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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information STRUCTURAL GEOLOGY An Introduction to Geometrical Techniques fourth edition Many textbooks describe information and theories about ...

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

STRUCTURAL GEOLOGY An Introduction to Geometrical Techniques fourth edition

Many textbooks describe information and theories about the Earth without training students to utilize real data to answer basic geological questions. This volume – a combination of text and lab book – presents an entirely different approach to structural geology. Designed for undergraduate laboratory classes, it is dedicated to helping students solve many of the geometrical problems that arise from field observations. The basic approach is to supply step-by-step instructions to guide students through the methods, which include well-established techniques as well as more cutting-edge approaches. Particular emphasis is given to graphical methods and visualization techniques, intended to support students in tackling traditionally challenging two- and three-dimensional problems. Exercises at the end of each chapter provide students with practice in using the techniques, and demonstrate how observations and measurements from the field can be converted into useful information about geological structures and the processes responsible for creating them. Building on the success of previous editions, this fourth edition has been brought fully up-to-date and incorporates new material on stress, deformation, strain and flow. Also new to this edition are a chapter on the underlying mathematics and discussions of uncertainties associated with particular types of measurement. With stereonet plots and full solutions to the exercises available online at www.cambridge.org/ragan, this book is a key resource for undergraduate students as well as more advanced students and researchers wanting to improve their practical skills in structural geology. D o n R a g a n was educated at Occidental College, University of Southern California and at the University of Washington in Seattle, receiving his Ph.D. in 1960. He spent a year as a Fulbright Scholar at the University of Innsbruck, and later, with a National Science Foundation Fellowship, at Imperial College, London, where he received a Diploma of Membership in Geology (DIC). His teaching career at the University of Alaska, Fairbanks, and at Arizona State University has spanned a total of 34 years, and has focused on imbuing students with a thorough understanding of geometrical and analytical techniques in structural geology. His research interests center on the role of structural settings in structure-making processes, including studies of Alpine peridotites, glacial ice and welded tuffs.

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

STRUCTURAL GEOLOGY An Introduction to Geometrical Techniques fourth edition

donal m. ragan Arizona State University, USA

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/ragan c D. M. Ragan 2009
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2009 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library ISBN 978-0-521-89758-7 hardback ISBN 978-0-521-74583-3 paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

For ´ Janne, Anneliese and Asta

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

Contents

Preface Acknowledgements

page xv xvii

1 Structural planes 1.1 Introduction 1.2 Definitions 1.3 Dip and strike 1.4 Accuracy of angle measurements 1.5 Graphic methods 1.6 Finding apparent dip 1.7 Analytical solutions 1.8 Cotangent method 1.9 True dip and strike 1.10 Dip vectors 1.11 Three-point problem 1.12 Observed apparent dips 1.13 Exercises

1 1 1 2 5 10 13 15 17 18 20 24 25 27

2 Thickness and depth 2.1 Definitions 2.2 Thickness determination 2.3 Thickness by direct measurement 2.4 Thickness from indirect measurements 2.5 Apparent thickness 2.6 Thickness between non-parallel planes 2.7 Thickness in drill holes 2.8 Depth to a plane 2.9 Distance to a plane 2.10 Error propagation 2.11 Exercises

30 30 31 31 32 36 39 41 43 44 46 54 vii

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viii

Contents

3 Lines and intersecting planes 3.1 Definitions 3.2 Linear structures 3.3 Plunge of a line 3.4 Pitch of a line 3.5 Intersecting planes 3.6 Cotangent method 3.7 Structure contours 3.8 Line vectors 3.9 Accuracy of trend determinations 3.10 Exercises

57 57 57 59 61 64 65 66 67 69 71

4 Planes and topography 4.1 Exposures on horizontal surfaces 4.2 Effect of topography 4.3 Dip and strike from a geological map 4.4 Linear interpolation 4.5 Parallel lines 4.6 Three-point problem 4.7 Structure contours 4.8 Predicting outcrop patterns 4.9 Exercises

72 72 74 76 77 79 80 82 84 87

5 Stereographic projection 5.1 Introduction 5.2 Stereogram 5.3 Stereonet 5.4 Plotting techniques 5.5 Measuring angles 5.6 Attitude problems 5.7 Polar net 5.8 Dip and strike errors 5.9 Intersection errors 5.10 Exercises

88 88 88 92 93 99 101 104 105 106 107

6 Rotations 6.1 Introduction 6.2 Basic techniques 6.3 Sequential rotations 6.4 Rotations about inclined axes 6.5 Rotational problems 6.6 Tilting problems

109 109 109 114 116 118 119

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

Contents

6.7 6.8 6.9 6.10

ix

Two tilts Folding problems Small circles Exercises

121 122 124 128

7 Vectors 7.1 Introduction 7.2 Sum of vectors 7.3 Products of vectors 7.4 Circular distributions 7.5 Spherical distributions 7.6 Rotations 7.7 Rotational problems 7.8 Three-point problem

130 130 134 136 143 147 149 154 157

8 Faults 8.1 Definitions 8.2 Fault classification 8.3 Slip and separation 8.4 Faults in three dimensions 8.5 Slip and its determination 8.6 Overthrusts 8.7 Fault terminations 8.8 Faults and folds 8.9 Extension and contraction 8.10 Rotation 8.11 Facing on faults 8.12 Dilation of dikes 8.13 Exercises

165 165 166 168 172 174 179 182 184 185 188 194 195 197

9 Stress 9.1 Introduction 9.2 Traction 9.3 Stress components 9.4 Stress in two dimensions 9.5 Mohr Circle for stress 9.6 Superimposed stress states 9.7 Pole of the Mohr Circle 9.8 Role of pore pressure 9.9 Deviatoric and hydrostatic stress 9.10 Stress ellipse

198 198 199 201 204 209 215 217 222 223 224

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

x

Contents

9.11 9.12 9.13

Tractions versus forces Stress tensor Exercises

227 229 238

10 Faulting 10.1 Introduction 10.2 Experimental fractures 10.3 Role of friction 10.4 Coulomb criterion 10.5 Limitations 10.6 Classification of faults 10.7 Faults and stresses 10.8 States of stress at depth 10.9 Magnitudes of stress components 10.10 Open fractures 10.11 Stress drop 10.12 Faults in anisotropic rocks 10.13 Oblique faults 10.14 Other limitations 10.15 Earthquakes 10.16 Exercises

240 240 240 241 247 250 251 251 254 257 261 262 263 264 266 266 267

11

269 269 273 276 278 284 287 290 300

Deformation 11.1 Introduction 11.2 Continuum assumption 11.3 Homogeneous deformation 11.4 Analysis of simple shear 11.5 Superimposed deformations 11.6 Inhomogeneous deformation 11.7 Deformation and related tensors 11.8 Exercises

12 Strain 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9

Introduction Deformed grains Deformed fossils Deformed pebbles Geometry of the strain ellipse Mohr Circle for finite strain Pole of the Mohr Circle Strain from measured angles Strain from measured stretches

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302 302 302 304 306 309 313 315 316 321

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

Contents

12.10 12.11 12.12 13 Flow 13.1 13.2 13.3 13.4 13.5 13.6 13.7 14 Folds 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11 14.12 14.13

xi

Restoration Strain and related tensors Exercises

328 331 343

Introduction Active tectonics Ancient tectonics Progressive deformation Kinematics Deformation rates from structures Exercises

346 346 346 349 350 356 365 367

Introduction Single surfaces Relationships between surfaces Associated structures Fold orientation Isogon classification Thickness variation Alternative graphs Inverse thickness Best-fit indicatrix Determining the flattening index Competence Exercises

369 369 369 375 375 379 382 385 386 388 392 397 399 409

15 Parallel folds 15.1 Introduction 15.2 Rounded folds 15.3 Rounded folds in cross section 15.4 Balanced cross sections 15.5 Depth of folding 15.6 Non-parallel modifications 15.7 Angular folds 15.8 Angular folds in cross section 15.9 Faults in fold cores 15.10 Some problems 15.11 Exercises

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410 410 410 416 426 427 430 433 435 438 439 439

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

xii

Contents

16 Similar folds 16.1 Introduction 16.2 Geometry of shear folds 16.3 Single-sense shear 16.4 Shear folds in three dimensions 16.5 Superposed folds in two dimensions 16.6 Wild folds 16.7 Superposed folds in three dimensions 16.8 Exercises

441 441 441 443 444 445 449 450 452

17 Folds and topography 17.1 Map symbols 17.2 Outcrop patterns 17.3 Down-plunge view 17.4 Fold profile 17.5 Hinge and hinge plane 17.6 Computer graphs 17.7 Transformation of axes 17.8 Cautionary note 17.9 Exercises

454 454 454 456 459 463 463 464 467 467

18 Structural analysis 18.1 Introduction 18.2 S-pole and beta diagrams 18.3 Fold axis and axial plane 18.4 Equal-area projection 18.5 Polar net 18.6 Equal areas 18.7 Contoured diagrams 18.8 Statistics of scatter diagrams 18.9 Computer-generated diagrams 18.10 Interpretation of diagrams 18.11 Superimposed folds 18.12 Sampling problems 18.13 Engineering applications 18.14 Exercises

468 468 468 469 470 473 473 474 478 480 482 484 487 489 490

19 Tectonites 19.1 Introduction 19.2 Isotropy and homogeneity 19.3 Preferred orientation 19.4 Planar and linear fabrics 19.5 Complex structures

493 493 493 494 494 500

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

Contents

19.6 19.7

xiii

LS tectonites Exercises

502 502

20 Drill hole data 20.1 Introduction 20.2 Oriented cores 20.3 Cores without orientation 20.4 Cores with a known plane 20.5 Two drill holes 20.6 Analytical solution 20.7 Three drill holes 20.8 Interpretation of folds 20.9 Exercises

504 504 505 507 510 511 513 515 516 517

21 Maps and cross sections 21.1 Geological maps 21.2 Other types of maps 21.3 Geological history 21.4 Structure sections 21.5 Other types of sections 21.6 Vertical exaggeration 21.7 Enlarged sections 21.8 Exercises

518 518 521 522 523 527 527 532 533

22 Block diagrams 22.1 Introduction 22.2 Isometric projection 22.3 Isometric cube as a strain problem 22.4 Orthographic projection 22.5 General cube 22.6 Computer plot of cube 22.7 Geological structure 22.8 Orthographic cube as a strain problem 22.9 Topography 22.10 Modified blocks 22.11 Exercises

534 534 534 536 539 540 541 543 544 547 548 550

Appendices A Descriptive geometry B Spherical trigonometry References Index

551 564 578 595

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

Preface

The first steps in the study of geological structures are largely geometrical. This is true in the historical development of our knowledge of such structures, in the initial stages of any field investigation, and in the education of a structural geologist. This concern for geometry includes the methods of describing and illustrating the form and orientation of geological structures, and the solution of various dimensional aspects of these structures. This book attempts to fill a need for an introduction to the geometrical techniques used in structural geology. I have sought an approach which is basic yet modern. The topics covered include well-established techniques, newer approaches which hold promise and an introduction to certain fundamental mechanical concepts and methods. Students who go no further in structural geology should have a working knowledge of the basic geometrical techniques and at least some appreciation of where the field is headed. Those who do go on, either in advanced courses or on their own should have the necessary foundation. The first few chapters apply the methods of orthographic projection to the solution of simple structural problems. An introduction or review of these methods is given in AppendixA.Application to geological and topographical maps are included and extensive use is made of Mackin’s powerful method of visualization – the down-structure view of geological maps. The method of stereographic projection and the stereonet, together with the methods of plotting and solving angular problems are introduced fairly early. Many of the same elementary problems as well as some more advanced ones are solved with their uses. Faults are described and classified. Problems of displacement are solved by combining orthographic and stereographic methods. The geometry of states of stress in two dimensions is then given in some detail. With this as background the Coulomb criterion of shear failure is applied to the interpretation of shear and extensional fractures in rocks. Folds are described and classified in a similar way. In particular, the orientation and geometry are treated thoroughly. The powerful isogon classification of the shape of a single folded layer is treated in some detail. The relationship of these shapes to deformation and strain is briefly outlined. Parallel and similar folds are the subject of separate chapters. xv

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

xvi

Preface

The subject has a mathematical side. It is a common observation that geology students, despite having been exposed to these matters in other courses, do not retain much of the material. As Vacher (1998, p. 292) put it, “Students leave that information in ‘that other building’ when they go to their geology classes.” An important part of the problem is that they do not have much opportunity, especially in introductory courses, to see how mathematics can be applied to geology. I have sought a variety of ways to address this deficiency by including a number of applications throughout the book. Most of this material has been placed in separate modules close to the areas to which they apply. Thus an instructor or reader can use them, or not, but they can not be easily ignored. With one exception, the mathematics will be recognized from introductory courses in physics and calculus. The exception is a brief introduction to matrix algebra, a powerful, natural language of vectors and tensors. Even at these early stages it is important to realize that geometry is not the end. The final goal, however elusive, is a complete understanding of the processes responsible for the structure in as great detail as possible. This is a branch of applied mechanics (see Pollard & Fletcher, 2005).While an introductory course is not the place to treat these matters in any great detail, it most certainly is the place to set the stage for such a consideration. In particular, it is important to understand the core concepts of stress, deformation, strain and flow.

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Cambridge University Press 978-0-521-74583-3 - Structural Geology: An Introduction to Geometrical Techniques, Fourth Edition Donal M. Ragan Frontmatter More information

Acknowledgements

There have been many bumps along the way, some small, some not so small. For their help over these, I thank Ray Arrowsmith, Declan De Paor, George Hilley, Richard Lisle, Win Means, Simon Peacock, Steve Semkin, Rick Stocker, Al Swimmer, Sue Treagus, Len Vacher, Frederick Vollmer, Dave Waltham, and Mark Zoback. Special thanks to Ramo´ n Arrows...