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The Morphology and Development of Folds A THE MORPHOLOGY AND DEVELOPMENT OF FOLDS A thesis submitted for the degree of Ph.D. of the University of London by Peter John Hudleston May 1969 2 ABSTRACT This thesis is concerned with the description, classification, analysis and interpretation of folds based on their morphologic properties. Existing methods of geometrical fold analysis are critically examined. Many are found to be impracticable. Two new analytical techniques are presented, one based on the use of dip isogons and the other based on harmonic analysis. A Visual method of rapid harmonic analysis is described that involves no measurements. Theories of fold development are discussed with particular reference to folds developed by buckling in isolated competent layers embedded in a less competent matrix. The geometric form of folds predicted by theory are examined. Emphasis is placed on the geometric forms taken up by buckle folds and by buckle folds modified by compression. A series of buckling experiments in single viscous layers embedded in a less viscous matrix at low viscosity contrasts are described. Progressive development of the shape of the experimentally formed folds is analysed and interpreted in terms of buckling theory. Detailed analyses of minor folds, in small parts of the Moine rocks in Scotland, the basement gneisses in the Swiss Alps and the Culm sediments on the Cornish coast are described. In the rocks of each region the geometric forms of the folds are shown to be different in each fold phase, and are also shown to be related to differences in layer composition. By analogy with the forms of folds predicted theoretically and observed experimentally the geometric forms of the natural folds are accounted for by processes of buckling and 'flattening'. Estimates of 'viscosity' contrast and bulk deformation within the profile planes of the folds are made in two instances. 3 CONTENTS Page CHAPTER 1 INTRODUCTION 1.1 General Statement 7 1.2 Soto Definiticns of Terms 9 1.3 Symbols Used in the Text 10 CHAPTER 2 DESCRIPTIVE FOLD GEOMETRY 2.1 Introduction 12 2.2 General Geometry 12 2.3 Folded Layer Geometry 15 2.3.1 Thickness Parameters 16 2.3.2 Isogons 16 2.3.3 Isogon Plot - k against a 21 2.3.4 Relationship between ta l 0a, and a 22 2.3.5 Fold Classification 26 2.3.6 Errors in Measurement and Datum Fixing 35 2.3.7 Discussion 36 2.4 The Geometry of Single Folded Surfaces 39 2.5 Harmonic (Fourier) Analysis of Folds 42 2.5.1 Fourier Analysis in Geology 45 2.5.2 Fold Analysis using Harmonic Analysis 45 2.5.3 Theory 46 2.5.4 Selection of Coordinates for Analysis 50 2.5.5 Procedure for Analysis 51 2.5.6 Representation of Computed Coefficients 52 2.5.7 Visual Harmonic Analysis 63 2.5.8 Errors and Reproducibility 68 2.6 Techniques of Natural Fold Measurement 71 CILIPThii 3 THE THEORIES OF FOLD DEVELOPMENT AND GEOMETRIC FORM OF FOLDS. 3.1 Introduction 73 3.2 Passive Folds 74 3.3 Exact Mathematical Treatments 75 4 Page 3.4 The Shape of Buckled Layers 84 3.5 Homogeneous Flattening of Folds 86 3.5.1 Oblique Flattening in the Profile.Plane 99 3.6 Simultaneous Buckling and Flattening 99 CHAPTER 4 EXPERIMENTS ON BUCKLING 4.1 Introduction 107 4.2 Model Study Problems 109 4.3 Apparatus and Materials 110 4.4 Experimental Methods 118 4.5 Homogeneity of Strain and Boundary Effects 122 4.6 Results 127 4.6.1 Changes in Arc Length 127 4.6.2 Thickness Variation in the Buckled Layers 134 4.6.3 Wavelength/Thickness Ratios 135 4.6.4 Amplification 135 4.6.5 Harmonic Analysis of Fold Shape 138 4.6.6 aperimental Simultaneous Buckling and Flattening. 143 4.7 Interpretation 150 4.8 Discussion 154 4.9 Interpretation of Naturally Formed Folds 161 4.10 Conclusions 163 CHAPTER 5 AN ANALYSIS OF MINOR FOLDS IN THE MOINIAN ROCKS OF MONAR, INVERNESS—SHIRE. 5.1 Introduction 164 5.2 Lithology 164 5.3 Metamorphism 170 5.4 Structural Geology 170 5.4.1 Rock Fabric 171 5.5 Descriptive Geometry 171 5 Page_ 5.5.1 Size of Folds 174 5.5.2 Fold Order and Asymmetry 177 5.5.3 Isogon Patterns 180 5.5.4 Interlimb Angle Variation 180 5.5.5 Thickness/Dip Variations 185 5.5.6 Harmonic Analysis of Fold Shape 202 5.5.6.1 Analysis of b1 205 1 5.5.6.2 Analysis of b3/b 208 5.6 Interpretation 223 5.6.1 Discussion 228 5.7 A Study of Wavelength/Thickness in Ptygmatic Folds in Pegmatitic Veins 230 5.8 An Analysis of Deformed Lineations 239 5.9 Conclusions 248 CHAPTER 6 AN ANALYSIS OF MINOR FOLDS IN PART OF THE MAGGIA NAPPE„ TICINO, SWITZERLAND 6.1 Introduction 250 6.1.1 Lithology and Mineralogy 253 6.1.2 Metamorphism 253 6.2 Structural Geology 254 6.2.1 Mineral Fabric 261 6.3 Descriptive Geometry 261 6.3.1 Isogon Plots and Thickness/Dip Relationships 262 6.3.2 Harmonic Analysis of Fold Shape 275 6.3.3 Refolded Folds 281 6.4 Interpretation 281 6.4.1 Discussion 289 6.5 A Wavelength/Thickness Study of F2 Folds 291 6.6 Conclusions 294 6 Page CHAPTER 7 AN ANALYSIS OF MINOR FOLDS IN THE CULM MEASURES AT BOSCASTLE, CORNWALL 7.1 Introduction 297 7.1.1 Lithology 297 7.2 Structural Geology 300 7.2.1 Fabric 306 7.3 Descriptive Geometry 307 7.3.1 Isogon Plots and Thickness/Dip Relationships 308 7.3.2 Harmonic Analysis of Fold Shape 318 7.3.3 Deformed Lineation Loci 321 7.3.4 Interlimb Angles and Limb Length Ratios 321 7.3.5 Miscellaneous Features 328 7.4 Interpretation and Discussion 328 7.5 Conclusions 336 CHAPTER 8 SYNTHESIS 8.1 A Comparison of the Results of the Three Detailed 337 Fold Studies 337 8.2 Summary and Conclusions 340 ACKNOWLEDGMENTS 342 REFERENCES 343 APPENDIX 352 7 CHAPTER 1 INTRODUCTION 1.1 GENERAL STATEMENT In many zones where the earth's crust has been deformed the litho— logical layers take up folded forms. For many years structural geologists have speculated as to the processes by which solid rock may become deformed by ductile flow without fracture, to form these familiar structures; and in recent years this problem has received increasing attention. Interest in the subject has followed several lines of approach, all of which have led to a better understanding of folds and folding processes. One approach has used mathematical analysis to provide a basis for predicting the geometrical features of folds (and involved making many simplifying assumptions for rock). A second approach has studied the experimental development of folds, usually in materials with properties scaled to simulate what are believed to be the properties of rock in the earth's crust. A third approach has investigated the forms of natural folds, using various methods of geometrical analysis in order to elucidate the fold geometry. Perhaps the most significant progress in this direction in recent years has been the elucidation of fold geometry in zones of complex and repeated deformation (as in the Moine and Dalradian rocks of Scotland). It is an unfortunate fact that in natural folds it is seldom possible to compute the sta- es of strain in the folded layers, and in most folds all that is available to the structural geologist is the geometric form of the bedding or foliation surfaces and tectonic structures such as cleavage or schistosity. Even in the most favourable situation where the state of strain may be evaluated in natural folds, it is impossible to know the 'strain path' by which the final fold form was attained (Ramsay, 1967, P.343). 8 In any classification of folds their geometric form (in terms of the shape of both folded layers and individual surfaces) is important, because it is one feature of folds that is always available for study. Methods of accurately describing these geometric features are necessary if analysis and classification of folds are to be made. By use of methods of accurate fold description a link between the three approaches to folding referred to above may be made. Some workers (e.g. Donath & Parker, 1964) consider that fold classification should be placed on a genetic basis. Whilst this seems to be the best way of classifying folds it is not practical because fold genesis in rocks is imperfectly understood at the present time, and has to be inferred from the end products of folding processes. It seems advisable to distinguish between classifications based on fold geometry and those based on folding processes. In the past geologists have often described the geometrical forms of folds in general impressions of fold shape and style. This practice has never been very satisfactory because of the absence of agreed nomenclature, and because no detailed analysis of fold shape can be made on this basis. This thesis is primarily concerned with fold morphology and concerns the problems of fold analysis and classification based upon the geometrical properties of folds. An attempt is made to link theoretical and experim— ental work to the interpretation of natural folds by means of detailed geometrical analysis. Several new analytical techniques are presented that have proved useful both in the determination of natural fold geometry and as an aid in the interpretation of folds in terms of folding processes. No attempt will be made to criticise or analyse the bulk of the previous work on the subject of folding; the relevant work on each aspect of folding considered in this thesis will be discussed at the beginning 9 of each Chapter.
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