Contents i GEOL 326 Cornell University Introduction to Structural Geology Spring 1999 by Richard W. Allmendinger Department of Geological Sciences Snee Hall Cornell University, Ithaca, NY 14853-1504 USA [email protected] R. W. Allmendinger © 1999 Contents ii Contents Lecture 1—Introduction, Scale, & Basic Terminology...............................................1 1.1 Introduction.................................................................................................................................. 1 1.2 Levels of Structural Study............................................................................................................ 2 1.3 Types of Structural Study............................................................................................................. 2 1.4 Importance of Scale..................................................................................................................... 3 1.4.1 Scale Terms.................................................................................................................... 3 1.4.2 Scale Invariance, Fractals...............................................................................................4 Lecture 2 —Coordinate Systems, etc....................................................................... 8 2.1 Introduction.................................................................................................................................. 8 2.2 Three types of physical entities.................................................................................................... 8 2.3 Coordinate Systems..................................................................................................................... 9 2.3.1 Spherical versus Cartesian Coordinate Systems..........................................................10 2.3.2 Right-handed and Left-handed Coordinate Systems.................................................... 10 2.3.3 Cartesian Coordinate Systems in Geology................................................................... 11 2.4 Vectors.......................................................................................................................................12 2.4.1 Vectors vs. Axes ........................................................................................................... 12 2.4.2 Basic Properties of Vectors...........................................................................................12 2.4.3 Geologic Features as Vectors.......................................................................................14 2.4.4 Simple Vector Operations............................................................................................. 17 2.4.5 Dot Product and Cross Product .................................................................................... 18 Lecture 3 — Descriptive Geometry: Seismic Reflection..........................................21 3.1 Echo Sounding...........................................................................................................................21 3.2 Common Depth Point (CDP) Method......................................................................................... 23 3.3 Migration .................................................................................................................................... 25 3.4 Resolution of Seismic Reflection Data.......................................................................................26 3.4.1 Vertical Resolution ........................................................................................................26 3.4.2 Horizontal Resolution....................................................................................................27 3.5 Diffractions.................................................................................................................................28 3.6 Artifacts...................................................................................................................................... 29 Contents iii 3.6.1 Velocity Pullup/pulldown ...............................................................................................29 3.6.2 Multiples........................................................................................................................ 29 3.6.3 Sideswipe......................................................................................................................30 3.6.4 Buried Focus.................................................................................................................31 3.6.5 Others ...........................................................................................................................32 Lecture 4 — Introduction to Deformation & Strain..................................................33 4.1 Introduction................................................................................................................................33 4.2 Kinematics .................................................................................................................................33 4.2.1 Rigid Body Deformations .............................................................................................. 33 4.2.2 Strain (Non-rigid Body Deformation).............................................................................34 4.2.3 Continuum Mechanics...................................................................................................36 4.2.4 Four Aspects of a Deforming Rock System: ................................................................. 37 4.3 Measurement of Strain............................................................................................................... 38 4.3.1 Change in Line Length:................................................................................................. 39 4.3.2 Changes in Angles:.......................................................................................................40 4.3.3 Changes in Volume (Dilation): ......................................................................................41 Lecture 5 — Strain II: The Strain Ellipsoid ............................................................42 5.1 Motivation for General 3-D Strain Relations ..............................................................................42 5.2 Equations for Finite Strain.......................................................................................................... 43 5.3 Extension of a Line .................................................................................................................... 43 5.4 Shear Strain...............................................................................................................................45 Lecture 6 — Strain III: Mohr on the Strain Ellipsoid...............................................47 6.1 Introduction................................................................................................................................47 6.2 Mohr’s Circle For Finite Strain ...................................................................................................47 6.3 Principal Axes of Strain..............................................................................................................48 6.4 Maximum Angular Shear ........................................................................................................... 49 6.5 Ellipticity.....................................................................................................................................50 6.6 Rotation of Any Line During Deformation ..................................................................................50 6.7 Lines of No Finite Elongation.....................................................................................................51 Lecture 7 — Strain IV: Finite vs. Infinitesimal Strain.............................................53 7.1 Coaxial and Non-coaxial Deformation .......................................................................................54 Contents iv 7.2 Two Types of Rotation............................................................................................................... 55 7.3 Deformation Paths .....................................................................................................................55 7.4 Superposed Strains & Non-commutability .................................................................................58 7.5 Plane Strain & 3-D Strain........................................................................................................... 58 Lecture 8—Stress I: Introduction ..........................................................................60 8.1 Force and Stress........................................................................................................................ 60 8.2 Units Of Stress...........................................................................................................................61 8.3 Sign Conventions:......................................................................................................................61 8.4 Stress on a Plane; Stress at a Point ..........................................................................................62 8.5 Principal Stresses ......................................................................................................................63 8.6 The Stress Tensor .....................................................................................................................64