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1、IntJGeomath(2012)3:139154DOI10.1007/s13137-011-0028-8ORIGINALPAPERAwaveletapproachtotheterraincorrectioningravimetryandgravitygradiometryC.JekeliReceived:29September2010/Accepted:26September2011/Publishedonline:13October2011©Springer-Verlag2011AbstractAtraditional,st
2、andardmethodtocomputethegravitationaleffectofthetopographicmassesusesafiniteelementdecompositionintorightrectangular,ver-ticalprisms,oneforeachterrainelevationdatapoint.Analternativeconstructionisproposedbasedonthetwo-dimensionalHaarwavelet,whichultimatelyisidentical,
3、butinsteadslicesthetopographyintohorizontalslabs.Itisshownthatfarfewersuchslabsneedtobeaccountedtoobtainthesameaccuracyinthegravitationaleffect,or,also,theterraincorrection.Themethodistestedonfirstandsecondderivativesofthegravitationalpotentialinareasofrelativelygentl
4、eandroughterrains.KeywordsTwo-dimensionalwavelet·Haarwavelet·Terraincorrection·Gravitationaleffect·GravitygradiometryMathematicsSubjectClassification(2000)65T60(Wavelets)·65D30(Numericalintegration)1IntroductionWhenprocessinggravimetricdataforgeophysicalandgeologicapp
5、lications,oneusuallyremovesthegravitationaleffectofthevisibletopographicmassesinordertoenhancetheinversionforsubsurfacesourcesthatgeneratetheremainingvaria-tionscontainedinthedata(see,e.g.,Telfordetal.1990;Blakely1995,amongmanyothertexts).Althoughpredominantlythought
6、ofasacorrectionappliedtogravi-metricdata,theterraincorrectionisequallyimportantforgravitygradiometry,notonly(andespecially)forterrestrialdata(e.g.,Badekas1967),butalsoforairborneC.Jekeli(B)DivisionofGeodeticScience,SchoolofEarthSciences,OhioStateUniversity,Columbus,O
7、H,USAe-mail:jekeli.1@osu.edu123140IntJGeomath(2012)3:139154gradiometry(Tziavosetal.1988;BellGeospace2004;KassandLi2008;DransfieldandZeng2009).Ingeodesy,theremovaloftheterraineffectisnecessaryinordertoreducethedatatothegeoidforfurtherprocessingasboundaryvaluesintheclas
8、sicalboundary-valueproblemsfortheexteriorgravitationalpotential(seeJekeliandSerpas2003,andreferencestherein).Thegravitationaleffect
