Global Dynamics of the Earth: Applications of Normal Mode Relaxation Theory to Solid-Earth Geophysics

337 Pages·2004·37.576 MB·English

by  Roberto Sabadini, Bert Vermeersen (auth.)

GLOBALDYNAMICS OFTHEEARTH
MODERN APPROACHES IN GEOPHYSICS
VOLUME 20
Editorial Advisory Board
B.L.N. Kennett, Research School of Earth Sciences,
The Australian National University, Canberra, Australia
R. Madariaga, Laboratoire de Geologie, Ecole Normale Superieure,
Paris, France
R. Marschall,Hannover, Germany
R. Wortel, Department of Theoretical Geophysics,
University of Utrecht, The Netherlands
The titles published in this series are listed at the end of this volume.
GLOBAL DYNAMICS
OF THE EARTH
Applications of Normal Mode Relaxation
Theory to Solid-Earth Geophysics
by
ROBERTOSABADINI
University of Milan,
Milan, Italy
and
BERTVERMEERSEN
Delft University of Technology,
Delft, The Netherlands
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4020-1268-6 ISBN 978-94-017-1709-0 (eBook)
DOI 10.1007/978-94-017-1709-0
Printed on acid-free paper
All Rights Reserved
©2004 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 2004
No part of this work may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming, recording
or otherwise, without written permission from the Publisher, with the exception
of any material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work.
ToGiuliaandArmanda
R.S.
Contents
Acknowledgments xi
Foreword xiii
1. NORMALMODETHEORYIN
VISCOELASTICITY 1
1. RheologicalModels 1
2. MomentumandPoissonEquations 3
3. Expansion in Spherical Harmonics: Spheroidal and Toroidal
Solutions 8
3.1 SpheroidalSolutionfortheIncompressibleCase 10
3.2 ToroidalSolutionfortheIncompressibleCase 16
4. FundamentalSpheroidalMatrixintheLaplaceDomain 17
5. PropagatorMatrixTechnique 18
5.1 PropagationoftheSpheroidalSolution 19
5.2 PropagationoftheToroidalSolution 23
6. InverseRelaxationTimesforIncompressibleEarthModels 24
7. Phase-changeInterface 26
8. LoadingtheEarth 29
8.1 InternalLoading: Earthquakes,Subduction 30
8.2 SurfaceLoading: PointMassandTidalForcing 31
8.3 Solving for the Displacement and Perturbation in the
GravitationalPotential 32
9. ApproximationMethodforHigh-DegreeHarmonics 35
9.1 ApproximationoftheSolution 36
9.2 RescalingtheSolution 39
2. MULTI-LAYERMODELS 45
1. Analytical Development of Stratified Viscoelastic Spherical
EarthModels 45
1.1 UniformMantleViscosityandElasticLithosphere 52
1.2 ConvexMantleViscosityandElasticLithosphere 58
1.3 ConvexMantleViscosityandViscoelasticLithosphere 71
2. ShallowInversionsinPREMDensityStratification 74
3. Volume-averagedvs. Fixed-boundaryContrast 77
viii GLOBALDYNAMICSOFTHEEARTH
4. IsolationFunctions 81
3. ROTATIONALDYNAMICSOFVISCOELASTIC
PLANETS 99
1. IntroductiontoEarthRotation 99
2. RotationalChangesforaRigidEarth 103
3. AdjustmentoftheEquatorialBulge 108
4. DevelopmentsofLinearizedRotationTheories 110
4.1 ComparisonBetweenDifferentRotationTheories 115
4.2 Omissionofthe Mo RotationMode 116
Mo
4.3 AnalyticalFormulaforthe RotationMode 119
4.4 UnificationoftheDifferentApproaches 122
5. Long-termBehavioroftheRotationEquation 123
4. POLARWANDERAND INDUCEDBY
ICE-SHEETLOADING 127
1. TheConceptofTruePolarWander(TPW) 127
2. TheInferenceofMantleViscosityFromTPWand Data 130
3. Loading 132
4. MantleViscosity 136
4.1 VariationsinDepthoftheTwo-LayerMantleViscosity
Profile 140
4.2 UpperMantleViscositiesLowerThan Pas 144
5. InferenceofLithosphericThicknessFromTPWandLengthof
DayVariations 149
6. IceAgeCyclesandthePolarWanderPath 150
7. InfluencesofPhase-Changevs. ChemicalStratification 156
8. Trade-offBetweenMantleViscosityandDensityContrasts 165
9. ImpactofMantleStratificationonTPWDuringtheIceAges 168
5. DETECTIONOFTHETIME-DEPENDENT
GRAVITYFIELDANDGLOBALCHANGE 173
1. Changes in the Long-Wavelength Geoid Components from
SatelliteLaserRangingTechniques 173
2. Trade-off between Lower Mantle Viscosity and Present-Day
MassImbalanceinAntarcticaandGreenland 179
6. SEA-LEVELCHANGES 189
1. Introduction 189
2. Sea-level Variations, Geoid and Gravity Anomalies Due to
PleistoceneDeglaciation 192
2.1 MathematicalFormulation 192
2.2 Sea-LevelVariations,theGeoidandFree-AirGravity
Anomalies 195
3. GlacialIsostaticAdjustment(GIA)vs. TectonicProcesses:the
ExampleoftheMediterraneanSea 202
Contents ix
4. Sea-LevelFluctuationsInducedbyPolarWander 210
5. Sea-LevelChangesInducedbySubduction 216
5.1 Sea-LevelVariations,GeoidAnomaliesandtheLong-
WavelengthDynamicTopography 218
5.2 ASingleSinkingSlab 219
5.3 ADistributionofSlabs 222
7. TECTONICSANDTHEROTATIONOFTHE
EARTHANDTERRESTRIALPLANETS 227
1. MountainBuildingandEarthRotation 227
1.1 UpliftHistories 229
1.2 Changesin andLinearRootFormationHistory 231
1.3 Polar Wander and Heaviside, Linear and Exponential
RootFormationHistory 234
2. SubductionEffectsonTPW 249
2.1 Non-linearRotationTheory 249
2.2 PolarWanderVelocityforaDistributionofSlabs 257
3. PolarWanderontheEarth,Moon,MarsandVenus 258
8. POST-SEISMICDEFORMATION 269
1. GlobalPost-seismicDeformation 269
2. Post-seismicDeformationforShallowEarthquakes 276
2.1 TheUmbria-Marche(1997)Earthquake 278
2.2 TheIrpinia(1980)Earthquake 286
Appendices 293
A– FundamentalMatrixfortheCompressibleCase 293
B– ComplexContourIntegration 299
1. AnalyticalFunctions 299
2. CauchyIntegralRepresentation 300
3. ResidueTheorem 302
C– ForcingTermsforaDislocationSource 305
1. Strike-slip 305
1.1 SpheroidalComponents 305
1.2 ToroidalComponents 306
2. Dip-slip 306
2.1 SpheroidalComponents 306
2.2 ToroidalComponents 307
References 309
Index 325
Acknowledgments
This book project could never have been conceived, written and completed
without the help of many. We would like to thank Petra van Steenbergen at
Kluwer Academic Publishers for the continuous support and advice she gave
duringtheyearsweworkedonthebook.
xi