Structural Geology Algorithms: Vectors and

State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also provide professional structural geologists with a valuable reference and refresher for calculations.

Preface	p. ix
Problem solving in structural geology	p. 1
Objectives of structural analysis	p. 1
Orthographic projection and plane trigonometry	p. 3
Solving problems by computation	p. 6
Spherical projections	p. 8
Map projections	p. 18
Coordinate systems, scalars, and vectors	p. 23
Coordinate systems	p. 23
Scalars	p. 25
Vectors	p. 25
Examples of structure problems using vector operations	p. 34
Exercises	p. 43
Transformations of coordinate axes and vectors	p. 44
What are transformations and why are they important?	p. 44
Transformation of axes	p. 45
Transformation of vectors	p. 48
Examples of transformations in structural geology	p. 50
Exercises	p. 65
Matrix operations and indicial notation	p. 66
Introduction	p. 66
Indicial notation	p. 66
Matrix notation and operations	p. 69
Transformations of coordinates and vectors revisited	p. 77
Exercises	p. 79
Tensors	p. 81
What are tensors?	p. 81
Tensor notation and the summation convention	p. 82
Tensor transformations	p. 85
Principal axes and rotation axis of a tensor	p. 88
Example of eigenvalues and eigenvectors in structural geology	p. 91
Exercises	p. 97
Stress	p. 98
Stress "vectors" and stress tensors	p. 98
Cauchy's Law	p. 99
Basic characteristics of stress	p. 104
The deviatoric stress tensor	p. 112
A problem involving stress	p. 113
Exercises	p. 119
Introduction to deformation	p. 120
Introduction	p. 120
Deformation and displacement gradients	p. 121
Displacement and deformation gradients in three dimensions	p. 125
Geological application: GPS transects	p. 128
Exercises	p. 132
Infinitesimal strain	p. 135
Smaller is simpler	p. 135
Infinitesimal strain in three dimensions	p. 138
Tensor shear strain vs. engineering shear strain	p. 140
Strain invariants	p. 141
Strain quadric and strain ellipsoid	p. 142
Mohr circle for infinitesimal strain	p. 143
Example of calculations	p. 144
Geological applications of infinitesimal strain	p. 147
Exercises	p. 164
Finite strain	p. 165
Introduction	p. 165
Derivation of the Lagrangian strain tensor	p. 166
Eulerian finite strain tensor	p. 167
Derivation of the Green deformation tensor	p. 167
Relations between the finite strain and deformation tensors	p. 168
Relations to the deformation gradient, F	p. 169
Practical measures of strain	p. 170
The rotation and stretch tensors	p. 173
Multiple deformations	p. 176
Mohr circle for finite strain	p. 176
Compatibility equations	p. 178
Exercises	p. 180
Progressive strain histories and kinematics	p. 183
Finite versus incremental strain	p. 183
Determination of a strain history	p. 199
Exercises	p. 213
Velocity description of deformation	p. 217
Introduction	p. 217
The continuity equation	p. 218
Pure and simple shear in terms of velocities	p. 219
Geological application: Fault-related folding	p. 220
Exercises	p. 252
Error analysis	p. 254
Introduction	p. 254
Error propagation	p. 255
Geological application: Cross-section balancing	p. 256
Uncertainties in structural data and their representation	p. 266
Geological application: Trishear inverse modeling	p. 270
Exercises	p. 279
References	p. 281
Index	p. 286
Table of Contents provided by Ingram. All Rights Reserved.

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Structural Geology Algorithms: Vectors and Tensors

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