Strain Patterns in Rocks (eBook)

Front Cover 1
Strain Patterns in Rocks 2
Copyright Page 3
Table of Contents 4
PREFACE 6
Chapter 1. Strain analysis using the shape of expected and observed continuous frequency distributions 8
INTRODUCTION 8
THEORETICAL JUSTIFICATION: DISTRIBUTION CLASSIFICATION 8
STRAIN ANALYSIS USING ß1 vs ß 
9 
CONCLUSIONS 14
REFERENCES 14
Chapter 2. Finite strain estimation using 'anti-clustered' distributions of points 
16 
INTRODUCTION 16
SOME THEORETICAL CONSIDERATIONS 16
INFLATING ELLIPSE METHOD 17
THE CASÉVEL SPILITE: A CASE STUDY 18
SUGGESTIONS FOR FURTHER STUDY 25
REFERENCES 26
Chapter 3. Finite strain determination of gneiss: application of Fry's method to porphyroid in the southern Massif Central (France) 28
INTRODUCTION 28
THE METHOD 28
GEOLOGICAL SETTING 28
THE MARKERS USED IN THE PORPHYROID GNEISSES: METHODOLOGICAL IMPLICATIONS 29
RESULTS 29
DISCUSSION 33
CONCLUSIONS 36
REFERENCES 36
Chapter 4. Orthographic analysis of geological structures— 
38 
INTRODUCTION 38
THE STRETCH TENSOR AND ELLIPSOID 42
SURFACES RELATED TO THE STRETCH ELLIPSOID 45
THE DEFORMATION TENSOR AND ELLIPSOID 49
HETEROGENEOUS DEFORMATION 58
CONCLUSIONS 59
REFERENCES 59
Chapter 5. Application of the Mohr-circle construction to problems of inhomogeneous deformation 62
NOMENCLATURE 62
INTRODUCTION 62
MOHR CIRCLES FOR ASYMMETRIC TENSORS 62
APPLICATION TO PROBLEMS OF INHOMOGENEOUS DEFORMATION 65
CONCLUSIONS 69
REFERENCES 69
Chapter 6. The compatibility equations and the pole to the Mohr circle 70
NOMENCLATURE 70
INTRODUCTION 70
THE EQUATIONS IN STANDARD FORM 70
SIMPLIFICATION BY TRANSFORMATION 71
EXPERIMENTAL VERIFICATION OF EQUATIONS 72
PURE FLATTENING AND COMPACTION OF A BED 73
UNIFORM AREA STRAIN 73
THREE-DIMENSIONAL STRAIN DISTRIBUTIONS 74
APPENDIX 1: DERIVATION OF THE FINITE STRAIN COMPATIBILITY EQUATIONS 78
APPENDIX 2: TRANSFORMATION OF THE COMPATIBILITY EQUATIONS 79
REFERENCES 79
Chapter 7. Spatial integration of strains using finite elements 82
INTRODUCTION 82
MATHEMATICAL BASIS FOR USING FINITE ELEMENTS 82
THE FINITE ELEMENT METHOD 83
FITTING OF FINITE ELEMENTS 84
ERRORS 86
CONCLUSIONS 87
REFERENCES 87
APPENDIX 88
Chapter 8. A general harmonic coordinate transformation to simulate the states of strain in inhomogeneously deformed rocks 90
INTRODUCTION 90
A GENERAL HARMONIC TRANSFORMATION APPLIED TO FOLDS 91
INTRODUCTION OF OTHER ASSUMPTIONS TO FURTHER CONSTRAIN STATES OF STRAIN 95
SUMMARY 102
REFERENCES 103
Chapter 9. Isotropic points and lines in strain fields 104
INTRODUCTION 104
FLOW MODELS 104
ASSOCIATIONS OF ISOTROPIC POINTS AND LINES RESULTING FROM DOUBLET-TYPE FLOW 105
ISOTROPIC POINTS RESULTING FROM SUPERPOSITION OF SEVERAL ELEMENTARY FLOWS 106
THREE-DIMENSIONAL ASPECTS OF ISOTROPIC FEATURES 107
DISCUSSION AND CONCLUSIONS 109
REFERENCES 109
APPENDIX 110
Chapter 10. Estimation of volume changes by comparative chemical analyses in heterogeneously deformed rocks (folds with mass transfer) 112
INTRODUCTION 112
PRINCIPLES AND LIMITS OF THE VOLUME CHANGE DETERMINATION METHOD 112
APPLICATIONS TO SOME FOLD EXAMPLES 116
CONCLUSIONS 121
REFERENCES 121
Chapter 11. Kinematic and mechanical discontinuity at a coherent interface 124
INTRODUCTION 124
KINEMATICS 124
MECHANICS 128
CONCLUSIONS 130
REFERENCES 131
Chapter 12. A theory of finite strain variation through contrasting layers, and its bearing on cleavage refraction 134
INTRODUCTION 134
THEORETICAL MODEL OF TWO-DIMENSIONAL FINITE STRAIN REFRACTION 136
STRAIN REFRACTION RESULTS, PLANE STRAIN 138
STRAIN REFRACTION RESULTS FOR NON-PLANE-STRAIN ELLIPSOIDS 142
STRAIN REFRACTION RESULTS FOR OTHER PRINCIPAL PLANES 143
GENERAL FINITE STRAIN REFRACTION 145
GEOLOGICAL DISCUSSION 145
CONCLUSIONS 149
REFERENCES 150
APPENDIX 1 150
APPENDIX 2 151
Chapter 13. Theoretical strain patterns in ductile zones simultaneously undergoing heterogeneous simple shear and bulk shortening 152
INTRODUCTION 152
MODEL 152
PARTICLE PATHS 153
FINITE STRAIN 154
CONTRACTION ACROSS SHEAR ZONE 155
PASSIVE STRAIN MARKERS 164
CONCLUSIONS 164
REFERENCES 164
Chapter 14. Complex strain patterns developed at the frontal and lateral tips to shear zones and thrust zones 166
TIPS TO THRUST AND SHEAR ZONES 166
DISPLACEMENTS IN SHEAR ZONES 169
DISCUSSION AND CONCLUSIONS 175
REFERENCES 180
APPENDIX 181
Chapter 15. State of strain in a quartzite mylonite, Central Australia 184
INTRODUCTION 184
GENERAL GEOLOGY 185
OPTICAL MICROSTRUCTURES 185
STRAIN DETERMINATION 188
DISCUSSION 191
CONCLUSIONS 192
REFERENCES 192
Chapter 16. Strain pattern in the Aar Granite (Central Alps): orthogneiss developed by bulk inhomogeneous flattening 194
INTRODUCTION AND GEOLOGICAL SETTING 194
GEOMETRY OF LARGE-SCALE STRUCTURES 194
ASPECTS OF INHOMOGENEOUS STRAIN AROUND WEAKLY-DEFORMED LENSES 195
DUCTILE-DEFORMATION GRADIENTS 198
FINITE STRAIN VERSUS DEGREE OF MYLONITIZATION 199
DISCUSSION AND DEFORMATION MODEL 199
CONCLUSIONS 200
REFERENCES 201
Chapter 17. Strain patterns of crescentic granitoid plutons in the Archean greenstone terrain of Ontario 202
INTRODUCTION 202
GREENWATER LAKE PLUTON: EXAMPLE OF AN ANTIFORMAL STRUCTURE 203
McNEVIN PLUTON: EXAMPLE OF A SYNFORMAL STRUCTURE 204
JACKFISH–WELLER LAKES PLUTON 206
VICKERS LAKE PLUTON, A COMPOSITE ANTIFORMAL INTRUSION 208
INTERPRETATION OF NATURAL STRAIN PATTERNS 208
SUMMARY AND CONCLUSIONS 211
REFERENCES 212
Chapter 18. Strain distribution within the Pardailhan Nappe (Montagne Noire, France) and structure of its basal thrust zone: implications for events associated with nappe emplacement 214
INTRODUCTION—GEOLOGICAL SETTING 214
THE PARDAILHAN NAPPE 214
STRAIN STUDY WITHIN THE PARDAILHAN NAPPE 216
THE FABRIC ELLIPSOID FROM TEXTURE GONIOMETRY 216
GEOMETRICAL ANALYSIS IN THE BASAL THRUST ZONE 220
ROTATION OF FIRST PHASE MICROSTRUCTURES 220
MICROSTRUCTURES IN THE THRUST ZONE 221
DISCUSSION AND CONCLUSION 222
REFERENCES 222
Chapter 19. Finite strain patterns in some Alpine nappes 224
INTRODUCTION 224
THE GLARUS NAPPE 224
THE MORCLES NAPPE 225
THE CHARTREUSE MASSIF 227
THE DIGNE NAPPE 230
DISCUSSION 230
REFERENCES 231
Chapter 20. Patterns of folding and strain influenced by linearly anisotropic bands 232
INTRODUCTION 232
FIELD OBSERVATIONS OF CRENULATED FIBRES 232
INTERPRETATION 236
DISCUSSION 237
REFERENCES 237
Chapter 21. Strain patterns in an ice cap and implications for strain variations in shear zones 238
INTRODUCTION 238
NUMERICAL MODEL FOR STEADY-STATE PLANE FLOW 238
MODIFICATION FOR RADIAL FLOW 240
PERTURBATION OF FLOW— GENERAL CONSIDERATIONS 241
EXAMPLE OF PERTURBATION OF GLACIAL FLOW 242
DISCUSSION AND CONCLUSIONS 245
REFERENCES 245
Chapter 22. Strain fields in and around boudins in a clay experiment 248
INTRODUCTION 248
THE CLAY EXPERIMENT 248
RESULTS 249
DISCUSSION 251
CONCLUSIONS 252
REFERENCES 252