Table Of ContentK. SWwe
Geodynamics of the Lithosphere
Springer-Verlag Berlin Heidelberg GmbH
Kurt Stowe
Geodynamics
of the
Lithosphere
with 210 Figures
Springer
DR. KURT STUWE
University of Graz
Department of Geology and Paleontology
Heinrichstrasse 26
8010 Graz
Austria
ISBN 978-3-662-04982-2
Library of Congress Cataloging-in-Publication Data
Sttiwe, Kurt, 1959-
Introduction to the geodynamics of the lithosphere : quantative description
of geological problems / Kurt Sttiwe.
p.cm.
Includes bibliographical references.
ISBN 978-3-662-04982-2 ISBN 978-3-662-04980-8 (eBook)
DOI 10.1007/978-3-662-04980-8
1.Geodynamics--Mathematics. 1. Title.
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I dislike very much to consider any quantita
-tive problem set by a geologist. In nearly ev
ery case, the conditions given are much too
vague for the matter to be in any sense satis
factory, and a geologist does not seem to mind
a few millions of years in matters relating to
time ...
John Perry, 1895
(In the paper in which he recalculated the age of
the Earth - previously estimated by Lord Kelvin
to be 90 my - to the still accepted age of 4.5 Gy.)
Preamble
Field geologists typically interpret their data in terms of tectonic models
that are consistent with their observations in a given terrain, but that often
lack an independent test. Such models can be strengthened considerably if
they are supported by independent estimates of the magnitude of the implied
geodynamic processes. For example, estimates of the thermal energy budget
of a metamorphic terrain are an invaluable aid for the tectonic interpreta
tion of metamorphic isograds mapped in the field; estimates for the orogenic
force balance of a certain nappe staking geometry interpreted from structural
mapping are a fantastic way to test its mechanical plausibility.
This book was written because there appears to be a strong bi-modality in
the nature of text books dealing with such problems. Books that introduce
the reader to the modeling of geodynamic processes often require a relatively
high maths background. On the other hand, books that deal with basic maths
usually lack any connection to geology. This book was written in an attempt
to bridge this gap. It is the aim of this book to introduce field based geologists
to the power of the quantitative treatment of their field data. Because of this,
the emphasis of this book lies on the interpretation of data that are typically
collected by structural geologists, petrologists and geochronologists in the
field, rather than those collected by seismologists or geophysicists.
As an introductory text, little mathematical knowledge is required. All
calculations are discussed in detail without omitting steps in the derivations
and an extensive appendix on mathematical tools is provided. All computer
codes used to calculate the figures are available from the author. They may
also be downloaded from the address http://wegeneLuni-graz.at.
Contents
1. Introduction.............................................. 1
1.1 What is a Model? ...................................... 2
1.2 Spatial Dimension of Geological Problems ................. 6
1.2.1 Reducing Spatial Dimensions. . . . . . . . . . . . . . . . . . . . .. 11
2. Plate Tectonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
2.1 Historical Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
2.2 Working on a Spherical Surface .......................... 20
2.2.1 ... or is the Earth Flat After All? . . . . . . . . . . . . . . . . . .. 20
2.2.2 Geometry on a Sphere ............................ 21
2.2.3 Kinematics on a Sphere . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
2.2.4 Mechanics on a Sphere. . . . . . . . . . . . . . . . . . . . . . . . . . .. 24
2.3 Map Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26
2.4 The Layered Structure of Earth. . . . . . . . . . . . . . . . . . . . . . . . .. 31
2.4.1 Crust and Lithosphere. . . . . . . . . . . . . . . . . . . . . . . . . . .. 33
2.4.2 The Lithospheric Plates .......................... , 37
2.4.3 The Plate Boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38
2.4.4 The Wilson Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
2.5 Problems.............................................. 44
3. Heat and Temperature ................................... 47
3.1 Principles of Heat Conduction. . . . . . . . . . . . . . . . . . . . . . . . . . .. 48
3.1.1 The Heat Conduction Equation. . . . . . . . . . . . . . . . . . .. 48
3.1.2 The Laplace Equation ............................ 56
3.1.3 The Error Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 56
3.1.4 Thermal Time Constants. . . . . . . . . . . . . . . . . . . . . . . . .. 57
3.2 Principles of Heat Production. . . . . . . . . . . . . . . . . . . . . . . . . . .. 60
3.2.1 Radioactive Heat Production ...................... 61
3.2.2 Mechanical Heat Production. . . . . . . . . . . . . . . . . . . . . .. 62
3.2.3 Chemical Heat Production. . . . . . . . . . . . . . . . . . . . . . . .. 70
3.3 Principles of Heat Advection. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74
3.3.1 Heat Advection by Intrusion. . . . . . . . . . . . . . . . . . . . . .. 75
3.3.2 Heat Advection by Erosion . . . . . . . . . . . . . . . . . . . . . . .. 76
3.3.3 Heat Advection by Fluids ......................... 79
x
Contents
3.3.4 The Peclet Number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80
3.4 Heat in the Continental Lithosphere. . . . . . . . . . . . . . . . . . . . .. 81
3.4.1 Stable Geotherms ................................ 83
3.5 Heat in the Oceanic Lithosphere. . . . . . . . . . . . . . . . . . . . . . . . .. 93
3.5.1 Aging Oceanic Lithosphere. . . . . . . . . . . . . . . . . . . . . . .. 95
3.5.2 Subduction Zones ................................ 98
3.6 Thermal Evolution of Intrusions .......................... 101
3.6.1 Step-Shaped Temperature Distributions ............. 102
3.6.2 One-dimensional Intrusions ........................ 103
3.6.3 Two-dimensional Intrusions ........................ 109
3.6.4 Other Examples of Boundary Conditions ............ 110
3.7 Selected Heat Transfer Problems ......................... 116
3.7.1 Temporally Periodic Temperature Fluctuations ....... 117
3.7.2 Folded Isotherms ................................. 118
3.7.3 Isotherms and Surface Topography ................. 121
3.7.4 Temperature Distribution Around Faults ............ 125
3.8 Problems .............................................. 127
4. Elevation and Shape ...................................... 133
4.0.1 Reference Levels ................................. 133
4.0.2 The ic-ii-Plane ................................. , 138
4.1 Vertical Motion in the Crust ............................. 140
4.1.1 Definition of Uplift and Exhumation ................ 140
4.1.2 Kinematic Description of Vertical Motions ........... 144
4.2 Isostasy ............................................... 149
4.2.1 Hydrostatic Isostasy .............................. 150
4.2.2 Flexural Isostasy ................................. 159
4.3 Geomorphology ........................................ 167
4.3.1 Erosion Models on Orogenic Scale .................. 169
4.3.2 Short Range Transport ............................ 171
4.3.3 The Shape of Volcanoes ........................... 180
4.3.4 Long Range Transport: Drainages .................. 182
4.3.5 Discontinuous Landscape Formation ................ 187
4.3.6 Fractals ......................................... 187
4.4 Problems .............................................. 190
5. Force and Rheology .. ..................................... 195
5.1 Stress and Strain ....................................... 196
5.1.1 The Stress Tensor ............................... , 196
5.1.2 Deformation Laws ................................ 205
5.2 Rheology of the Lithosphere ............................. 218
5.2.1 Rheology of the Continental Lithosphere ............ 218
5.2.2 Rheology of the Oceanic Lithosphere ................ 226
5.3 Forces Applied to Lithospheric Plates ..................... 230
5.3.1 Transmission Mechanisms ......................... 230
Contents XI
5.3.2 Forces in Oceanic Lithosphere ...................... 237
5.3.3 Forces in Continental Plates ....................... 241
5.4 Problems .............................................. 245
6. Dynamic Processes ....................................... 251
6.1 Continents in Extension ................................. 251
6.1.1 Basin Subsidence Mechanisms ...................... 253
6.1.2 Basin Types ..................................... 254
6.1.3 Subsidence Analysis .............................. 255
6.1.4 Models of Continental Extension ................... 261
6.2 Continents in Collision .................................. 269
6.2.1 Thermal Evolution of Collisional Orogens ........... 269
6.2.2 Mechanical Description of Colliding Continents ....... 279
6.2.3 Accretionary Wedges ............................. 294
6.3 Selected Geodynamic Processes .......................... 298
6.3.1 Flood Basalts and Mantle Plumes .................. 298
6.3.2 Delamination of the Mantle Lithosphere ............. 301
6.3.3 Low Pressure - High Temperature Metamorphism .... 304
6.3.4 High Pressure Metamorphism ...................... 306
6.3.5 Tectonic Overpressure ............................ 308
6.3.6 Feedback and Episodicity .......................... 311
6.4 Problems .............................................. 317
7. P-T-t-D-Paths ............................................ 321
7.1 Introduction ........................................... 321
7.1.1 What Exactly are P-T- and P-T-t-D-Paths? ......... 322
7.2 Basic Principles of Petrology ............................. 323
7.2.1 Equilibrium Information: Thermobarometry ......... 326
7.2.2 Non-equilibrium Information: Kinetics .............. 330
7.3 Documentation of P-T-Paths ............................ 334
7.3.1 Qualitative Shape of P-T-Paths .................... 334
7.3.2 Slope and Curvature of P-T-Paths ... ............... 335
7.4 Interpretation of P-T-t-D-Relationships in Orogens ......... 338
7.4.1 Interpreting Temporal Relationships ................ 340
7.4.2 Interpreting Spatial Relationships .................. 341
7.5 Problems .............................................. 345
A. Mathematical Tools ....................................... 349
A.l What is a Differential Equation? ......................... 349
A.1.1 Terminology Used in Differential Calculus ........... 351
A.2 The Finite Difference Method ............................ 354
A.2.1 Grids and Boundary Conditions .................... 357
A.2.2 Stability and Accuracy ............................ 358
A.2.3 Implicit and Explicit Finite Difference Methods ...... 359
A.2.4 Approximation of the Transport Equation ........... 361
XII Contents
A.2.5 Dealing with Irregular Grid Boundaries ........... 0 0 364
Ao2.6 Recommended Reading 00000000000000000 ... 0.0 .. 0. 365
Ao3 Scalars, Vectors and Tensors 00 0 0 0 0 00 . 0 0. . 0 0. 00 . 0 0. . 0. 0 00 0 365
A.4 An Example for Using Fourier Series 00 0 00 0 00 0. 0 0 0 00 0. 0 0. 0 0 368
Ao5 Selected Numerical Tricks 0 0 00 0 0 00 0 0 00 0 0 00 0. 00 . 0 0. . 0 0. . 0. 372
A.501 Integrating Differential Equations .. 0. 0 0. . 0 0. 00 . .. 0. 372
Ao5.2 Analytically Unsolvable Equations 00 0 0 0. 0 0 0 00 0. 0 0. . 0 372
A.503 The Least Squares Method 0000000.00 .. 00 ..... 0.0 .. 373
A.5.4 Basic Statistical Parameters 00 0 0 0 0 00 0 0. 0 0 0 00 0 0 00 0. 0 375
A.6 Problems. 0 0 0 00 0 0 00 00 00.00 .. 0 0. 0 0. 00 0. 0 0 0. 0 0 00 ,0' 00 0 0 0 0 0 377
B. Maths Refresher 00 00 00 0 0 0. 0 0. . 0 0. 0 0 0. 0. . 0 0. 0 0 0. 0 0 00 0 0 00 0. 0 379
C. Symbols and Units 000.00 .. 00 .. 0.000.000 .. 00 ... 0000000.00. 385
D. Answers to Problems. 00.00000 .. 0 00 . 0 0 0 0.00000000000000000 395
E. Internet Addresses 0 00 . 0 0. 0 0. . 0 0. . 0. .. 0. 0 0. . 0 0. 0 0 0. . 0 0 0 0 0 0 415
References .. 0. 0. .. 00 . .. 0 ... 0. . 0. .. 0. .. 0. . 0. . 0 0. . 0 0. 0 0 0. 0 0 0 0 0 0 0 421
Index 0 00 . 0 00 . 0 00 .000.0000000000000.000.000000.00 .. 0 0.00 ...... 0 441
