusive eruption, in which erupted lava ﬂows in streams away from the volcanic

vent. Basalts ﬂow rapidly, but more viscous magma may be extruded very slowly,

forming a lava dome.

The other types of eruption are explosive, and these range in ferocity from the

relatively gentle Hawaiian and Strombolian, to the ferocious Plinian. Various other

names are also used (Vulcanian, Peléean, and so on), but for our present purposes

we can think of explosive eruptions as occurring in a spectrum which ranges from

Strombolian to Plinian.

Essentially, the differences in eruption types are largely due to magma chem-

istry. The two principal constituents which affect the behaviour of the magma in an

eruption are the silica content and the volatile content. Silica affects the viscosity,

with more siliceous magma having higher viscosity. While basaltic magma has a

typical viscosity of 10

Pa s, silica-rich rhyolite has a viscosity of 10

Pa s. Viscos-

ity is also affected by temperature (about an order of magnitude every 100 K), by

crystal content, and by the wetness of the magma, which is due to the other main

important constituent, water. Silicate magmas are essentially solutions of (mostly

9.7 Volcanic Eruptions 597

metal) oxides in silica, and some of the dissolved oxides are volatile, and prone to

exsolution (as gas). The principal such oxides are water, carbon dioxide and sul-

phur dioxide, and of these, water is usually the most important. It is the wetness of

magma which causes most explosive eruptions,

in the following way. As magma

rises in a conduit from the magma chamber, its pressure decreases. At some point,

volatiles will be exsolved, in the same way that champagne effervesces when the

cork is popped. Continued magma rise causes the bubbles to grow, and because of

the expansion involved, there are large pressures exerted on the interstitial liquid. If

the bubble volume rate of increase is sufﬁciently slow, then the liquid can deform to

accommodate the increasing void fraction (volume fraction of bubbles) and the exit

of the resulting two-phase ﬂow at the vent leads to mildly explosive eruption.

On the other hand, if the exsolution rate is rapid, the liquid ﬁlms between the bub-

bles may not be able to withstand the differential stresses, and may shatter. Once the

integrity of the liquid is broken, the magma is essentially transformed to a gas/liquid

droplet mixture which explodes from the vent. The size of the liquid droplets will

depend on the degree of fragmentation, and the very smallest form the huge ash

clouds which are such a dominant feature of explosive eruptions.

9.7.2 Strombolian Eruptions

Strombolian volcanoes are named for Stromboli, a volcano between Italy and Sicily,

which has apparently been ‘erupting’ continuously for thousands of years. The erup-

tions consist largely of explosions, which occur fairly regularly every few minutes,

and consist largely of gas. The mechanism of these eruptions can be understood by

reference to gas-liquid two-phase ﬂows.

The classic situation of industrial interest in two-phase ﬂows is the formation of

steam as water rises in an externally heated pipe. This forms the basis for studies of

ﬂow in boilers and nuclear cooling systems. As the water rises and is heated past

the boiling point, bubbles of steam are nucleated and break off into the (usually

turbulent) ﬂow, forming a ‘bubbly’ ﬂow. This ﬂow régime is stable (the bubbles

remain separate) until there is a transition to a régime called ‘slug ﬂow’, in which

the bubbles coalesce into large Taylor bubbles

which ﬁll the width of the pipe,

separated by large slugs of liquid, perhaps with some (small) bubbles also. This

transition may be due to an instability in bubbly ﬂow which is manifested (in steam–

water ﬂows) when the void fraction α reaches about 0.25. As α increases further,

there is another transition to ‘annular ﬂow’, when the liquid ﬂows up the walls, with

the gas forming a continuous (and much faster) interior core. The transition from

This may not quite be true (at least in the way we will describe) for vulcanian eruptions, which are

short term explosive events, and may be due to the build-up of (volatile) pressure in a vent which

has been capped by a plug of solidiﬁed magma.

After G.I. Taylor.

598 9 Magma Transport

slug to annular ﬂow is by way of an intermediate ‘churn ﬂow’ régime, where the

Taylor bubbles become irregular and intermittent.

The ﬂow in a Strombolian vent is a two-phase ﬂow, where the exsolution of

volatiles as ﬂuid rises is not due to external heating, but to depressurisation. The

effect, however, is the same. Initially at depth the gas forms bubbles, and the ﬂow

is that of a bubbly ﬂow. As the ﬂuid rises, the void fraction increases, and we may

expect coalescence to lead to slug ﬂow. It is the appearance of the Taylor bubbles

at the outlet of the conduit which causes the ‘Strombolian burps’, which are the

manifestation of the eruption.

The situation is complicated by the obvious fact that if this style of eruption

has been going on for millennia, then the conduit to the surface from the magma

chamber has been continually open during that period. The only way this can be true

when the net liquid ejection at the surface is negligible is if there is a countercurrent

ﬂow in the conduit: otherwise the liquid would simply freeze. This countercurrent

ﬂow must be due to convection of the magma in the conduit, driven by the buoyant

release of volatiles. Thus we can expect the gas-rich magma to rise in the core of the

conduit, while the gas-poor magma descends at the walls (or it could be the other

way round).

Convection in the conduit may be periodic in time, as happens in the somewhat

analogous case of a geyser, in which case the periodicity of the eruptions may be a

consequence of the periodicity of the bubble rise, rather than simply being due to

the inter-arrival time between bubbles.

In this scheme of things, bubbly ﬂow leads to effusive eruptions. It is also possi-

ble to have eruptions which appear to correspond to churn ﬂow, and these have been

observed at Villarrica volcano in Chile, for example.

9.7.3 Plinian Eruptions

The formation of large Taylor bubbles from the coalescence of small bubbles in-

volves the collapse of liquid ﬁlms between bubbles. This is driven by the excess

pressure in the bubbles caused by the volume expansion on exsolution. If the liq-

uid viscosity is sufﬁciently low, then the liquid can drain from the ﬁlms without

mishap. For larger viscosities, however, this is not true, and the stress on the liquid

can become so large that it ruptures. The shattering of the magma foam then causes

an explosion, as the released gas erupts from the vent, carrying the shards of the

liquid ﬁlms with it. With the sudden release of pressure, the shards are quenched,

and depending on their size, form clots of pumice and cinders, or ash. The resultant

distinctive ash column is a typical product of the explosive Plinian eruption.

Pliny the Younger observed the eruption which is named for him in A. D. 79. This

was the eruption of the Italian volcano Vesuvius near the present-day city of Napoli,

which obliterated the Roman towns of Pompeii and Herculaneum. As is now well

known, the devastation of Pompeii was caused by a dense pyroclastic ﬂow, which

rushed down the slopes of the volcano, roasting everything in its path. A pyroclastic

9.8 Notes and References 599

ﬂow is an example of a turbidity current, a turbulent gravity-driven ﬂow which is

driven by the excess density of the ash particles within it. As such, it is analogous to

katabatic winds on ice slopes, snow avalanches, and submarine turbidity currents,

which are instrumental in building the convoluted patterns of offshore canyons on

the edges of continental shelves.

An explosive eruption column consists of a turbulent two-phase mixture of hot

gas and ash. It is propelled explosively from the vent. In some circumstances, en-

trainment and heating of air causes a further self-driven buoyant convective uprise

of the plume to the tropopause or beyond. Ash and pumice rain out from the plume,

forming deposits, sometimes metres thick, over a wide surrounding area. If the ash

column is too dense, or is not rising fast enough, then the fountain can collapse, and

the mixture of hot gas and ash will fall back on to the slopes of the volcano, where

it then forms a terrifying pyroclastic ﬂow. The ash cloud ﬂows downslope at speeds

of tens of metres per second, devastating everything in its path. As it progresses, the

heavier ash particles fall out, so that the density of the current rises. At some point,

the current comes to a fairly abrupt halt; the remaining ash is deposited, and the hot

gas rises harmlessly into the atmosphere.

9.8 Notes and References

The subject of magma generation, transport through the asthenosphere and litho-

sphere, emplacement of magma chambers, eruption and solidiﬁcation, is one in

which there are no ﬁnal answers, and there is no one book which describes the

whole sequence of events from a theoretical point of view, apart from that of Dobran

(2001). The contents of his book encompass most of those of the present chapter,

and provide an excellent source for both the physical ingredients of magma pro-

cesses, and how to build mathematical models of them.

On the other hand, a number of textbooks describe the general phenomena,

amongst which Holmes (1978) is invigorating. There are several volumes compris-

ing edited individual chapters, in which many of the protagonist constituents are

described. Among these are the volumes edited by Morgan et al. (1992) and Ryan

(1990) on magma transport. The book edited by Hargraves (1980) provides a very

broad synthesis of many different physical aspects of magma behaviour. Books on

petrology and geochemistry are those by McBirney (1984), Hess (1989), Nockolds

et al. (1978), Albarède (2003) and Mason and Moore (1982). A classic is the book

by Bowen (1956). Pitcher (1997) describes the enduring complexities involved in

the formation of granites.

Superplumes, Eruptions and Extinctions It is commonly thought that the ex-

tinction of the dinosaurs at the Cretaceous–Tertiary boundary some 65 My ago was

caused by the impact of a meteorite in the Yucatán peninsula in Mexico, a hypothesis

ﬁrst proposed by the father and son Alvarez (Alvarez et al. 1980); initially contro-

versial, the impact hypothesis has become widely accepted (Schulte et al. 2010),

though not by all: see the letters in Science 328, 973–976 (2010). An alternative