Pressure Solution and Coble Creep in Rocks and Minerals: a Review

Pressure solution and Coble creep in rocks and minerals: a review

K. R. McCLAY

SUMMARY A brief review of research on pressure solution grained quartz and calcite rocks may give rise is given. The mechanisms of pressure solution to geological strain rates at temperatures from and Coble creep are discussed. Deformation by 2oo-35o°C. Coble creep is expected to give rise diffusive mass transfer processes is generally to geological strain rates in fine-grained galena accompanied by grain boundary sliding and at low temperatures and also in fine-grained this will have important effects on the textures calcite rocks at temperatures around 35o°(I. and microstructures produced during deform- The chemistry of natural rock pressure solution ation. Experiments using relaxation testing systems is expected to have significant effects seem promising in allowing access to the slow and needs further detailed study. Further strain rates necessary to observe pressure research is needed to elucidate the nature and solution phenomena. The thermodynamics of role of grain boundaries during diffusive mass non-hydrostatically stressed solids is discussed transfer. Pressure solution phenomena are and an analysis of possible diffusion paths in important in the compaction behaviour of some rocks is presented. Evaluation of theoretical petroleum reservoir rocks and perhaps in some rate equations for pressure solution and Coble faults where sliding is accommodated by creep indicates that pressure solution in fine- pressure solution.

MANY ROCKS DEFORMED IN LOW GRADE METAMORPHIC ENVIRONMENTS, particularly in the range of T = i5o°C--35o°C and at confining pressures of 2--8 kb, i.e. up so lower greenschist facies (Fyfe I974, Turner I968 , p. 366) exhibit textures such as tectonic stylolites, truncated fossils, tectonic overgrowths and striped cleavages. These textures suggest deformation involving diffusive mass transfer processes. Since the pioneering work of Sorby (I863, I865, I9O8 ) and the early research at the turn of the century (e.g. Van Hise I9o4, Becke x9o3, Adams & Coker i91o), little advance was made until research interest was re- newed in the fifties and sixties (e.g. Heald I956 , Plessman I964, Weyl i959, Ramsay i967) and by the discussion of the thermodynamics of non-hydrostatically stressed solids (Correns i949, McDonald i96o , Kamb I96I , McLellan i966 , I968 , I970 and Paterson i973). A Tectonic Studies Group meeting held at Imperial College on 5 November I976 (see the Conference Report following this review) aimed to review current research on pressure solution and geological deformation which is accomplished by diffusive mass transfer. This paper gives a brief review of pressure solution and Coble creep (grain boundary diffusion) as deformation mechanisms in rocks and minerals. It has not been possible to make a complete survey of the literature or of current research work for this review, which is intended mainly as an introduction to the subject and to the synopses of the papers read at the Tectonic Studies Group meeting which follow.

3l geol. Soc. Lond. vol. x:~l, I977, pp. 57-7o, 4 figs, x plate. Printed in Great Britain.

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I. Pressure solution and Coble creep

(A) MECHANISMS Rock deformation mechanisms may be divided into three broad categoriesg (I) cataclastic processes, (2) intracrystaUine processes involving dislocation move- ments, (3) diffusive mass transfer processes. If a grain boundary is subjected to compressive and tensile stresses, then a chemical potential gradient for vacancy flow is set up (see review by Burton 1977, Nabarro 1948 and Herring 1950). The flux of matter, which is equal and opposite to the vacancy flux, leads to depletion of material at relatively compressive boundaries and deposition at relatively tensile boundaries. If the diffusion of matter is essentially through the grains, i.e. lattice diffusion, the process is termed Nabarro-Herring creep, whereas if it is predominantly around the grain boundaries, the flow is called Coble creep (Coble 1963). Grain neighbour switching in superplastic flow (Ashby & Verrall 1973, Edington et al. 1976) is essentially grain boundary sliding with accommodation by diffusional creep. Lattice diffusion (Nabarro-Herring creep) is important at high temperatures in metals (see review by Burton 1977) and perhaps in the Earth's mantle (Stocker & Ashby 1973). At lower temperatures, however, lattice diffusivities and solid state grain boundary diffusivities are expected to be too slow to account for the observed strains found in low grade metamorphic rocks (see section on rates of deformation later in this paper). Many textures in low grade metamorphic rocks (T = 2oo-35o°C) are interpreted as indicating deformation by diffusive mass transfer (P1. i A, B. C). It is therefore inferred that the presence of a fluid phase in the grain boundaries enhances diffusive mass transfer in low grade metamorphic rocks--hence the term 'pressure solution'.

(B) THE EVIDENCE FOR PRESSURE SOLUTION IN ROCKS Evidence for pressure solution in rocks and minerals is readily found, from a macroscopic scale down to the microscopic scale. Since Sorby (I 865) first ascribed the pitting of pebbles (P1. IB) to pressure solution, many authors have discussed the textures and structures attributed to this form of diffusive mass transfer (e.g. Voll I96O , Ramsay 1967, Plcssman 1964, 1972 , Spry 1969, Groshong I975a and b, Trurnit 1968 , Ayrton & Ramsay 1974, Kerrich 1975, Logan & Semeniuk 1976 , Mitra 1976 ) . Limestones display a wide variety of pressure solution phenomena which occur both during diagenesis and deformation. Stylolites are extensively developed in many limestones (Arthaud & Mattauer 1969, 1972 ) with an accumulation of quartz and phyllosilicates in the stylolite and clay seams which often truncate fossils (P1. IA). Logan & Semeniuk (1976) have described in detail pressure solution and stylolite development in the limestones of the Canning Basin, Western Australia. The formation of some rock cleavages is often thought to involve pressure solution (Borradaile I977, Cosgrove 1976, Alvarez et al. 1976 , Williams 1972 , Groshong I975a, Siddans 1972 , Durney i972b ). Detailed high voltage electron microscopic studies by Knipe & White (I977) , however, have shown the corn-

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plexities of cleavage development and in particular they emphasize the effects of crystallization involving the formation of new phyllosilicates. Striped (or spaced) cleavage in limestones (Alvarez et al. 1976) and in the greywacke rocks of South Devon (P1. I C) has been attributed to pressure solution processes (Ramsay I967). Beach (I974) and Kerrich (1975) have studied the chemical changes resulting from pressure solution of the Devonian greywackes of SW England and found that at least some of the vein minerals are supplied from the surrounding rock. Differentiation of minerals into low pressure zones during folding (Stephansson 1974) has often been attributed to pressure solution, particularly during the formation of crenulation cleavages (Dumey I972a, Williams I972, Cosgrove 1976 ). Tectonic overgrowths (P1. IA) which often have a fibrous appearance (Durney & Ramsay 1973, Mitra 1976 ) and pressure shadows (Stromgard 1973) are also considered as evidence of pressure solution processes in low grade metamorphic rocks. Mitra (1976) has presented a very elegant analysis of deformation mechanisms in quartzites in which he has been able to separate strain components due to dislocation creep and to pressure solution. A very detailed and historical review of research on pressure solution and of pressure solution structures is given by Kerrich (I977). (C) THE EXPERIMENTAL EVIDENCE Grain boundary diffusional creep was first postulated by Coble (1963) for creep in AltOs. Coble creep was later found to operate in pure magnesium (Jones 1965) and in other metals and ceramics such as copper (Burton & Greenwood 197o ) and cadmium (Crossland I974) , (for details see Burton 1977). Grain boundary creep was found to have a lower activation energy than that for lattice diffusion and a strain rate dependence on the reciprocal of the grain size cubed (see later section on rate equations). It has been found to be important in metals at low homologous temperatures (,-o o.6 T melting, Burton 1977) whereas Nabarro- Herring creep occurs only at high temperatures (,~ o. 9 T melting).

~IG. I. A B ,I, C EXIENSION A. Undeformed hexagonal array of grains with marker line. The compressive stress axis is horizontal. B. If diffusional creep occurs without grain boundary sliding (i.e. the centres of the hexagonal grains and the marker line are not displaced) then there would be a volume increase and voids (black areas) would form against the compressive stress. This is an unlikely mechanism and the diffusional creep is accompanied by grain boundary sliding-- I (], C. Diffusional creep with grain boundary sliding resulting in offset of the marker line and no voids forming (constant volume deformation).

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Diffusional creep in polycrystals whether Nabarro-Herring or Coble creep, is generally accompanied by grain boundary sliding (Lifshitz z963, Gifkins i967, z976, Raj & Ashby z97z and Ashby & Verrall i973) if voids are not to form (i.e. constant volume deformation) during creep (Fig. z). Diffusional creep may be inhibited when second phase particles are present in the material (Harris z973). During diffusional deformation the relatively immobile second phase particles accumulate in compressive stress grain boundaries and become denuded in tensile grain boundaries (Harris 1973). Plate I D shows the microstructure of a magnesium- zirconium alloy which has undergone diffusional creep. Denuded zones free of precipitates can be seen. Grain boundary sliding has occurred resulting in displace- ment and rotation of the grains. In rocks and minerals, experimental evidence for creep by diffusive mass transfer and grain boundary sliding has been found for Solenhofen limestone (Schmid I976a , b) and in fine grained galena (Atkinson, unpublished work). Good textural evidence for pressure solution has been found in experiments by De Boer (I975) , De Boer et al. (x977), and Sprunt & Nur (z976). Rutter & Main- price (pers. com. I977) found that the presence of a pore fluid strongly affected the relaxation behaviour of Tennessee sandstone (Fig. 2). They inferred from the observed rheological behaviour that deformation was accomplished by grain boundary sliding accommodated by pressure solution. In salt-mica analogue experiments Means & Williams (I974) have observed mineral segregation in microfolds possibly resulting from pressure solution. Experimental investigations to determine the rheological flow laws of pressure solution have met only with limited success. Plastic deformation by dislocation movement and cracking are difficult to suppress and the inferred low heat of activation (Rutter I976, Rutter & Mainprice pers. com. z977) prevents significant speeding up of the pressure solution process by substituting higher temperatures for slower strain rates. Relaxation experiments, however, may provide access to the low strain rate necessary to observe pressure solution phenomena.

3.9, 8 "7 Fxo. 2. 3.8 <~ L6- -'" ..... I'- o,-,eNp,, l_.#~,gb,,m:_ ,_.. m TS 30 DRY Relaxation data expressed as log stress oo 3.7" 6O ~5.¢n.... ,~1,,4 versus log strain rate (Rutter & Main- IJJ n," price, pars. corn. ,977) for Tennessee 3.6 sandstone. Both tests were conducted o u~u~ TS 33 WET e% ~ee • at effective confining pressures of t"5 o, 3.s. uJ •3 m % ,°" kb and Ts 33 had a pore fluid pressure °.~e • 200 bars. The dry test Ts 30 shows no 3"~' -2.5 "r= 3oo'c "~- ,~ significant drop in strength over 8 = % orders of magnitude in strain rate 3"3 !0 while the wet test Ts 33 shows significant drop in strength at strain rates -,0% sty,. RATE less than zo -s SeC -1.

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PLATE I A. Truncated Globigerina in calcareous slate. The dark lines on each side of the fossil (S) are clay seams with accumulations of phyllosilicate minerals. Fibrous overgrowths of calcite (C) have formed in a pressure shadow. (Photograph D. Durney (I972a), Imperial College, Department of Geology slide collection). B. Pitted pebbles in the Molassic conglomerates of Carboniferous age, Mieres. Interpenetration of pebbles can clearly be seen. (Photograph J. G. Ramsay). C. Striped cleavage (attributed to pressure solution processes, by Ramsay (1967)) in Devonian greywackes, Torcross, Devon. D. Microstructure of polycrystalline magnesium containing very fine particles of zirconium hydride aligned in stringers which were initially parallel. The specimen has been crept at 4oo'C with the tensile axis horizontal in the photograph, at a strain rate of I'2 IO a/hour and with a final strain of 427o. The grains have undergone grain boundary sliding and relative rotation. Denuded zones free of hydride particles can be clearly seen. Photograph Dr R. B..]ones, CEGB Berkeley Nuclear Laboratories.

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2. Thermodynamics A considerable amount of literature has been devoted to the thermodynamics of non-hydrostatically stressed solids (e.g. Gibbs I9o6, Correns I949, McDonald x96o, Kamb i96I , McLellan i966 , i968 , i97o , Durney I972b, I976, Paterson I973 and De Boer i975, i977). The basic principles stem from the work of Thompson (I862), Poynting (I88I), Le Chatalier (I892), Riecke (I894) and Gibbs (x 9o6). Thompson (I862) reported that an increase in hydrostatic pressure increased the solubility of a crystal in its saturated solution. Poynting (x88I), however, stated that the increase in solubility due to pressure applied simul- taneously to both the solid and the liquid phases is small compared with the solubility change resulting from pressure on the solid alone. Le Chatalier (i 89~ ) showed mathematically that a deviatoric stress has a greater effect on solubility than hydrostatic stress. Riecke (1894 ) stated that if two prisms of the same solid are originally in equilibrium with a common saturated solution, then the application of stress to one of the prisms causes it to go into solution while the unstressed crystal grows at its expense. Gibbs (I 9o6) presented a thermodynamic analysis of non-hydrostatically stressed solids. Paterson (I973) has reviewed and rederived the thermodynamic relationships for non-hydrostatically stressed solids while Durney (pers. com.) has summarized the historical research on non-hydrostatic thermodynamics. Following the particularly lucid presentation of Paterson (1973), the equilibrium conditions at the interface between a solid and its solution under non-hydrostatic conditions can be stated thus: ~L = Us -- Ts s + an us (Paterson I973, eqn. 8) where ~T. is the chemical potential of the component of the solid in the solution; Us is the molar internal energy of the stressed solid; T is the abolute temperature; ss is the molar entropy of the solid in its stressed state; an is stress component normal to the surface of the solid and us is the molar volume of the solid in the stressed state. An increase in the equilibrium chemical potential ~T. is concommitant with an increase in the solubility of the solid in the solute. The implications of the thermodynamic analysis have been discussed by Paterson (x973) and Durney (I976) and the reader is referred to these papers for greater detail. For pressure solution the following generalizations, following Durney (I976), can be made: (a) a positive increase in the normal stress an always increases the equilibrium solute concentrafionBi.e, pressure solution occurs--whereas if an decreases, precipitation occurs. (b) a positive increase in the pore fluid pressure p achieved without changing the normal stress will reduce the effective normal stress (an-p) and hence the solute concentration in the interface--i.e, precipitation occurs. (c) an increase in both the pore fluid pressure and the normal stress most likely produces an increase in equilibrium solute concentration in the interface--i.e, pressure solution occurs.

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3- Diffusion paths The rate of diffusion is generally considered to be the rate controlling factor for deformation by pressure solution (Elliott I973, Durney i976 , Rutter I976 ). In a polycrystalline aggregate five main types of diffusion path may be recognized (Fig. 3). The possible diffusion paths involving lattice and fluid assisted diffusion are: (i) vacancy diffusion through the crystal lattice--Nabarro-Herring creep (Fig. 3a). (2) vacancy diffusion along the grain boundaries--Coble creep (Fig. 3a). (3) diffusion along dislocation cores and low angle (sub-grain) boundaries, Ashby i972 , Knipe (pers. com. i977) , (Fig. 3b). (4) diffusion of matter along an intergranular fluid film and local deposition (Fig. 3c). (5) diffusion of matter over large distances through the pores of the material (Fig. 3d). Mass transfer along the diffusion paths outlined above will lead to grain shape changes but paths 4 and 5 may also lead to changes in chemistry and a mineralogical differentiation into a new layering (of. crenulation cleavage, Cosgrove x976). The recognition of the possible diffusion paths characterized by different diffusivities is very important when considering the rates for diffusion processes.

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0 4' FxG. 3. Possible diffusion paths in a polycrystalline aggregate. A. Lattice diffusion (Nabarro-Herring creep) and grain boundary diffusion (Coble creep). B. Diffusion along sub grain boundaries (Knipe pets. com. I977). C. Pressure solution diffusion along a thin intergranular fluid film and deposition on less stressed crystal faces. D. Pressure solution and stylolite formation but with transport over considerable distance to give rise to fibrous overgrowths.

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4. Rate equations

Pressure solution models (Weyl I959, Durney I972b , I976 and Rutter I976 ) have been generally simplistic in that they consider an isolated grain contact without grain boundary sliding. Elliott (i 973) noted that pressure solution is geometrically similar to diffusion creep in metals and ceramics. Rutter (I976) has erected a theoretical model for pressure solution at low stresses (aa < 300 bars). The strain rate 6 is given by 6 = 32~aV Co Db w/RTpd 3 where aa is the applied stress, d the grain diameter, p the density of the solid, w the effective grain boundary width, R the gas constant, T the absolute temperature, V the molar volume of the solid, Co the concentration of a saturated solution in equilibrium with the unstressed solid and Db is the grain boundary diffusivity. Nabarro (i948) and Herring (i95o) proposed that the creep rate for lattice diffusion would be = B (craVDo/kTd') where Dv is the volume diffusivity and k the Boltzman's constant. Coble (1963) proposed that, for grain boundary diffusion, the creep rate would be: 6 = B' oa V~Db/kTd 3 where ~ is the effective grain boundary width and Db the grain boundary diffusivity. The values of the numerical constants B and B' in these equations depend on the assumed grain shape and diffusion path geometry. These rate equations have been evaluated for quartz, calcite (using the modified forms and the data of Rutter I976 ) and galena (using the data of Atldnson I976a, 1977). The results of strain rate calculations for two temperatures, 2oo°C and 35o°C, considered on geological grounds to be the range over which pressure solution and fluid assisted diffusive mechanisms are important, are plotted in Fig. 4. Geologically feasible strain rates for the formation of natural ductile structures (e.g. folds) are thought to be in the range lO-9--Io -1. sec -1 (Price 1975). In the equation for grain boundary (Coble) creep, the effective grain boundary width was taken as ten times the smallest Burgers vector (a axis for quartz and calcite, V'2 a axis for galena). Although Rutter (x 976) and White ( i976) have used 2 × b (b = Burgers vector) for the grain boundary width 8 in their analysis of creep in calcite and quartz (i.e. similar to that in metals), Mistier & Coble (1974) have shown that ionic compounds have considerably larger grain boundary widths ( ~ too × b). It is therefore probable that in minerals the effective grain boundary widths in minerals would be significantly larger than 2 × b, that taken for metals. Grain boundary widths are also discussed by Elliott (I973). In this theoretical analysis, xo × b was chosen as being a compromise between 8 for metals and 8 for ionic materials (see also Atkinson I977). Inaccuracies in the diffusion data for quartz (discussed by White x976 and Rutter I976 ) result in these theoretical calculations being no more than order of

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magnitude estimates. White (op. cit.), however, has shown that electron microscopic evidence of naturally deformed quartz supports the theoretical calculations for diffusional creep. For quartz it can be seen that, except for very small grain sizes (i-xo ~m), Nabarro-Herring and Coble creep may not give rise to geological strain rates at the two particular temperatures (White I976 ) . Pressure solution, as formulated by Rutter (I976), may give rise to geological strain rates for grains up to several hundred microns in size. Similarly in calcite Nabarro-Herring creep may only give rise to geological strain rates at very small grain sizes (i ~m). There is good experimental evidence that diffusional creep or grain boundary sliding, however, may give rise to geological strain rates in fine-grained calcite rocks at low temperatures (eft results of Schmid I976a, b). Pressure solution may also give rise to geological strain rates in calcite rocks. However, in the region of T -- 35o°C, the boundary between pressure solution and Coble creep will be very diffuse because of the large variation in the calculated strain rates which can be caused by small variations in the assumed activation enthalpy. The activation enthalpy is related to the diffusivity and temperature by the relation DT = Do e -H/aT where Do is the extrapolated diffusivity at infinite T, H the activation enthalpy, T the absolute temperature, R the gas constant and DT the diffusivity at a particular temperature T. At low temperatures (2oo-3oo°C) small changes in H will give rise to large changes in DT and hence in 6. The activation enthalpy H may also be very sensitive to the presence of alio-valent impurities. The value of H for calcite probably decreases at c. T = 4oo°C from 25okJ mole -1 to about half this value at lower temperatures (Rutter I976 ). Hence, at about 35o°C the strain rates for Coble creep and pressure solution have been calculated to be nearly equivalent. The plots for stoichiometric galena show that geological strain rates will arise from deformation by Nabarro-Herring and Coble creep in fine-grained galena ores (Atkinson I977). Further complications are liable to arise; for example, Burton (I977) has indicated that at low homologous temperatures ( .~ o'4 T melting), the stresses needed to create sources and sinks for vacancy diffusion may be sufficiently high to inhibit Coble creep in favour of dislocation mechanisms. In geological systems, the presence of clays along the grain boundaries is expected to increase the rate of pressure solution (Heald I956), whereas in metallurgical systems, the presence of second phase particles may inhibit diffusional creep (Harris i973). The nature and role of grain boundaries and subgrain boundaries during diffusive mass transfer will undoubtedly be extremely important. Only Knipe (pets. com. I977) has attempted to evaluate this role in quartz and more detailed studies involving chemical analysis and electron microscopic observations are needed in order to evaluate grain boundary behaviour during pressure solution.

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5- Chemical effects Impurity ions and stoichiometry defects will have marked effects on the creep and pressure solution behaviour of geological materials. Atkinson (1976a) has discussed the effects of non-stoichiometry and impurities on the behaviour of polycrystalline galena. However, very little is known about the stoichiometric and chemical effects on the behaviour of quartz and calcite (see section on rate equations). Trace quantities of hydroxyl ions in the quartz structure appear to reduce its strength considerably, enabling plastic deformation and recrystallization to occur below 5oo°C, (Griggs 1967, Blacic 1975, Jones 1975). Little is known, however, about the effects of hydroxyl ions on surface diffusion in quartz and it is expected that this will have important effects on the pressure solution and fluid assisted diffusion around quartz grain boundaries. Fyfe (1976) emphasized that chemical changes during prograde metamorphism (e.g. dehydration reactions, kaolinite ~ pyrophyllite) can have profound effects on mechanical properties of rocks through the provision of free pore water under pressure. He also considers that crystal growth and solution process (i.e. pressure solution) can give rise to strain rates of the order of Io -ix sec -~ (Fyfe 1976 ) at ioo bars differential stress. Knipe & White (1976, I977) have demonstrated that cleavage lamellae in slates are sites of chemical reactions with new, chemically distinct phyllosilicates developed in kinks and deformation bands.

6. Conclusions This paper has aimed to review current literature and research on pressure solution and Coble creep in rocks and minerals. Pressure solution is a complex problem and although theoretical models have been proposed, care must be taken in applying metallurgical theories to diffusion in rocks where, in particular, the chemistry is undoubtedly more complicated. The nature and role of high and low angle grain boundaries will be very important during diffusive mass transfer processes and these factors are very much unknown quantities in natural rock systems. Very detailed microstructural and microchemical research in natural and experimental rock pressure solution systems is needed, together with electron microscopic studies, in order to determine the nature of grain boundaries in rocks which have undergone pressure solution. To date, only theoretical flow laws have been proposed for pressure solution whereas experiments have established that solid state diffusion processes can give rise to geological strain rates in fine-grained galena and fine-grained calcite rocks. Although pressure solution textural features have been produced experimentally, direct experimental studies to determine the flow laws for pressure solution have had limited success, but increased use of relaxation testing may provide access to the low strain rates necessary to observe the process. Studies of pressure solution phenomena are not only important for understanding rock deformation but they are also important in the compaction behaviour of some petroleum reservoir rocks. In addition, sliding along some faults may be accommodated by pressure solution processes.

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ACKNOWLEDCmMENTS. Dr E. Rutter and D. Mainprice are thanked for permission to use unpublished data for Fig. 2. R. Knipe is also thanked for permission to refer to unpublished work (Fig. 3b). Dr D. Durney, Professor J. G. Ramsay and Drs B. Burton and R. B. Jones (CEGB) are thanked for providing information and for permission to use the photographs for Plate IA, B and D. Drs E. Rutter, B. Atkinson, S. White, G. Lister, R. Knipe and N. Shaw are thanked for many useful discussions and criticisms for this review.

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Received 7 February I977; revised manuscript received 17 March 1977. K. R. McClay, Department of Geology, Imperial College, London SW7 2BP.

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