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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 combi- nation 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. Exer- cises 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.

Don Ragan 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 Sci- ence Foundation Fellowship, at Imperial College, London, where he received a Diploma of Membership in Geology (DIC). His teaching career at the University of Alaska, Fair- banks, 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.

© in this web service Cambridge University Press www.cambridge.org 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

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao˜ 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.

For Janne, Anneliese and Asta´

Contents

Preface page xv Acknowledgements xvii

1 Structural planes 1 1.1 Introduction 1 1.2 Deﬁnitions 1 1.3 Dip and strike 2 1.4 Accuracy of angle measurements 5 1.5 Graphic methods 10 1.6 Finding apparent dip 13 1.7 Analytical solutions 15 1.8 Cotangent method 17 1.9 True dip and strike 18 1.10 Dip vectors 20 1.11 Three-point problem 24 1.12 Observed apparent dips 25 1.13 Exercises 27

2 Thickness and depth 30 2.1 Deﬁnitions 30 2.2 Thickness determination 31 2.3 Thickness by direct measurement 31 2.4 Thickness from indirect measurements 32 2.5 Apparent thickness 36 2.6 Thickness between non-parallel planes 39 2.7 Thickness in drill holes 41 2.8 Depth to a plane 43 2.9 Distance to a plane 44 2.10 Error propagation 46 2.11 Exercises 54

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viii Contents

3 Lines and intersecting planes 57 3.1 Deﬁnitions 57 3.2 Linear structures 57 3.3 Plunge of a line 59 3.4 Pitch of a line 61 3.5 Intersecting planes 64 3.6 Cotangent method 65 3.7 Structure contours 66 3.8 Line vectors 67 3.9 Accuracy of trend determinations 69 3.10 Exercises 71

4 Planes and topography 72 4.1 Exposures on horizontal surfaces 72 4.2 Effect of topography 74 4.3 Dip and strike from a geological map 76 4.4 Linear interpolation 77 4.5 Parallel lines 79 4.6 Three-point problem 80 4.7 Structure contours 82 4.8 Predicting outcrop patterns 84 4.9 Exercises 87

5 Stereographic projection 88 5.1 Introduction 88 5.2 Stereogram 88 5.3 Stereonet 92 5.4 Plotting techniques 93 5.5 Measuring angles 99 5.6 Attitude problems 101 5.7 Polar net 104 5.8 Dip and strike errors 105 5.9 Intersection errors 106 5.10 Exercises 107

6 Rotations 109 6.1 Introduction 109 6.2 Basic techniques 109 6.3 Sequential rotations 114 6.4 Rotations about inclined axes 116 6.5 Rotational problems 118 6.6 Tilting problems 119

Contents ix

6.7 Two tilts 121 6.8 Folding problems 122 6.9 Small circles 124 6.10 Exercises 128

7 Vectors 130 7.1 Introduction 130 7.2 Sum of vectors 134 7.3 Products of vectors 136 7.4 Circular distributions 143 7.5 Spherical distributions 147 7.6 Rotations 149 7.7 Rotational problems 154 7.8 Three-point problem 157

8 Faults 165 8.1 Deﬁnitions 165 8.2 Fault classiﬁcation 166 8.3 Slip and separation 168 8.4 Faults in three dimensions 172 8.5 Slip and its determination 174 8.6 Overthrusts 179 8.7 Fault terminations 182 8.8 Faults and folds 184 8.9 Extension and contraction 185 8.10 Rotation 188 8.11 Facing on faults 194 8.12 Dilation of dikes 195 8.13 Exercises 197

9 Stress 198 9.1 Introduction 198 9.2 Traction 199 9.3 Stress components 201 9.4 Stress in two dimensions 204 9.5 Mohr Circle for stress 209 9.6 Superimposed stress states 215 9.7 Pole of the Mohr Circle 217 9.8 Role of pore pressure 222 9.9 Deviatoric and hydrostatic stress 223 9.10 Stress ellipse 224

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9.11 Tractions versus forces 227 9.12 Stress tensor 229 9.13 Exercises 238

10 Faulting 240 10.1 Introduction 240 10.2 Experimental fractures 240 10.3 Role of friction 241 10.4 Coulomb criterion 247 10.5 Limitations 250 10.6 Classiﬁcation of faults 251 10.7 Faults and stresses 251 10.8 States of stress at depth 254 10.9 Magnitudes of stress components 257 10.10 Open fractures 261 10.11 Stress drop 262 10.12 Faults in anisotropic rocks 263 10.13 Oblique faults 264 10.14 Other limitations 266 10.15 Earthquakes 266 10.16 Exercises 267

11 Deformation 269 11.1 Introduction 269 11.2 Continuum assumption 273 11.3 Homogeneous deformation 276 11.4 Analysis of simple shear 278 11.5 Superimposed deformations 284 11.6 Inhomogeneous deformation 287 11.7 Deformation and related tensors 290 11.8 Exercises 300

12 Strain 302 12.1 Introduction 302 12.2 Deformed grains 302 12.3 Deformed fossils 304 12.4 Deformed pebbles 306 12.5 Geometry of the strain ellipse 309 12.6 Mohr Circle for ﬁnite strain 313 12.7 Pole of the Mohr Circle 315 12.8 Strain from measured angles 316 12.9 Strain from measured stretches 321

Contents xi

12.10 Restoration 328 12.11 Strain and related tensors 331 12.12 Exercises 343

13 Flow 346 13.1 Introduction 346 13.2 Active tectonics 346 13.3 Ancient tectonics 349 13.4 Progressive deformation 350 13.5 Kinematics 356 13.6 Deformation rates from structures 365 13.7 Exercises 367

14 Folds 369 14.1 Introduction 369 14.2 Single surfaces 369 14.3 Relationships between surfaces 375 14.4 Associated structures 375 14.5 Fold orientation 379 14.6 Isogon classification 382 14.7 Thickness variation 385 14.8 Alternative graphs 386 14.9 Inverse thickness 388 14.10 Best-fit indicatrix 392 14.11 Determining the flattening index 397 14.12 Competence 399 14.13 Exercises 409

15 Parallel folds 410 15.1 Introduction 410 15.2 Rounded folds 410 15.3 Rounded folds in cross section 416 15.4 Balanced cross sections 426 15.5 Depth of folding 427 15.6 Non-parallel modiﬁcations 430 15.7 Angular folds 433 15.8 Angular folds in cross section 435 15.9 Faults in fold cores 438 15.10 Some problems 439 15.11 Exercises 439

xii Contents

16 Similar folds 441 16.1 Introduction 441 16.2 Geometry of shear folds 441 16.3 Single-sense shear 443 16.4 Shear folds in three dimensions 444 16.5 Superposed folds in two dimensions 445 16.6 Wild folds 449 16.7 Superposed folds in three dimensions 450 16.8 Exercises 452

17 Folds and topography 454 17.1 Map symbols 454 17.2 Outcrop patterns 454 17.3 Down-plunge view 456 17.4 Fold proﬁle 459 17.5 Hinge and hinge plane 463 17.6 Computer graphs 463 17.7 Transformation of axes 464 17.8 Cautionary note 467 17.9 Exercises 467

18 Structural analysis 468 18.1 Introduction 468 18.2 S-pole and beta diagrams 468 18.3 Fold axis and axial plane 469 18.4 Equal-area projection 470 18.5 Polar net 473 18.6 Equal areas 473 18.7 Contoured diagrams 474 18.8 Statistics of scatter diagrams 478 18.9 Computer-generated diagrams 480 18.10 Interpretation of diagrams 482 18.11 Superimposed folds 484 18.12 Sampling problems 487 18.13 Engineering applications 489 18.14 Exercises 490

19 Tectonites 493 19.1 Introduction 493 19.2 Isotropy and homogeneity 493 19.3 Preferred orientation 494 19.4 Planar and linear fabrics 494 19.5 Complex structures 500

Contents xiii

19.6 LS tectonites 502 19.7 Exercises 502

20 Drill hole data 504 20.1 Introduction 504 20.2 Oriented cores 505 20.3 Cores without orientation 507 20.4 Cores with a known plane 510 20.5 Two drill holes 511 20.6 Analytical solution 513 20.7 Three drill holes 515 20.8 Interpretation of folds 516 20.9 Exercises 517

21 Maps and cross sections 518 21.1 Geological maps 518 21.2 Other types of maps 521 21.3 Geological history 522 21.4 Structure sections 523 21.5 Other types of sections 527 21.6 Vertical exaggeration 527 21.7 Enlarged sections 532 21.8 Exercises 533

22 Block diagrams 534 22.1 Introduction 534 22.2 Isometric projection 534 22.3 Isometric cube as a strain problem 536 22.4 Orthographic projection 539 22.5 General cube 540 22.6 Computer plot of cube 541 22.7 Geological structure 543 22.8 Orthographic cube as a strain problem 544 22.9 Topography 547 22.10 Modiﬁed blocks 548 22.11 Exercises 550

Appendices A Descriptive geometry 551 B Spherical trigonometry 564 References 578 Index 595

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.

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.

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 Ramon´ Arrowsmith who took over the introductory course when I retired. He made a number of suggestions which led to important improvements and helped in many other ways. Finally I wish to acknowledge the many years of support and encouragement by the late Troy L. Pew´ e.´ By his own admission he regretted his lack of proﬁciency in mathematics. And yet, far better than most, he understood its important role in the teaching and practice of geology.

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