Earth Dynamics: Deformations and Oscillations of the Rotating Earth

558 Pages·2013·2.265 MB·English

by  Smylie D.E.

EARTH DYNAMICS
Deformations and Oscillations of the Rotating Earth
The Earth is a dynamic system. It has a fluid, mobile atmosphere, a continually
changing global distribution of ice, snow and water, a fluid core, a thermally con-
vecting mantle and mobile tectonic plates. Internal dynamic processes, together
with external gravitational forces of the Sun, Moon and planets, exert torques on
thesolidEarthordisplaceitsmass,affectingtheEarth’sshape,rotationandgravi-
tationalfield.
D. E. Smylie provides a rigorous overview of the dynamical behaviour of the
solid Earth, explaining the theory and presenting methods for numerical imple-
mentation. Topics include advanced digital analysis, earthquake displacement
fields,freecorenutationsobservedbytheverylongbaselineinterferometrictech-
nique,translationalmodesofthesolidinnercoreobservedbythesuperconducting
gravimetersanddynamicsofthefluidoutercore.
Thisbookisfullysupportedbyopensourcecomputercode,availableonlinefor
studentstoexploreandtestthetheory.Alsoonlineareasuiteofgraphicsgenerated
fromthenumericalanalysis,whichcombinewith100graphicalworkedexamples
in the book to make this an ideal tool for researchers and graduate students in the
fieldsofgeodesy,seismologyandsolidEarthgeophysics.
DouglasSmylie is a Professorof Geophysics at York University, Toronto. He has
conductedresearchonearthquakedisplacementfields,therotationoftheEarthand
thedynamicsofthedeepinteriorwhilelecturingingeophysicsattheUniversityof
Toronto,theUniversityofWesternOntario,theUniversityofBritishColumbiaand
YorkUniversityinToronto.In2002hewasawardedtheJohnTuzoWilsonMedal
by the Canadian Geophysical Union for his achievements. Professor Smylie is a
Fellow of the Royal Astronomical Society, a member of the American Geophys-
ical Union and has served as Founder and President of the Canadian Geophysical
Union.

EARTH DYNAMICS
Deformations and Oscillations of the Rotating Earth
D. E. SMYLIE
YorkUniversity, Toronto
cambridge university press
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Firstpublished2013
PrintedandboundintheUnitedKingdombytheMPGBooksGroup
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloging-in-PublicationData
Smylie,D.E.
Earthdynamics:deformationsandoscillationsoftherotatingEarth/D.E.Smylie,YorkUniversity,Toronto.
pagescm
ISBN978-0-521-87503-5(Hardback)
1. Geodynamics. 2. Earth–Rotation. I. Title.
QE517.5.S6782013
551.1–dc23
2012040769
ISBN 978-0-521-87503-5Hardback
Additionalresourcesforthispublicationatwww.cambridge.org/smylie
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accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto
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websitesis,orwillremain,accurateorappropriate.
Dedication
This book is dedicated to my wife Susan, my children Diane, Janet, Hugh and
AndreaandmygrandchildrenGrace,Gavin,Ben,Ella,Jay,Quinn,Andreas,Alan,
Lance,BobandAshley.

Contents
Prefaceandacknowledgments pagexi
Thebookwebsitewww.cambridge.org/smylie xiii
1 Introductionandtheoreticalbackground 1
1.1 Scalar,vectorandtensoranalysis 1
1.2 Separationofvectorfields 25
1.3 Vectorsphericalharmonics 27
1.4 Elasticitytheory 33
1.5 Linearalgebraicsystems 74
1.6 Interpolationandapproximation 79
2 Timesequenceandspectralanalysis 93
2.1 Timedomainanalysis 94
2.2 LinearoptimumWienerfilters 105
2.3 Frequencydomainanalysis 119
2.4 Fourierseriesandtransforms 154
2.5 Powerspectraldensityestimation 171
2.6 Maximumentropyspectralanalysis 198
3 Earthdeformations 212
3.1 Equilibriumequations 212
3.2 ThereciprocaltheoremofBetti 215
3.3 Radialequations:spheroidalandtorsional 217
3.4 Dynamicalequations 223
3.5 Solutionsnearthegeocentre 231
3.6 Numericalintegrationoftheradialequations 245
3.7 Fundamental,regularsolutionsintheinnercore 256
viii Contents
4 Earth’srotation:observationsandtheory 273
4.1 Referenceframes 273
4.2 Polarmotionandwobble 274
4.3 Thedynamicsofpolarmotionandwobble 294
4.4 Nutationandmotionofthecelestialpole 307
5 Earth’sfigureandgravitation 323
5.1 Historicaldevelopment 323
5.2 Externalgravityandfigure 325
5.3 Equilibriumtheoryoftheinternalfigure 341
5.4 Gravitycoupling 371
6 Rotatingfluidsandtheoutercore 386
6.1 Theinertialwaveequation 386
6.2 Dynamicsofthefluidoutercore 398
6.3 Scalingofthecoreequations 407
6.4 Compressibilityanddensitystratification 412
7 Thesubseismicequationandboundaryconditions 420
7.1 Thesubseismicwaveequation 420
7.2 Deformationoftheshellandinnercore 423
8 Variationalmethodsandcoremodes 445
8.1 Asubseismicvariationalprinciple 445
8.2 Representationofthefunctional 450
8.3 Finiteelementsupportfunctions 453
8.4 Boundaryconditionsandconstraints 456
8.5 Numericalimplementationandresults 459
8.6 Rotationalsplittingandviscosity 467
8.7 Aviscosityprofilefortheoutercore 478
9 Staticdeformationsanddislocationtheory 482
9.1 Theelasticitytheoryofdislocations 482
9.2 ThetheoryforrealisticEarthmodels 497
9.3 Changesintheinertiatensorandthesecularpolarshift 509
AppendixA Elementaryresultsfromvectoranalysis 514
A.1 Vectoridentities 514
A.2 Vectorcalculusidentities 514
A.3 Integraltheorems 516
AppendixB PropertiesofLegendrefunctions 517
B.1 Recurrencerelations 518
B.2 EvaluationofLegendrefunctions 519
Contents ix
AppendixC NumericalEarthmodels 522
C.1 TheEarthmodels 522
References 531
Fortranindex 536
Subjectindex 537