Fundamentals of Structural Geology Fundamentals of Structural Geology provides a new working in related disciplines, including geophysics, framework for the investigation of geological struc- rock mechanics, field mapping, hydrogeology, petro- tures by integrating field mapping and mechanical leum and geotechnical engineering, and natural analysis. It emphasizes the observational data, hazard mitigation. The book is supported by a modern mapping technology, principles of contin- website (www.cambridge.org/ 0521839270) hosting uum mechanics, and the mathematical and compu- images from the book, additional colour images, tational skills, necessary to map, describe, model, student exercises and MATLAB® scripts. Solutions to and explain deformation in the Earth’s lithosphere the exercises are available to instructors. quantitatively. Assuming a basic knowledge of physical geology, david pollard is the Morris Professor of Earth introductory calculus, and physics, this advanced Sciences in the Department of Geological and textbook builds on more traditional courses that Environmental Sciences at Stanford University emphasize descriptive terminology, geometric tech- where he co-directs the program in Structural niques, and kinematics. In a significant departure Geology and Geomechanics. He and his students are from conventional textbooks on the subject, differ- using quantitative field data and principles of struc- ential geometry is introduced and applied to quan- tural geology, combined with laboratory and com- tify descriptions of geological structures. Differential puter modeling, to address questions about processes geometry integrates the spatial information conven- of faulting, fracturing, and rock deformation. The tionally found on maps with orientation data from research aims to understand how faults and fractures stereograms to provide reproducible descriptions of evolve in the Earth’s crust; how they affect the flow geological structures. By starting from the funda- of magma, groundwater, and hydrocarbons; and mental conservation laws of mass and momentum, what role fractures play in earthquake generation the constitutive laws of material behavior, and the and volcanic eruption kinematic relationships for strain and rate of defor- mation, the authors demonstrate the relevance of raymond fletcher is a Research Professor in solid and fluid mechanics to structural geology. theDepartment of Geosciences at the Pennsylvania The constitutive relations used in the book are StateUniversity. He and his collaborators study the sufficiently elementary to enable students to gain continuous deformation of rock as in the emplace- physical insight from analytical solutions, but are ment of mantled gneiss domes, rock folding, and adequately realistic to provide compelling correla- basin and range necking. He also works on processes tions to observational data. linking chemical aspects of mineral growth or disso- This book offers a modern quantitative approach lution in rocks and deformation. Currently he is to structural geology for advanced undergraduate studying folding near the base of ice sheets, and the and graduate students and researchers in structural evolution of structures and rheological behavior of geology and tectonics. It will also interest those composite rock masses. Fundamentals of Structural Geology David D. Pollard Stanford University and Raymond C. Fletcher The Pennsylvania State University Contents Preface pageix Acknowledgments xi Chapter 1 Motivations and opportunities 1 1.1 Earthquake hazards in southern California 2 1.2 Radar lineaments on Venus 9 1.3 Faulting in a North Sea hydrocarbon reservoir 11 1.4 Anticracks in southern France 16 1.5 Mountain building on the Colorado Plateau 20 1.6 Concluding remarks 24 Chapter 2 Structural mapping techniques and tools 25 2.1 Geographic coordinates and map projections 27 2.2 Local coordinates and position vectors 34 2.3 Orientations of structural elements 52 2.4 Structural mapping using GPS technology 69 2.5 Concluding remarks 74 Chapter 3 Characterizing structures using differential geometry 75 3.1 The concept and description of lineations 77 3.2 The concept and description of curved surfaces 91 University Printing House, Cambridge cb2 8bs, United Kingdom 3.3 Applications of differential geometry to structural geology 114 3.4 Concluding remarks 119 Published in the United States of America by Cambridge University Press, New York Cambridge University Press is part of the University of Cambridge. Chapter 4 Physical quantities, fields, dimensions, and scaling 120 It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. 4.1 Physical quantities and the continuum 121 4.2 Physical dimensions and dimensional analysis 127 www.cambridge.org Information on this title: www.cambridge.org/9780521839273 4.3 Dimensionless groups and the scaling of structural processes 132 4.4 Scaled laboratory models 143 © D. D. Pollard and R. C. Fletcher 2005 4.5 Concluding remarks 150 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, Chapter 5 Deformation and flow 152 no reproduction of any part may take place without the written permission of Cambridge University Press. 5.1 Rock deformation: some observations and a simple First published 2005 description 154 4th printing 2010 5.2 Evolving geometry of a structure: kinematic models, velocity A catalogue record for this publication is available from the British Library models, and deformation 158 5.3 Relation between deformation and velocity fields 168 isbn 978-0-521-83927-3 Hardback 5.4 Velocity fields: the instantaneous state of motion 177 Cambridge University Press has no responsibility for the persistence or accuracy of 5.5 General results 183 URLs for external or third-party internet websites referred to in this publication, 5.6 Concluding remarks 192 and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface pageix Acknowledgments xi Chapter 1 Motivations and opportunities 1 1.1 Earthquake hazards in southern California 2 1.2 Radar lineaments on Venus 9 1.3 Faulting in a North Sea hydrocarbon reservoir 11 1.4 Anticracks in southern France 16 1.5 Mountain building on the Colorado Plateau 20 1.6 Concluding remarks 24 Chapter 2 Structural mapping techniques and tools 25 2.1 Geographic coordinates and map projections 27 2.2 Local coordinates and position vectors 34 2.3 Orientations of structural elements 52 2.4 Structural mapping using GPS technology 69 2.5 Concluding remarks 74 Chapter 3 Characterizing structures using differential geometry 75 3.1 The concept and description of lineations 77 3.2 The concept and description of curved surfaces 91 3.3 Applications of differential geometry to structural geology 114 3.4 Concluding remarks 119 Chapter 4 Physical quantities, fields, dimensions, and scaling 120 4.1 Physical quantities and the continuum 121 4.2 Physical dimensions and dimensional analysis 127 4.3 Dimensionless groups and the scaling of structural processes 132 4.4 Scaled laboratory models 143 4.5 Concluding remarks 150 Chapter 5 Deformation and flow 152 5.1 Rock deformation: some observations and a simple description 154 5.2 Evolving geometry of a structure: kinematic models, velocity models, and deformation 158 5.3 Relation between deformation and velocity fields 168 5.4 Velocity fields: the instantaneous state of motion 177 5.5 General results 183 5.6 Concluding remarks 192 vi CONTENTS CONTENTS vii Chapter 6 Force, traction, and stress 194 11.4 Continuum properties of composite materials 446 11.5 Anisotropic fluids and internal instability 450 6.1 Concepts of force and traction 196 11.6 Concluding remarks 455 6.2 Concept and analysis of stress 207 6.3 State of stress in the Earth 227 Chapter 12 Model development and methodology 456 6.4 Concluding remarks 241 12.1 Idealization of field observations 457 Chapter 7 Conservation of mass and momentum 243 12.2 Selection of general boundary conditions 462 12.3 A methodology for the practice of structural geology 474 7.1 Particle dynamics 245 12.4 Concluding remarks 477 7.2 Rigid-body dynamics and statics 248 7.3 Conservation of mass and momentum in a deformable References 478 continuum 260 Index 497 7.4 Field equations for the elastic solid and viscous fluid 276 7.5 Concluding remarks 285 Chapter 8 Elastic deformation 287 8.1 Estimating rock properties from geological field tests 288 8.2 The idealized elastic material 292 8.3 Quasi-static displacement boundary value problems 299 8.4 Quasi-static traction boundary value problems 308 8.5 Elastic properties from laboratory and engineering field tests 319 8.6 Elastic heterogeneity and anisotropy 323 8.7 Concluding remarks 331 Chapter 9 Brittle behavior 333 9.1 Brittle deformation in the laboratory and in the field 334 9.2 Strength of laboratory samples 337 9.3 Brittle failure in a field of homogeneous stress 357 9.4 Brittle failure in a field of heterogeneous stress 364 9.5 Fracture propagation and fault growth 371 9.6 Concluding remarks 382 Chapter 10 Viscous flow 384 10.1 Rock deformation by viscous flow 385 10.2 Constitutive relations for isotropic viscous fluids 386 10.3 Plane and antiplane flow 388 10.4 Viscous flow in layers: mullions and folds 396 10.5 Flow of anisotropic viscous fluids 416 10.6 Concluding remarks 420 Chapter 11 Rheological behavior 421 11.1 Departures from linear viscous flow 422 11.2 Boudinage and the non-linear power-law fluid 423 11.3 Coupling of viscous flow and macroscopic diffusional transport 440 vi CONTENTS CONTENTS vii Chapter 6 Force, traction, and stress 194 11.4 Continuum properties of composite materials 446 11.5 Anisotropic fluids and internal instability 450 6.1 Concepts of force and traction 196 11.6 Concluding remarks 455 6.2 Concept and analysis of stress 207 6.3 State of stress in the Earth 227 Chapter 12 Model development and methodology 456 6.4 Concluding remarks 241 12.1 Idealization of field observations 457 Chapter 7 Conservation of mass and momentum 243 12.2 Selection of general boundary conditions 462 12.3 A methodology for the practice of structural geology 474 7.1 Particle dynamics 245 12.4 Concluding remarks 477 7.2 Rigid-body dynamics and statics 248 7.3 Conservation of mass and momentum in a deformable References 478 continuum 260 Index 497 7.4 Field equations for the elastic solid and viscous fluid 276 7.5 Concluding remarks 285 Chapter 8 Elastic deformation 287 8.1 Estimating rock properties from geological field tests 288 8.2 The idealized elastic material 292 8.3 Quasi-static displacement boundary value problems 299 8.4 Quasi-static traction boundary value problems 308 8.5 Elastic properties from laboratory and engineering field tests 319 8.6 Elastic heterogeneity and anisotropy 323 8.7 Concluding remarks 331 Chapter 9 Brittle behavior 333 9.1 Brittle deformation in the laboratory and in the field 334 9.2 Strength of laboratory samples 337 9.3 Brittle failure in a field of homogeneous stress 357 9.4 Brittle failure in a field of heterogeneous stress 364 9.5 Fracture propagation and fault growth 371 9.6 Concluding remarks 382 Chapter 10 Viscous flow 384 10.1 Rock deformation by viscous flow 385 10.2 Constitutive relations for isotropic viscous fluids 386 10.3 Plane and antiplane flow 388 10.4 Viscous flow in layers: mullions and folds 396 10.5 Flow of anisotropic viscous fluids 416 10.6 Concluding remarks 420 Chapter 11 Rheological behavior 421 11.1 Departures from linear viscous flow 422 11.2 Boudinage and the non-linear power-law fluid 423 11.3 Coupling of viscous flow and macroscopic diffusional transport 440 Preface Fundamentals of Structural Geologyis a textbook that and a physics course covering mechanics and emphasizes modern techniques of field data heat. We consider these courses to be the essential acquisition and analysis, the principles of contin- mathematical and scientific pre-requisites for a uum mechanics, and the mathematical and com- course using this textbook. Elementary concepts putational skills necessary to describe, model, of vector analysis, matrix theory, linear algebra, and explain quantitatively the deformation of ordinary and partial differential equations, and rock in Earth’s lithosphere. computer programming with Matlab® are used With precise location data now available from throughout, but are introduced in such a way that the Global Positioning System (GPS) and powerful a formal course in these subjects, while helpful, computer systems now transportable in a back- should not be considered a pre-requisite. The pack, the quantity of reproducible field data has authors view this textbook as appropriate for a increased dramatically. These new data sets first course in structural geology, but recognize demand better methods for describing the geom- that many students will come to a course using etry of structures, and we address this demand by this book after a traditional course that empha- introducing the basic concepts of differential sizes the descriptive terminology, geometric tech- geometry, which provide unambiguous descrip- niques, and kinematic concepts of the discipline. tions of curved lineations and surfaces in three Although designed as a text for students, this dimensions. Data sets from a variety of field areas book also should be useful as a reference for are provided via the textbook website to promote researchersinstructuralgeology,andasanaidfor the practice of opening field “notebooks” to the updating instructors and professionals who have entire community of researchers, and as input for beenexposedonlytotraditionalcoursesandtext- student exercises (see below). books on the subject. Furthermore, this book Textbooks in structural geology provide el- should be attractive to scientists in related dis- ements of continuum mechanics (e.g. separate ciplines (geophysics, rock mechanics, tectonics, chapters on stress and strain), but rarely are these geotechnical engineering, and petroleum engi- concepts tied together with constitutive laws or neering)whoarelookingforamodernsummaryof formulated into equations of motion or equilib- thefundamentalsofstructuralgeology.Weencour- rium to solve boundary or initial value problems. age students and professionals from these disci- These textbooks largely beg the questions: what plines to learn about the modern methods and methodology should one adopt to solve the prob- tools of structural geology so that they can effec- lems of structural geology; and what are the fun- tivelyinteractwithgeologistsonmulti-disciplinary damental constructs that must be acknowledged projects. and honored? These constructs are the conserva- One of the opportunities and challenges of tion laws of mass, momentum, and energy, com- publishing a textbook in the twenty-first century bined with the constitutive laws for material is the fact that the printed volume is no longer the behavior and the kinematic relationships for only vehicle for communication between authors strain and rate of deformation. We use these con- and readers. Accordingly, we have prepared a structs to build a rational methodology for the homepage for Fundamentals of Structural Geology investigation of tectonic processes and their struc- that is available on the World Wide Web (www. tural products. cambridge.org/0521839270) and provides the fol- This textbook is designed for senior under- lowing supplementary materials for readers, graduate students and graduate students who instructors, and students: have taken an introductory physical geology course, mathematics courses that include differ- • Full color images for all outcrop photographs ential and integral calculus in several variables, used in the text