Authors:

Richard W. Allmendinger
Cornell University, New York

Nestor Cardozo
Universitetet i Stavanger, Norway

Donald M. Fisher
Pennsylvania State University

Motivation:

Richard Allmendinger, myself and Donald Fisher wrote Structural Geology Algorithms: Vectors and Tensors because of our conviction that, to do modern structural geology, one needs to be introduced to the linear algebra techniques that underly our science. We view this book as a combination of a 21st Century lab manual for structural geology, a structural geology "Numerical Recipes", and a basic reference on linear algebra techniques in a structural geology context.

State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This 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.

Key features:

• Relates basic topics such as fold geometry to more complicated concepts such as tensors, allowing students to develop an intuitive feel for vectors and tensors before applying them in the context of stress and strain
• Provides a concise review of error analysis, which is an increasingly important topic for structural analysis
• Supported by a full suite of MATLAB codes available online, which can be modified and developed for solving other structural problems

Contents:

Preface; 1. Problem solving in structural geology; 2. Coordinate systems, scalars and vectors; 3. Transformations of coordinate axes and vectors; 4. Matrix operations and indicial notation; 5. Tensors; 6. Stress; 7. Introduction to deformation; 8. Infinitesimal strain; 9. Finite strain; 10. Progressive strain histories and kinematics; 11. Velocity description of deformation; 12. Error analysis; References; Index.

Errata:

We proofread the manuscript of the book many times, but errors have nonetheless crept into the final version. We apologize in particular to student users for whom small typos can be particularly frustrating! The most current Errata sheet can be downloaded here (2017.04.14).

Reviews:

From Roland Bürgmann in Mathematical Geoscience: "I highly recommend this book to all structural geology students and practitioners, as well as to earth scientists from a wide range of fields, who will benefit from this clear introduction of the principles and application of linear algebra in the analysis of commonly encountered vector and tensor quantities." (continue reading)

From Dave Healy in Geological Magazine: "I like this book. The material covered, the level of detail and the inclusion of MATLAB scripts make this a timely, relevant and very useful textbook." (continue reading)