径向基函数在高密度电阻率数据处理中的应用-豆柴文库

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径向基函数在高密度电阻率数据处理中的应用
Introduction
Inthefieldofgeophysics,highdensityresistivitymethodisanimportantexplorationmethodforminerals,groundwater,andengineeringgeology,whichhasthecharacteristicsofnon-contact,non-invasive,andhighprecision.Thehigh-densityresistivitydataprocessingtechnologyplaysacrucialroleintheaccuracyofexplorationresults.Amongthemanymethodsofhigh-densityresistivitydataprocessing,theradialbasisfunction(RBF)methodiswidelyusedduetoitsexcellentnon-linearinterpolationandfittingperformance.Thispaperwilldiscusstheapplicationoftheradialbasisfunctioninhigh-densityresistivitydataprocessing.
PrincipleofRadialBasisFunction
Radialbasisfunctionisageneraltermforaclassoffunctionswitharadialstructureinn-dimensionalspace.Inthefieldofhigh-densityresistivitydataprocessing,theradialbasisfunctioncanbeusedtoestablishamappingfunctionbetweentheresistivitydataofeachpointandthetargetvalueofthepoint.Themappingfunctionisdescribedasfollows:
f(x)=∑i=1nciφ(||x−xi||)
Wheref(x)isthetargetvalueatthepointx;xi(i=1,2,…,n)istheresistivitydataofeachpoint;ci(i=1,2,…,n)istheweightcoefficient,andφ(·)istheradialbasisfunction.
Thechoiceofradialbasisfunctionwillaffecttheaccuracyoftheinterpolationandfitting.CommonlyusedradialbasisfunctionsareGaussianfunction,multiquadricfunction,inversequadraticfunction,andthinplatesplinefunction.
ApplicationofRadialBasisFunctioninHighDensityResistivityDataProcessing
Interpolation
Interpolationistheprocessofestimatingthevalueofagivenfunctionatapointbetweentwoknownpoints.Inhigh-densityresistivitydataprocessing,interpolationisusedtoestimatetheresistivityvalueofeachpointaccordingtotheresistivitydataoftheadjacentpoints.Theradialbasisfunctioninterpolationmethodiswidelyusedduetoitsaccurateandcontinuousinterpolationcharacteristics.
Whenusingtheradialbasisfunctionforinterpolation,theresistivitydataofeachpointservesasasamplingpoint,andthentheradialbasisfunctionisusedtoapproximatetheresistivityvalueatanyposition.Theinterpolationcanbeperformedintwoandthreedimensions.Theinterpolati