Showing papers in "Philosophical Transactions of the Royal Society A in 1976"

The Energy Balance and Deformation Mechanisms of Thrust Sheets

Abstract: The total energy involved in emplacing a thrust sheet is expended in initiation and growth of the thrust surface, slip along this surface, and deformation within the main mass of the sheet. This total energy can be determined from potential energy considerations knowing the initial and final geometry from balanced cross sections after defining the thrust’s thermodynamic system boundaries. Emplacement of the McConnell thrust in the Canadian Rockies involved ca. 1019 J of gravitational work, an order of magnitude greater than any possible work by longitudinal compressive surface forces. A new theory for the initiation and growth of thrusts as ductile fractures is based on a demonstration that thrust displacement is linearly related to thrust map length and that fold complexes at the ends of thrusts are constant in size for a given metamorphic grade. Much of the total work is dissipated within the body of the sheet. Field observations show which mechanisms of dissipation are most important at various positions within the thrust sheet, and it is found that only the top 5 km of the McConnell was dominated by frictional sliding. A novel type of sliding along discrete surfaces is pressure solution slip, in which obstacles are by-passed by diffusive mass transfer. Fibres and pressure solution grooves are diagnostic features of this sliding law, in which slip velocity is linearly related to shear stress. Pressure solution slip is widespread at depths greater than about 5 km, but at this depth penetrative whole rock deformation by pressure solution becomes dominant - marked by cleavage and stretching directions - and accounts for much of the finite strain within the thrust sheet. The McConnell thrust has an outer layer which deformed by frictional sliding and this overlies a massive linearly viscous core responsible for much of the energy dissipation and gross mechanical behaviour.

The Symmetry of Electron Diffraction Zone Axis Patterns

Abstract: The convergent beam and bend extinction contour techniques of electron microscopy are capable of providing much more information than can be obtained from conventional diffraction patterns and it is the objective of this work to examine the symmetry properties of each of these patterns. The diffraction of fast electrons by a thin parallel-sided slab has been studied by group theory and by a graphical construction. We find that the pattern symmetries may be described by thirty-one diffraction groups and that each of these diffraction groups is isomorphic to one of the point groups of diperiodic plane figures and to one of the thirty-one Shubnikov groups of coloured plane figures. A graphical representation of each diffraction group is given, together with tables showing how the diffraction groups are related to the specimen point groups and under certain assumptions to the crystal point groups. These tables assume the symmetric Laue condition and ignore the presence of irreducible lattice translations normal to the slab. By using the tables, crystal point groups can be obtained from convergent beam or bend contour patterns. The method is demonstrated by experiments on several materials, but particularly on germanium and gallium-arsenide specimens since the similarity of these materials exemplifies the sensitivity of the technique.

The Effects of Strain on the Microstructures, Fabrics, and Deformation Mechanisms in Quartzites

Abstract: The oaxes fabrics and the intracrystalline microstructures of naturally deformed quartz indicate that dislocation deformation mechanisms are important natural deformation processes. Two mechanisms, dynamic recovery and cyclic dynamic recrystallization, can lead to steady state flow which is necessary if large strains are to be attained. Cold working followed by cataclasis can also produce a steady state flow, but is limited to low temperature, high stress environments. Available data indicates that the c-axes preferred orientations and the optical strain features develop progressively as the strain increases. Recrystallization occurs by the continual rotation of sub-grains or by the development of small strain free grains. The new grains develop preferentially in the most misorientated areas of the deformed host grains, especially along deformation bands and in grain mantles. They have c axes orientations similar to the range in orientation of the host grain in deformation bands and mantles Grain growth is inhibited if there is a rapid increase in the dislocation density in the new grains. Grain refinement then accompanies recrystallization and produces a quartz mylonite. The new grains may be subjected to further phases of deformation and grain refinement. Deformation maps for quartz show that Coble creep replaces dislocation creep as the main deformation process when the grain size is less than 100 pm. The change is accompanied by strain softening and the maps imply that fine grained quartz mylonites are superplastic.

A Magnetic Model of the Solar Transition Region

Abstract: A two-dimensional model of the chromosphere and corona has been constructed. This is based upon the magnetic flux concentrations which occur at the boundaries of the supergranule convection cells. The expansion of the magnetic flux is determined by the vertical extent of the convecting plasma. The distribution of atmospheric material is consistent both with observed spectral intensities and with energy balance requirements. The model predicts a primary transition region which is confined to an area about 10" wide overlying the supergranule boundaries. A secondary transition region which is much thinner covers the cell centres. The predictions are fully consistent with recent ultraviolet observations.

The theory of rubber elasticity

Abstract: This paper attempts to improve several weaknesses in the classical theories of rubber elasticity. It develops a formulation of the statistical thermodynamics of amorphous materials analogous to the Gibbs formalism for conventional statistical mechanics. This then permits the replacement of ‘phantom chains’, i.e. long polymer molecules with the fictitious property that they experience no forces except at cross link points and are transparent to one another, by realistic molecules which do experience forces and which can become entangled. The crosslinked points are no longer assumed to deform affinely with the gross behaviour of the solid. Under the simplest conditions forms like the classical are recovered but with a different coefficient, and the term representing the degrees of freedom lost by crosslinking, over which the classical theories are in dispute, is found to lie between the previous values in a formula which can reproduce the classical results by making different assumptions. The entanglements give rise to more complicated forms than the classical sum of squares of strain ratios, which under certain circumstances can reproduce the Mooney-Rivlin term which when added empirically to the free energy usually improves the fit with experiment. The general expression is complicated, but is nevertheless an explicit function of the density of crosslinks, the density of the rubber and the interchain forces.

Late Proterozoic Cratonization in Southwestern Saudi Arabia

Abstract: Early cratonal development of the Arabian Shield of southwestern Saudi Arabia began with the deposition of calcic to calc-alkalic, basaltic to dacitic volcanic rocks, and immature sedimentary rocks that subsequently were moderately deformed, metamorphosed, and intruded about 960 Ma ago by dioritic batholiths of mantle derivation ($^{87}$Sr/$^{86}$Sr = 0.7029). A thick sequence of calc-alkalic andesitic to rhyodacitic volcanic rocks and volcanoclastic wackes was deposited unconformably on this neocraton. Regional greenschistfacies metamorphism, intensive deformation along north-trending structures, and intrusion of mantle-derived ($^{87}$Sr/$^{86}$Sr = 0.7028) dioritic to granodioritic batholiths occurred about 800 Ma. Granodiorite was emplaced as injection gneiss about 785 Ma ($^{87}$Sr/$^{86}$Sr = 0.7028-0.7035) in localized areas of gneiss doming and amphibolite to granulite facies metamorphism. Deposition of clastic and volcanic rocks overlapped in time and followed orogeny at 785 Ma. These deposits, together with the older rocks, were deformed, metamorphosed to greenschist facies, and intruded by calc-alkalic plutons ($^{87}$Sr/$^{86}$Sr = 0.7035) between 600 and 650 Ma. Late cratonal development between 570 and 550 Ma involved moderate pulses of volcanism, deformation, metamorphism to greenschist facies, and intrusion of quartz monzonite and granite. Cratonization appears to have evolved in an intraoceanic, island-arc environment of comagmatic volcanism and intrusion.

The interrelations of fluid transport, deformation, geochemistry and heat flow in early Proterozoic shear zones in the Lewisian complex

Abstract: The Lewisian complex of northwest Scotland shows a pattern of evolution typical of a number of early Proterozoic provinces. During the period 2500-1600 Ma, deformation occurred along steeply dipping shear zones, resulting in both vertical and lateral movements. The largest of these shear zones, forming the northern boundary to the Scourian granulites (Archaean), must have penetrated to considerable depth, possibly to the mantle. Modal and chemical analysis of rocks from shear zones are presented and discussed in relation to rocks sampled outside shear zones. The mineralogy and composition of all rocks deformed in the shear zones have been considerably altered by synkinematic metasomatism. In the early stages, immediately prior to and during the intrusion of the regional doleritic dyke swarm, this metasomatic activity involved addition of H$\_{2}$O and Na to the rocks. Subsequently, more significant changes in rock chemistry occurred (addition of H$\_{2}$O, K, Na, loss of Fe, Ca, Mg). These changes resulted from the interaction between large volumes of water and the rocks in the shear zones along which the fluid travelled. A combination of modal and chemical data allow general chemical reactions to be written which describe the evolution of the gneisses during reworking and retrogression from pyroxene bearing granulite facies rocks to hornblende and biotite bearing amphibolite facies rocks in shear zones. The reactions are written as ionic equilibria and suggest that the fluid phase in the shear zones had a low pH. Adiabatic transport of water upwards through the crust will result in moderate warming of the fluid, and can cause large temperature increases above the preexisting geothermal gradient in rocks through which the fluid travels. It is suggested that both deformation and metamorphism in these shear zones are related to transport of fluid by hydraulic fracturing. Grain size reduction by hydraulic fracturing increases the strain rate in the shear zones. Deformation may cease in a shear zone when the fluid pressure drops and hydraulic fracturing no longer occurs. Thus fluid transport, mineral reactions, chemical changes, grain size reduction and convective heat flow will cease. A close relation should exist between the intensity of deformation, the extent of metasomatism and the thermal history in these important shear belts.

Strain and Anisotropy in Rocks [and Discussion]

Abstract: The evaluation of finite strain in naturally deformed rocks is restricted by the limited occurrence of good natural strain indicators which are also homogeneous with respect to the matrix. This problem is overcome by establishing the relation between measured finite strain and those physical behaviour characteristics of rocks that are dependent upon the anisotropy resulting from deformation. Accordingly, the strain measured from natural indicators is calibrated against ( degree of preferred orientation, (b) magnetic susceptibility anisotropy, and (r) seismic anisotropy. This _ will permit three approaches to be used independently for the evaluation of strain, provided that a minimal number of actual strains are available. The relation between measured strain and the degree of preferred orientation of layer silicates as revealed by X-ray transmission goniometry is established for a group of fine grained tectonites of dominantly planar fabric which have an average deformation ellipsoid of form 1.6:1 :,0.26. The strains measured from the degree of preferred orientation are in remarkable agreement with those measured from natural strain indicators. The measured deformation ellipsoids for a wide range of strains are also compared to the correlative ellipsoids of magnetic susceptibility anisotropy. The axes of both sets of ellipsoids are coincidental and the shape relationship between deformation and magnetic susceptibility ellipsoids is established by linear regression. Finally, the anisotropy of seismic velocities is determined by measuring the pseudocompressional velocity and two orthogonally polarized pseudo shear wave velocities for each of a minimum of nine non-coplanar directions. The velocity surfaces thus obtained define an elastic or seismic velocity anisotropy ellipsoid, the axes of which are also precisely coincidental with those of the finite deformation ellipsoid. The influence of rock fabric upon seismic velocities is such that for a rock which has undergone a principal finite extension of 135 % and a finite shortening of 65 %, the difference of compressional and shear wave velocities between these two directions is in the ratio 1.26:1 for P waves and 1.33:1 for S waves.

Patterns of strain variation in arcuate fold belts

Abstract: Many mountain ranges (Alps, Carpathians, Himalayas) and volcanic island ridges (Aleutians, Banda, Mariana) are curved or sinuous, often so regularly as to be described as arcs. Their curvature may be primary or secondary. Among numerous models proposed to account for the curvature are the orocline or secondary bending hypothesis of Carey (1958), the inextensional bending model of Frank (1968) and the spreading of marginal seas and lateral compression (Matsuda & Uyeda 1971). Different models imply different patterns of finite strain. Palaeomagnetic measurements can also be used to discriminate between them. Criteria for discriminating are examined, with particular reference to the Variscan arc in the Iberian Peninsula.

The Lake Mungo geomagnetic excursion

Abstract: Archaeomagnetic studies have been made of prehistoric aboriginal fireplaces occurring along the ancient shore of Lake Mungo, a dried out lake in southeastern Australia. Directions of magnetization preserved in ovenstones and baked hearths show that wide departures of up to 120° from the axial dipole field direction occurred about 30000 years ago. The determination of the variation in geomagnetic field strength from the baked material is complicated by non-ideal behaviour during Thellier’s double heating method. The problem appears to arise from the subsequent (postfiring) formation of iron oxyhydroxides during a period in which the water level in the lake rose. During laboratory heatings these oxyhydroxides dehydrate causing the non-ideal behaviour observed. The ancient field strengths deduced are therefore probably minimum values. The geomagnetic excursion recorded between at least 30780 ±520 and 28140 ±370 years b.p. on the conventional radiocarbon time scale is associated with very high field strengths between 1 and 2 Oe (1 Oe » 79.6 A m_ 1 ). The field strength subsequently decreased to between 0.2 and 0.3 Oe after the excursion. This main excursion is referred to as the Lake Mungo geomagnetic excursion. There is evidence that a second excursion associated with low field strengths of 0.1-0.2 Oe occurred around 26000 years b.p. A review of geomagnetic excursions less than 40 000 years in age shows that it may be premature to assume that these are world-wide synchronous features. The range of ages and their groupings in different parts of the world may indicate they are temporary non-dipole features of continental extent. However, the duration of most excursions (order of 103 years) is very similar to that of polarity transitions and this could indicate they are aborted reversals.

Early and Middle Proterozoic history of the Great Lakes area, North America

Abstract: Two major supracrustal sequences, the Huronian Supergroup in Ontario and the Marquette Range Supergroup and Animikie Group of Michigan and Minnesota, overlie an Archean basement. These sequences are about 2200—2300 Ma and 1900-2000 Ma old respectively. The major Early Proterozoic tectonic event is the ‘Penokean Orogeny’, which occurred about 1850-1900 Ma ago and included deformation, high-grade regional metamorphism, and extrusive and intrusive igneous activity. This was followed by formation of rhyolitic, ignimbritic volcanic rocks and emplacement of associated granites about 1790 Ma ago. The entire region was subsequently subjected to low-grade regional metamorphism 1650-1700 Ma ago, followed by emplacement of anorogenic quartz-monzonite, in part rapakivi, plutons 1500 Ma ago. Late Proterozoic Grenville and Keweenawan events represent the youngest major Precambrian activity in the region. The rocks involved in the Penokean Orogeny lie along the southern margin of the Archean craton of the Superior Province and are interpreted as representing Early Proterozoic cratonic-margin orogenic activity. The distribution of rocks types and structures associated with the Penokean Orogeny and with similar orogenic belts along the margin of the Archean craton of North America suggest that these orogenic belts may have formed as a result of processes similar to modern plate tectonics, although the data are far from conclusive at present.

Continental displacement and expansion of the earth during the Mesozoic and Cenozoic

Abstract: Most reconstructions of Pangaea, the early Mesozoic supercontinent, assume an Earth of modern dimensions. Such reconstructions produce major geometric and Earth of modern dimensions. Such reconstructions produce major geometric and geological fit inconsistencies particularly in areas such as the Arctic, Caribbean, Mediterranean, and southeast Asia and Indonesia. The ocean floor spreading history of these regions and the adjacent oceans indicates that they have grown by areal expansion since their initiation. In contrast, the various reconstructions of Mesozoic and Cenozoic stages which assume an Earth of constant dimensions, require that these regions, either initially or during their development, should contract in area. The geological evidence from the continental margins and from the Earth’s oceans does not support the amount of subduction, either in whole or in part, required by the constant dimension hypothesis. It is shown that an exact fit of the various continental fragments together to reform Pangaea, which agrees with the geometric and geological matches, is obtained when the value of the Earth’s surface curvature is increased to the point at which the diameter of the globe is 80 % of its current mean value. This corresponds in time to the late Triassic-early Jurassic. It is asserted that the early Upper Jurassic to Recent ocean floor spreading data now available, displayed here in maps, also demonstrate progressive global expansion commensurate with an increase in diameter of 20 % of the Earth’s current mean value. Series of maps employing a zenithal equidistant projection are used to illustrate stages in the inferred development of certain regions during the Mesozoic and Cenozoic according to the ocean floor spreading data. The global expansion deduced from the geometric requirements of the spreading data in these maps permits a much more straightforward reading of the development of ocean basins and associated displacement of continents; one which accords with the field evidence. The inconsistencies seen in constant dimensions reconstructions do not arise. The results are summarized in outline hemisphere maps for which a new cartographic projection has been developed.

Pressure-Solution and Crystallization Deformation

Abstract: Pressure-solution and associated crystallization are subclasses of a diffusive mass transport process which involves diffusion in grain boundary and pore solutions. The manner in which they give rise to permanent deformation is examined in three steps: (a) A simplified reversible non-hydrostatic crystal-solution thermodynamic criterion (first order, 2-components) based on Gibbs provides a manageable basis for determining the direction in which the process will run (regions of dissolution or growth) in stressed porous, non-porous, closed and open systems. (b) Considerations of irreversible diffusion and deformation indicate certain restrictions on the displacements accompanying permanent growth or dissolution and hence on the form of the solution-transfer strain rate tensor. (c) The way in which the process develops, and its rate, are governed by kinetic factors, especially diffusion kinetics. As well as having an exponential dependence on stress, the displacement rate is influenced by absolute temperature, grain boundary diffusivity, initial solubility and geometric scale.

Proterozoic Magnetostratigraphy and the Tectonic Evolution of Laurentia [and Discussion]

Abstract: There have been two major orogenic cycles in the Proterozoic of Laurentia which culminated at about -1850 (Hudsonian) and -1000 Ma (Grenvillian). A third event, the so-called Elsonian ‘Orogeny’ ( —1400Ma) was dominantly a phase of igneous intrusion. The palaeomagnetic poles from Laurentia are reviewed, and an attempt is made to order them into a path of apparent polar wander (a.p.w.). We have constructed this path so as to minimize its length without violating the palaeomagnetic or geological observations. This a.p.w. path defines a magnetic stratigraphy for the Proterozoic of Laurentia which bears on the nature of the above orogenic events and the tectonic evolution that they may signify. If the results from the Grenville Structural Province are excluded, a single polar path for the interval —2200 to -1300 Ma can be constructed, indicating that Laurentia has not been dismembered and that the Hudsonian Orogeny occurred by internal deformation. The geological evidence is consistent with this view, and also indicates that deformation occurred marginally in the Coronation Geosyncline at about 1800 Ma. Poles from the Grenville Province available at present are displaced from the poles from the rest of Laurentia, and may indicate that the southern part of the Grenville Province was displaced 5000 km at about -1150 Ma. The geological evidence is insufficient to determine whether or not such a reconstruction is correct, but it is notable that the Grenville orogenic cycle is preceded by, and is in part contemporaneous with, extensive rift systems, which developed following the Elsonian ‘Orogeny’. The Grenville Province may then be a product of marginal tectonics and the first instance of the opening and closing of an ocean basin whose descendant is the present day North Atlantic. It is concluded that during the interval —2200 to —1400 Ma both marginal and internal tectonics occurred in Laurentia, whereas in the later Proterozoic marginal tectonics dominated. The Elsonian ‘Orogeny’ was apparently the time of changeover from one regime to the other. Nothing can yet be concluded from the palaeomagnetic evidence about the nature of orogenesis in the earliest Proterozoic ( -2600 to -2200 Ma). It must be emphasized that these conclusions flow from the basic assumption (that of minimizing polar path length) used in constructing our polar path. The data are also compatible with other more complex reconstructions, requiring greater polar path length, and which do not require this tectonic evolution.

Precambrian and Early Palaeozoic Palaeomagnetism in Australia

Abstract: The apparent polar wander path for Australia between 750 and 400 million years (Ma) shows rapid polar motion averaging 1 degrees /Ma. The data are derived from strati-graphic sequences, mainly in northern, central and southern Australia, that have good age control. This contrasts with other Gondwanic continents where age control is relatively poor. On the Smith-Hallam reconstruction of Gondwanaland, data from all these continents are consistent with the Australian path and suggest Gondwanaland was a unit at least as far back as 750 Ma ago. The common pole path is consistent with the widespread occurrences of Late Precambrian glacial deposits in Australia and Africa, suggesting their timing and location are related to rapid polar migration. The apparent unity of Gondwanaland through the Pan-African Orogeny at 550 $\pm $ 100 Ma provides strong support for the view that these orogenic belts were of ensialic origin. Extensive Precambrian palaeomagnetic data are consistent with a common apparent polar wander path for Australia back to at least 2500 Ma ago. The average polar wander rate of 0.3 degrees /Ma is similar to that derived for other continents. The consistency of the data irrespective of craton or the presence of some younger intervening orogenic belts provides some support to the view that these belts were also of ensialic origin.

Two Dimensional Normal Modes in Arbitrary Enclosed Basins on a Rotating Earth: Application to Lakes Ontario and Superior

Abstract: A method for determining the free periods of oscillation of an arbitrary enclosed homogeneous water body on a rotating earth is considered. Bathymetry and shape of the water body are taken into account. The oscillations are quasi-static and horizontally two dimensional. Analytical foundation of the theory is based upon a method developed by Proudman (1916). The method requires the construction of two sets of orthogonal functions; one set satisfies a condition of vanishing normal derivative on the boundary and the other set of functions have a zero value on the boundary. These orthogonal functions are numerically constructed for two real water bodies. The numerical orthogonal functions are used as a basis for the expansion of velocity and height fields. The expansion coefficients are then determined so as to satisfy the dynamical equations. The coefficients appear as eigenvectors of a Hermitian matrix. The corresponding eigenvalues represent the frequencies of oscillation. Structures are determined by numerical evaluation of the velocity and height field expansions. Application of the above procedure to Lake Ontario gives for the lowest gravitational mode a period of 5.11 h and for Lake Superior, the period of the corresponding mode is 7.86 h. Periods of the lowest six gravitational modes and their structures in both lakes are presented. Comparison of Lake Superior calculations with the data analysis of Mortimer & Fee (1976, preceding paper) shows very good agreement. A few examples of rotational modes are also presented.

Diophantine approximation in Fuchsian groups

Abstract: This paper is concerned with the geometric and measure-theoretic structure of the limit set of a Fuchsian group. By a Fuchsian group we shall understand a finitely generated Fuchsian group; we shall not attempt to investigate the pathologies of infinitely generated Fuchsian groups. The present work splits into two parts. Up to § 7 we give a complete account of the geometry of the action of a Fuchsian group both on the open disk and on the unit circle. Although this has been studied in the past, the account given here is more detailed and systematic than anything in the literature. The detail, which at times may seem excessive, is required for applications in the second part. The other part §§8—10, adopts the following point of view. The rational numbers can be characterized as the parabolic vertices of the modular group r . The theory of diophantine approximation (see, for example, Cassels 1965) gives ways of describing how well the rationals approximate a given number. The corresponding question for a Fuchsian group is: how well do the images of a distinguished point approximate an arbitrary limit point? This problem has already been raised by (Rankin 1957) and (Lehner 1964), and to some extent answered by them. The first part of this paper contains a complete solution. In the second part we push the analogy further and seek theorems concerning the behaviour of almost all points-that is, corresponding to ‘metric number theory’. In fact we can obtain results almost (but not quite) as sharp as their classical counterparts. This is carried out in § 9 and the structure of the exceptional set is described in § 10. O f course, this is only meaningful for groups of the first kind.

Comparison of the Flow Properties of Rocks at Crustal Conditions

Abstract: It is inferred that, although both primary and tertiary creep may be important in certain regions, large-scale ductile deformation in the Earth’s crust must be governed by secondary creep (steady state). This flow involves plastic deformation resulting from dislocation motion and diffusion. Geological, geophysical and geochemical observations constrain the temperature ( T ), strain rate (i), and stress difference (cr) for rocks undergoing secondary creep to: — 30-800 °C, 10_7-10-15 s-1, and up to 300 MPa (3 kbar). The actual conditions of secondary creep are strongly dependent on rock type and depth of deformation. Useful laboratory data on rocks obtained over wide ranges of T, e and cr are limited to ice, halite, marble, dolomite, quartzite and dunite. Steady-state flow results are available for both wet and dry rocks; H2O strongly affects the behaviour of both quartzite and dunite, but has a negligible effect on halite and marble. Secondary creep data for each rock are well fitted by exp ( ) crn, where Q is an activation energy for creep (diffusion) and A, R, n are constants. Comparison between those rocks expected in the deep crust indicates that at the highest T and at e of 10~12-10-15 s_1, cr is largest for dry dunite and dolomite, followed by dry quartzite, marble and wet quartzite. Equivalent viscosities ( ) range from 1018-1022 Pa s (1019-1023 P). At intermediate depths (at T = 300-500 °G), o9 in dolomite is slightly greater than dry quartzite; both are much stronger than marble. In the shallow crust, secondary creep is expected only in marble >250 °C) and in halite (T >2 5 °C). The y of halite at 25-250 °C, range from 1021—1017 Pas. At the surface and at e of 10~7—10_1° s-1 (glacier flow), of ice would be 1015 to 1012 Pa s between — 30 and 0 °C. Values of y for all rocks examined appear insensitive to T except wet quartzite and all dunite.

Minimum Work as a Possible Criterion for Determining the Frictional Conditions at the Tool/Chip Interface in Machining

Abstract: An approximate theory of machining is described in which the average shear flow stress in the plastic zone in the chip adjacent to the tool/chip interface, which is allowed to vary with strain rate and temperature, is used as the friction parameter and this is shown to be far more effective than the normally used average coefficient (or angle) of friction. It is proposed that the average thickness of the tool/chip interface plastic zone is determined by a minimum work criterion, its value being such that for given cutting conditions the average shear flow stress within the plastic zone will be minimized, thus minimizing both the frictional and total work done in chip formation. A comparison is made between results predicted by assuming minimum work and experimental results.

The Grenville Province in Helikian Times: A Possible Model of Evolution

Abstract: It is suggested that the Helikian (1650-1000 million years (Ma) ago) evolution of the Grenville Province in the Canadian Shield was marked by three events: emplacement of anorthosites around 1450-1500 Ma ago, rifting associated with opening of a proto-Atlantic ocean between 1200 and 1300 Ma ago, and continental collision responsible for the Grenvillian 'orogeny' about 1100-1000 Ma ago. Emplacement of rocks of the anorthosite suite (anorthosites and adamellites or mangerites) into continental crust was accompanied by formation of aureoles in the granulite facies. The Grenville Group was deposited in the southern part of the Province between 1300 and 1200 Ma ago and comprises marbles, clastic metasedimentary rocks and volcanics. It occupies a roughly triangular area limited on the northwest by the Bancroft-Renfrew lineament and on the southeast by the Chibougamau-Gatineau lineament. It is thought to have been accumulated in an aulacogen that would have developed along a fracture zone separating two basement blocks. The Grenvillian thermotectonic event may represent a Tibetan continental collision in the sense of Burke & Dewey. The suture zone would now be hidden under the Appalachians. Collision would cause reactivation of continental crust and renewed movement on pre-existing lineaments. The east-central part of the Grenville Province appears to have been more intensively reactivated than the western part.

Fold shapes as functions of progressive strain

Abstract: The folding of the components (layers or texture) of a rock system is viewed as an unstable strain-dependent process. The folds undergo successive stages of development, including initiation, amplification, propagation and decay. Fold shapes are functions of (i) initial morphology, (ii) mechanical behaviour of the rock, including stiffness contrasts and frictional properties of adjacent components, (iii) overall finite strain. The folded components may or may not adopt periodic waveforms, depending on (i) the relative rates of propagation versus amplification of the folds and (ii) the boundary conditions of the rock system.

Pan-African Structures

Abstract: A large proportion of the African Crust yields Pan-African radiometric ages (650-450 Ma). The Pan-African domains form a network of mobile belts surrounding cratons which remained relatively stable, cool and undeformed. The crust in the Pan-African domains had a similar previous history to that in the cratons. There is no process of cratonization and no progressive increase in cratonic dimensions, only a progressive reduction in the area unaffected by successive deformations. Neither tectonic, structural, stratigraphic or palaeomagnetic data suggest large-scale plate motions. No convincing ophiolites or sutures have been recognized within the PanAfrican domains. In situ deformation rather than collision orogeny seems probable.

Tectonics of the North Atlantic Proterozoic Dyke Swarm

Abstract: The Proterozoic North Atlantic dyke swarm occurs in Scotland, East and West Greenland, and Labrador, over an area of at least 250000 km2, and includes two dominant dyke sets which in West Greenland strike NNE-SSW, and ESE-WNW. The intrusive relations of the two sets, and their association with ductile shear zones and other lateral displacements of country rocks, show the dykes to represent a conjugate swarm emplaced along shear fractures, rather than along tensional openings. The mechanical behaviour of the Proterozoic lithosphere is considered in the context of the regional fracture system.

Cambering and Valley Bulging in the Gwash Valley at Empingham, Rutland [and Discussion]

Abstract: The construction of a dam at Empingham, Rutland has provided an opportunity to investigate the nature and effect of cambering and valley bulging. A detailed lithostratigraphic sequence has been established and the Upper Lias has been divided into a series of micropalaeontological zones. These features have enabled the internal structure of the Upper Lias to be determined in boreholes and at outcrop. The cambering process results in a progressive valley ward thinning which affects almost the entire Upper Lias sequence. The valley bulges are complex anticlinal structures developed in the valley floors. At depth the steeply inclined strata caught up in the valley bulge gives way along a possible decollement plane to largely undisturbed strata. The valley bulge structures occur throughout the valley and their courses are reminiscent of the trends of the modern valley system. This suggests that they may have been developed in the floors of the ancestral drainage system. The superficial structures were developed at the time of the Chalky Boulder Clay glaciation. Subsequent development of the valley has been a process of continued downcutting with landslipping and solifluxion being the dominant processes since the last glaciation. Possible mechanisms for the development of the superficial structures are discussed in the Appendix.

Deformed Rocks and their Textures [and Discussion]

Abstract: Modern analytic methods enable finite strain states on the scale of a hand specimen and textures on a much smaller scale to be determined in some rocks, together with error measures. Some recent publications describe attempts to calculate finite strain states from observed textures of phyllosilicates in slates. Petrographic, finite strain and textural data for several slates are presented, which suggest that such calculations are in fact often impossible and in general give inconsistent and erroneous results. The reasons for this are discussed, and it is suggested that there are no simple relations between finite strain states and textures in slates.

Vertical movements in Proterozoic structural provinces

Abstract: The extent, consistency and timing of vertical movements both in cratonic and in mobile segments of the continental crust are discussed with particular reference to movements taking place during Proterozoic times. The distribution of unconformities and erosion-surfaces, and the variations in cover-successions, in metamorphism, in style of igneous activity and in the closing of isotopic systems are considered in this context. Many of the most ancient cratonic masses appear to have undergone only very small vertical movements over periods up to 2000 Ma in length. Erosion of the basement of many cratonic regions seems to have been concentrated in periods of only a few hundred million years and was not renewed by persistent later uplift. The responses of these cratonic regions were influenced by the distribution of Archaean massifs in them. The history of uplift in certain Proterozoic mobile provinces is seen to have a bearing on the problem of the origin of these provinces.

Free surface oscillations and tides of Lakes Michigan and Superior

Abstract: From records of water levels at nineteen shoreline stations on Lakes Michigan, Huron and Superior (figure 1), we have prepared power spectra from 95 station-data sets and 128 spectra of interstation coherence and phase difference. Those spectra have been used to (1) identify the first five free gravitational, barotropic modes (surface seiches) of the three basins; (ii) estimate the corresponding seiche frequencies, Lake Huron table 2, Lake Michigan tables 3 and 4, Lake Superior table 7; (iii) determine, for some modes, the phase progression around the basin imposed by the Earth's rotation; and (iv) speculate on the structure of other oscillations, including diurnal and semidiurnal tides. Because the number of recording stations was limited, the phase progression of individual modes could only be determined with confidence for the first and second in Lake Michigan (figure 13), for the first, second, third, and eighth mode in Lake Superior (figures 22 and 32b) and for the semidiurnal tide in both basins (figure 31). Except for the Superior semidiurnal tide, which progresses clockwise, all the modes illustrated in figures 13 and 22 and the Lake Michigan semidiurnal tide conform to a positive amphidromic pattern - counterclockwise progression. Possible reasons for the difference in tidal behaviour in the two basins are discussed in section 4 and by Hamblin (1976). There is very close agreement between the observed frequency and the phase progression of the first three and eighth Superior modes and results from the two dimensional computations of Platzman (1972) and Rao & Schwab (1976). Because some of the level recorders were not protected from local harbour oscillations in the period range below 2 h, and because some of the data sets listed in tables 1 and 6 were available only in the form of hourly readings, spectra from some stations exhibited contamination by aliasing. Section 2 (b) is devoted to a discussion of: (i) the nature of this spectral contamination (see figure 4); (ii) its extent in our examples; and (iii) attempts to minimize its influence through identification of the principal aliases and exploitation of the discovery that useful information can still be extracted from interstation coherence and phase spectra, even if the power spectra from one or both stations of the pair are badly aliased. With aliases identified or absent, the remaining spectral and interstation coherence peaks correspond to free modes (and tides). In Lake Michigan the first three modes are the most strongly excited and are clearly identified as longitudinal seiches (section section 2 (c-f), 2(i)). A transverse (E-W) seiche is also strongly excited, probably in the form of a negative amphidrome, in the south-central reach of the basin (for example T1 in figure 6), but the structure and identity of oscillations corresponding to spectral peaks at higher frequencies cannot yet be resolved. For Green Bay, a 192 km (120 mile) long gulf opening into Lake Michigan, a remarkable double resonance is described in section 2 (g). The Bay responds as a viscously damped system driven by two forcing oscillations - the semidiurnal tide and the first mode of the main Michigan basin - at respective frequencies 1.93 and 2.67 cycles per day (c/d), one on each side of the natural frequency of the Bay-Lake system, 2.2 c/d (figures 9 and 10). In the Superior basin, topographically more complex than Michigan, the first three longitudinal modes are also the most conspicuous, but some modes above the third are also strongly excited. Of these, the fourth, fifth, and eighth modes can be identified through comparison with Rao & Schwab's (1976) numerical determinations. The most striking feature of the eighth mode, often strongly excited, is a transverse (N-S) oscillation of the eastern half of the basin as a negative amphidrome (figure 32b). In spite of prior removal of a linear trend from the input data, the spectra exhibit a steep rise in power as the low-frequency end is approached, where interpretation is therefore difficult. However, examination of the frequency range below 4 c/d, in section section 2 (h) and 3 (e) and in figure 11, establishes the following points: (i) for reasons discussed in the text, the semidiurnal tidal peak covers a narrower frequency range than peaks corresponding to the seiche modes; (ii) there is minor but persistent evidence of a co-oscillation of the main Michigan basin and Green Bay; (iii) diurnal oscillations arising from tidal and meterorological forcing, section 4, are generated more strongly in the Superior than in the Michigan basin; (iv) no spectral peaks are unambiguously identified as surface manifestations of internal waves known to be present, for example in the near-inertial frequency range 1.3-1.4 c/d; and (v) there is a small but significant rise in power near 0.35 c/d in spectra from both basins. Possible but not yet verified explanations of this rise are: meteorological forcing; excitation of a rotational mode (Rao & Schwab 1976); or both. For Lake Michigan a possible further explanation is provided by excitation of the lowest gravitational mode of the combined Michigan-Huron basin, seen in the currents of the connecting straits (figure 12).

The Structure and Energy Balance of Solar Active Regions

Abstract: The interpretation of the emission measures calculated from e.u.v. and X-ray line intensities is discussed. A general method for deriving the temperature and density structure and energy balance in either the quiet Sun or active regions is given. In particular simple relations are found between the coronal temperature, the pressure in the chromosphere-corona transition region, P$\_{0}$, the conductive flux at P$\_{0}$, the mechanical energy dissipated above P$\_{0}$ and the radiation losses above P$\_{0}$. A range of models for quiet and active regions is given. The rate of change of the mechanical energy deposition as a function of height is used to find empirical damping lengths which are compared with those expected from either the conduction damping of sound waves or the viscous damping of Alfven waves. The wave frequencies and peak amplitude velocities required to satisfy both the empirical and theoretical damping lengths and energy deposition rates are discussed.

Chemical Aspects of Rock Deformation [and Discussion]

Abstract: Studies of the rates of crystal growth at low supersaturations show that solutiongrowth processes may be dominant in the mechanism of deformation of wet rocks at very low values of differential stress. Strain rates in the order of 10-11 s"1 may be attained with differential stresses of 10 MPa. Rocks undergoing progressive burial metamorphism will pass through depth-temperature regions where fluids are generated and new phases developed. During such discontinuous dehydration bursts, the rocks will be porous and permeable and of low strength. When rocks are not dehydrating, or absorbing pore fluids as during uplift, solid-state deformation mechanisms may predominate.

Archaean Deformation Patterns in Southern Africa

Abstract: Strain measurements have been made to help quantify the intensity of deformation and amount of displacement across Archaean greenstone belts in Rhodesia and Botswana and across the gneisses of the Limpopo mobile belt. The area has been divided into three domains based on the orientation of the finite strain fabric and the orientation of the maximum extension direction in associated shear zones. The domains are considered to have different movement patterns and to be similar to small orogenic belts. Early deformation within the greenstone belts accompanied the intrusion of the diaipric granites, but there was also bulk translation and rotation of greenstone belt and gneiss leading to imbrication of the stratigraphic pile and the formation of large nappes of overturned rock. This was followed by regional phases of deformation which affected all the greenstone belts and the gneisses of the Limpopo belt. Detailed strain measurements show a variation in amount of shortening during this phase, from under 30 % across the Shabani-Bellingwe belt in central Rhodesia, to over 60 % across the Tati and Matsitama belts in northern Botswana. Many local variations in intensity of deformation occur within large ductile shear zones and deviations from plane strain may be partly due to such rotational deformation. The regional deformation pattern suggests that there was movement of the Rhodesian craton approximately 200 km to the southwest relative to the gneisses of the Limpopo belt, producing a dominantly flattening deformation in the southwest of Rhodesia, but dominantly simple shear with a nearly horizontal sinistral movement, in the southeast.