Structural geology algorithms: vectors and tensors
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Cover Inhaltsverzeichnis |
| Physical Description: | XI, 289 S. Ill., graph. Darst. |
| ISBN: | 9781107012004 9781107401389 |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PREFACE PAGE IX
1 PROBLEM SOLVING IN STRUCTURAL GEOLOGY 1
1.1 OBJECTIVES OF STRUCTURAL ANALYSIS 1
1.2 ORTHOGRAPHIC PROJECTION AND PLANE TRIGONOMETRY 3
1.3 SOLVING PROBLEMS BY COMPUTATION 6
1.4 SPHERICAL PROJECTIONS 8
1.5 MAP PROJECTIONS 18
2 COORDINATE SYSTEMS, SCALARS, AND VECTORS 23
2.1 COORDINATE SYSTEMS 23
2.2 SCALARS 25
2.3 VECTORS 25
2.4 EXAMPLES OF STRUCTURE PROBLEMS USING VECTOR OPERATIONS 34
2.5 EXERCISES 43
3 TRANSFORMATIONS OF COORDINATE AXES AND VECTORS 44
3.1 WHAT ARE TRANSFORMATIONS AND WHY ARE THEY IMPORTANT? 44
3.2 TRANSFORMATION OF AXES 45
3.3 TRANSFORMATION OF VECTORS 48
3.4 EXAMPLES OF TRANSFORMATIONS IN STRUCTURAL GEOLOGY 50
3.5 EXERCISES 65
4 MATRIX OPERATIONS AND INDICIAL NOTATION 66
4.1 INTRODUCTION 66
4.2 INDICIAL NOTATION 66
4.3 MATRIX NOTATION AND OPERATIONS 69
4.4 TRANSFORMATIONS OF COORDINATES AND VECTORS REVISITED 77
4.5 EXERCISES 79
V
IMAGE 2
VI CONTENTS
5 TENSORS 81
5.1 WHAT ARE TENSORS? 81
5.2 TENSOR NOTATION AND THE SUMMATION CONVENTION 82
5.3 TENSOR TRANSFORMATIONS 85
5.4 PRINCIPAL AXES AND ROTATION AXIS OF A TENSOR 88
5.5 EXAMPLE OF EIGENVALUES AND EIGENVECTORS IN STRUCTURAL GEOLOGY 91 5.6
EXERCISES 97
6 STRESS 98
6.1 STRESS VECTORS AND STRESS TENSORS 98
6.2 CAUCHY S LAW 99
6.3 BASIC CHARACTERISTICS OF STRESS 104
6.4 THE DEVIATORIC STRESS TENSOR 112
6.5 A PROBLEM INVOLVING STRESS 113
6.6 EXERCISES 1 19
7 INTRODUCTION TO DEFORMATION 120
7.1 INTRODUCTION 120
7.2 DEFORMATION AND DISPLACEMENT GRADIENTS 121
7.3 DISPLACEMENT AND DEFORMATION GRADIENTS IN THREE DIMENSIONS 125 7.4
GEOLOGICAL APPLICATION: GPS TRANSECTS 128
7.5 EXERCISES 132
8 INFINITESIMAL STRAIN 135
8.1 SMALLER IS SIMPLER 135
8.2 INFINITESIMAL STRAIN IN THREE DIMENSIONS 138
8.3 TENSOR SHEAR STRAIN VS. ENGINEERING SHEAR STRAIN 140
8.4 STRAIN INVARIANTS 141
8.5 STRAIN QUADRIC AND STRAIN ELLIPSOID 142
8.6 MOHR CIRCLE FOR INFINITESIMAL STRAIN 143
8.7 EXAMPLE OF CALCULATIONS 144
8.8 GEOLOGICAL APPLICATIONS OF INFINITESIMAL STRAIN 147
8.9 EXERCISES 164
9 FINITE STRAIN 165
9.1 INTRODUCTION 165
9.2 DERIVATION OF THE LAGRANGIAN STRAIN TENSOR 166
9.3 EULERIAN FINITE STRAIN TENSOR 167
9.4 DERIVATION OF THE GREEN DEFORMATION TENSOR 167
9.5 RELATIONS BETWEEN THE FINITE STRAIN AND DEFORMATION TENSORS 168 9.6
RELATIONS TO THE DEFORMATION GRADIENT, F 169
9.7 PRACTICAL MEASURES OF STRAIN 170
9.8 THE ROTATION AND STRETCH TENSORS 1 73
9.9 MULTIPLE DEFORMATIONS 176
9.10 MOHR CIRCLE FOR FINITE STRAIN 176
9.11 COMPATIBILITY EQUATIONS 178
9.12 EXERCISES 180
IMAGE 3
CONTENTS VII
10 PROGRESSIVE STRAIN HISTORIES AND KINEMATICS 183
10.1 FINITE VERSUS INCREMENTAL STRAIN 183
10.2 DETERMINATION OF A STRAIN HISTORY 199
10.3 EXERCISES 213
11 VELOCITY DESCRIPTION OF DEFORMATION 217
11.1 INTRODUCTION 217
11.2 THE CONTINUITY EQUATION 218
11.3 PURE AND SIMPLE SHEAR IN TERMS OF VELOCITIES 219
11.4 GEOLOGICAL APPLICATION: FAULT-RELATED FOLDING 220
11.5 EXERCISES 252
12 ERROR ANALYSIS 254
12.1 INTRODUCTION 254
12.2 ERROR PROPAGATION 255
12.3 GEOLOGICAL APPLICATION: CROSS-SECTION BALANCING 256
12.4 UNCERTAINTIES IN STRUCTURAL DATA AND THEIR REPRESENTATION 266
12.5 GEOLOGICAL APPLICATION: TRISHEAR INVERSE MODELING 270
12.6 EXERCISES 279
REFERENCES 281
INDEX 286
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
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| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie Geographie |
| edition | 1. publ. |
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| isbn | 9781107012004 9781107401389 |
| language | English |
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| physical | XI, 289 S. Ill., graph. Darst. |
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| spelling | Allmendinger, Richard W. Verfasser aut Structural geology algorithms vectors and tensors Richard W. Allmendinger ; Nestor Cardozo ; Donald M. Fisher 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2012 XI, 289 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Strukturgeologie (DE-588)4225664-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Strukturgeologie (DE-588)4225664-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Cardozo, Nestor Verfasser aut Fisher, Donald M. Verfasser aut http://assets.cambridge.org/97811070/12004/cover/9781107012004.jpg Cover SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024529173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Allmendinger, Richard W. Cardozo, Nestor Fisher, Donald M. Structural geology algorithms vectors and tensors Strukturgeologie (DE-588)4225664-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4225664-1 (DE-588)4114528-8 |
| title | Structural geology algorithms vectors and tensors |
| title_auth | Structural geology algorithms vectors and tensors |
| title_exact_search | Structural geology algorithms vectors and tensors |
| title_full | Structural geology algorithms vectors and tensors Richard W. Allmendinger ; Nestor Cardozo ; Donald M. Fisher |
| title_fullStr | Structural geology algorithms vectors and tensors Richard W. Allmendinger ; Nestor Cardozo ; Donald M. Fisher |
| title_full_unstemmed | Structural geology algorithms vectors and tensors Richard W. Allmendinger ; Nestor Cardozo ; Donald M. Fisher |
| title_short | Structural geology algorithms |
| title_sort | structural geology algorithms vectors and tensors |
| title_sub | vectors and tensors |
| topic | Strukturgeologie (DE-588)4225664-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Strukturgeologie Mathematisches Modell |
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