Solving the ”Sea Level Equation”

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1、Solvingthe”SeaLevelEquation”PartI–TheoryGiorgioSpadaandPaoloStocchiIstitutodiFisica–Universit`adiUrbinoViaSantaChiara2761029Urbino(PU)Italyspada@fis.uniurb.it
cSamizdatPress,2005FirstEditionFebruary8,2005iiContentsPreface..................................vAcknowledgments...........

2、.................vi1Green’sfunctions,surfaceloads,andtheGIAproblem11.1Green’sfunctions.........................21.1.1RigidEarth........................21.1.2ElasticEarth.......................41.1.3ViscoelasticEarth.....................61.2Surfaceloads...........................81.

3、2.1Iceload..........................81.2.2Oceanload........................91.3ThesimplifiedGIAproblem...................101.3.1Responsetotheiceload.................121.3.2Responsetotheoceanload...............131.3.3SolutionofthesimplifiedGIAproblem.........142TheSeaLevelEquation172.

4、1Background............................172.2ObtainingtheSLE........................202.3”Gravitationallyself–consistent”SLE..............232.4ApproximatesolutionsoftheSLE................242.4.1Eustaticsolution.....................242.4.2Woodward’ssolution...................262.4.3A

5、nice–freeapproach...................282.4.4Anexplicitapproach...................282.5By–productsoftheSLE.....................302.5.1Observedsealevelvariations...............302.5.2Velocityfields.......................322.5.3Stokescoefficients.....................33iiiiv3Numericalappro

6、achtotheSLE353.1Discretizationscheme.......................363.2DiscretizingtheSLE.......................383.2.1Time............................393.2.2Space...........................433.3IterativesolutionoftheSLE...................484Appendices514.1SphericalHarmonics..............

7、.........51Bibliography53vPrefaceThisbookletisdevotedtothestudyofsometheoreticalandpracticalaspectsoftheso–called”SeaLevelEquation”(SLE),anintegralequationthatpre-dictsthetime–dependentshapeoftheequipotentialsurfaceofadeformablebodysubjecttosurfaceforces.Inthefieldofglobalgeodynamic

8、s,theSLEservesasatoolforco