Modelling approaches to geodynamic processes - am Institut für

259 Pages·2004·23.65 MB·English

Diss. ETH No. 15860
Modelling approaches to
geodynamic processes
A dissertation submitted to the
Swiss Federal Institute of Technology, Zu¨rich
for the degree of Doctor of Natural Sciences
Presented by
Boris Jozef Paul Kaus
Dipl. Natw. ETH
born 4. December, 1976
from the Netherlands
Accepted on the recommendation of
Prof. Dr. J.-P. Burg ETH Zu¨rich examiner
Prof. Dr. Y.Y. Podladchikov PGP, University of Oslo co-examiner
Prof. Dr. P.J. Tackley University of California, Los Angeles co-examiner
2004

Contents
Abstract 9
Zusammenfassung 11
1 Introduction 13
1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Basin subsidence 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Subsidence model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.1 Basin subsidence with and without phase transitions . . . . . . 33
2.4.2 Effect of stretching factor on basin subsidence . . . . . . . . . . 35
2.4.3 Parameterized density models . . . . . . . . . . . . . . . . . . . 37
2.4.4 Deviations from the TDD pure-shear stretching model . . . . . 38
2.5 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.7 Simplified phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 44
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3
4 CONTENTS
3 Folding versus Diapirism 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 Crustal-scale folds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.1 Geological information . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.2 Mechanical background . . . . . . . . . . . . . . . . . . . . . . . 57
3.3 Magmatic/diapiric domes . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.1 Geological Information . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 Mechanical background . . . . . . . . . . . . . . . . . . . . . . . 61
3.4 Analytical perturbation method . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.2 Phase diagram: folding versus diapirism . . . . . . . . . . . . . 65
3.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.5 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5.1 Numerical technique . . . . . . . . . . . . . . . . . . . . . . . . 72
3.5.2 Comparison between numerics and analytics . . . . . . . . . . . 73
3.5.3 Geometries developing at finite amplitude stages . . . . . . . . . 73
3.5.4 Dynamics of dome-formation . . . . . . . . . . . . . . . . . . . . 77
3.6 Strain in and around domes . . . . . . . . . . . . . . . . . . . . . . . . 79
3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.9 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.10 Perturbation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4 Shear Localization 97
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.2 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.2.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . 102
4.2.2 Non-dimensionalization . . . . . . . . . . . . . . . . . . . . . . . 103
4.3 Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.3.1 0-D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.3.2 1-D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.3.3 2-D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
CONTENTS 5
4.4 Initiation stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.4.1 0-D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.4.2 1-D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.4.3 Link to classics . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.4.4 2-D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.5 Shear localization on planets . . . . . . . . . . . . . . . . . . . . . . . . 131
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.7 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.7.1 Powerlaw creep . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.7.2 Diffusion creep . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.7.3 Peierls low temperature plasticity . . . . . . . . . . . . . . . . . 140
4.7.4 Conversion to simplified model . . . . . . . . . . . . . . . . . . 141
4.8 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.9 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5 3D Rayleigh Taylor instability 153
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.2 Mathematical model and numerical method . . . . . . . . . . . . . . . 154
5.3 Growthrate calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.4 Forward modeling results . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.5 Reverse modeling results . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6 Finite amplitude diapirism 165
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.2 Model and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.3 Initial stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.4 Finite amplitude effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.5 2D vs 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.6 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 172
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6 CONTENTS
7 Diapiric patterns 177
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2 Model and numerical methods . . . . . . . . . . . . . . . . . . . . . . . 180
7.3 2D simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7.3.1 Linear stability analysis . . . . . . . . . . . . . . . . . . . . . . 182
7.3.2 Initial random perturbations . . . . . . . . . . . . . . . . . . . . 184
7.3.3 Initial step-like perturbation . . . . . . . . . . . . . . . . . . . . 186
7.4 3D simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.4.1 Linear and nonlinear stability . . . . . . . . . . . . . . . . . . . 187
7.4.2 Initial random noise . . . . . . . . . . . . . . . . . . . . . . . . 189
7.4.3 Initial step-like perturbations . . . . . . . . . . . . . . . . . . . 194
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
7.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8 Numerical Method 209
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.2 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3 Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
8.3.1 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
8.3.2 Iterative approach . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.3.3 Plasticity formulation . . . . . . . . . . . . . . . . . . . . . . . . 219
8.3.4 Further numerical issues . . . . . . . . . . . . . . . . . . . . . . 221
8.4 Verification of the numerical code . . . . . . . . . . . . . . . . . . . . . 222
8.4.1 0D rheology tests . . . . . . . . . . . . . . . . . . . . . . . . . . 222
8.4.2 Linear stability analysis of folding and RT-instability . . . . . . 225
8.4.3 Viscoelastic buckling . . . . . . . . . . . . . . . . . . . . . . . . 226
8.4.4 Stress around a weak inclusion . . . . . . . . . . . . . . . . . . . 227
8.4.5 Diapirism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8.4.6 Shearband inclination . . . . . . . . . . . . . . . . . . . . . . . . 230
8.4.7 Thermal advection and diffusion . . . . . . . . . . . . . . . . . . 231
CONTENTS 7
8.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
8.6 Appendix A: stress rotation . . . . . . . . . . . . . . . . . . . . . . . . 234
8.7 Appendix B: finite element formulation . . . . . . . . . . . . . . . . . . 235
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
A CO driven aftershocks 241
2
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
A.2 Aftershock patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
A.3 Modeling results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
A.4 Aftershock triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
A.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
A.6 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Acknowledgements 257
Curriculum vitae 259
8 CONTENTS
Abstract
This thesis addresses problems from a geodynamic perspective. Numerical methods
and analytical techniques are used to obtain insight in the mechanics of geodynamic
processes.
The interaction between petrology and tectonics, for example, is studied in a model
of sedimentary basin subsidence. It is demonstrated that metamorphic phase transi-
tions, which affect rock density, have a first order effect on the basin subsidence. In
particular mantle phase transitions reduce the amount of synrift-subsidence, in agree-
ment with observations.
The mechanics of a model that allows for erosion, compressional and density-driven
deformation are studied in detail. The concept of mechanical phase diagrams is em-
ployed to study the key parameters controlling the dynamics of the system. In the
model, up to eight deformation modes exist, as a function of two non-dimensional pa-
rameters. Good agreement is demonstrated between analytical and numerical results.
Mechanical phase diagrams are also applied to shear-localization in visco-elasto-
plastic materials. Localization is initiated through shear-heating-induced increase of
temperature, whereas it may be inhibited by thermal diffusion. Results are derived for
0D,1Dand2Dsettingswithconstantstressandconstantvelocityboundaryconditions.
Up to six deformation modes exist as a function of four nondimensional parameters.
Scaling laws, derived for the various deformation modes demonstrate that the model
may be relevant to natural conditions.
The Rayleigh-Taylor (RT) instability is formed if a fluid of low density underlies a
fluid of higher density. The deformation of the fluid interface is investigated analyt-
ical and numerically in both two and three dimensions. It is shown that the purely
three-dimensional normal modes amplify faster then 2D modes. The superposition of
different normal modes may result in relatively complex patterns. The 2D-3D transi-
tion is studied for various boundary conditions. The limits of existing linear stability
theory are examined and a new finite-amplitude theory is proposed, which yields a
better description of finite-amplitude structures growing from thin source layers. Re-
versibility issues of the RT-instability are discussed for different initial structures.
Thetoolsusedthroughoutthisthesisincludeanalyticaltechniques(thick-andthin-
plate methods), and numerical methods (finite-difference, finite-element and hybrid
finite-difference/spectral methods) that have been specifically tailored to the investi-
gated problems. Progress has been made in the incorporation of solid-like (elasto-
plastic) and fluid-like (viscous) behavior in a single computational framework.