地质数据处理插值方法.docx
- 文档编号:5484269
- 上传时间:2023-05-08
- 格式:DOCX
- 页数:22
- 大小:326.32KB
地质数据处理插值方法.docx
《地质数据处理插值方法.docx》由会员分享,可在线阅读,更多相关《地质数据处理插值方法.docx(22页珍藏版)》请在冰点文库上搜索。
地质数据处理插值方法
二维数据场的插值方法
1.二维数据场描述及处理目的
数据场数据
{(xi,yi,zi),i=1,…,n},即某特征在二维空间中的n个预测值列表:
x坐标
y坐标
观测数据
x坐标
y坐标
观测数据
164648.47
84648
127
164658.97
84658
130
164658.97
84648.5
128
164649.47
84658.5
127
164649.47
84649
127
164649.95
84659
126
164649.95
84649.5
126
164650.45
84659.5
126
164650.45
84650
126
164650.95
84660
125
164650.95
84650.5
125
164651.45
84660.5
125
164651.45
84651
125
164652
84661
124
164652
84651.5
124
164652.48
84661.5
124
164652.48
84652
124
164652.97
84650.5
124
164652.48
84657.5
129
164653.47
84651
123
164652.97
84652.5
124
164653.97
84651.5
126
164653.47
84653
125
164654.47
84652
127
164653.97
84653.5
126
164654.95
84652.5
128
164654.47
84654
129
164658.97
84658
130
164654.95
84654.5
128
164649.47
84658.5
127
164655.45
84655
126
164656.98
84656.5
127
164655.95
84655.5
127
164657.48
84657
126
164656.44
84656
129
164648.47
84657.5
127
164654.3688
84653
128
处理目的
了解该数据场的空间分布情况
处理思路
网格化绘制等值线图
网格化方法:
二维数据插值
2.空间内插方法
Surfer8.0中常用的插值方法
GriddingMethods
InverseDistancetoaPower(距离倒数加权)
Kriging(克立格法)
MinimumCurvature(最小曲率法)
ModifiedShepard'sMethod(改进Shepard方法)
NaturalNeighbor(近邻法)
NearestNeighbor(最近邻法)
PolynomialRegression(多项式回归法)
RadialBasisFunction(径向基函数法)
TriangulationwithLinearInterpolation(线性插值三角形法)
MovingAverage(移动平均法)
DataMetrics(数据度量方法)
LocalPolynomial(局部多项式法)
GeostatisticsAnalystModelinArcGIS9
2.1反距离加权插值
反距离加权插值(InverseDistanceWeighting,简称IDW),反距离加权法是最常用的空间内插方法之一。
它的基本原理是:
空间上离得越近的物体其性质越相似,反之亦然。
这种方法并没有考虑到区域化变量的空间变异性,所以仅仅是一种纯几何加权法。
反距离加权插值的一般公式为:
其中,
为未知点
处的预测值,
为已知点
处的值,n为样点的数量,
为样点的权重值,其计算公式为:
式中
为未知点与各已知点之间的距离,p是距离的幂。
样点在预测过程中受参数p的影响,幂越高,内插的平滑效果越佳。
尽管反距离权重插值法很简单,易于实现,但它不能对内插的结果作精度评价,所得结果可能会出现很大的偏差,人为难以控制。
2.2全局多项式插值(趋势分析法)
根据有限的样本数据拟合一个表面来进行内插,称之为全局多项式内插方法。
一般多采用多项式来进行拟合,求各样本点到该多项式的垂直距离的和,通过最小二乘法来获得多项式的系数,这样所得的表面可使各样本点到表面之间距离的平方和最小。
如果表面平滑、无弯曲,使用一次多项式拟合;有一处弯曲的表面则用二次多项式进行拟合;若有两处弯曲则需使用三次多项式,依次类推。
全局多项式内插一般适用于表面变化平缓的研究区域,或者仅研究区域内全局性趋势的情况[3]。
2.3局部多项式内插
局部多项式内插与全局多项式内插相对应,是用多个多项式拟合表面的一种方法,它更多地用来表现研究区域西部的变异情况。
其基本原理与全局多项式内插相同。
TheLocalPolynomialgriddingmethodassignsvaluestogridnodesbyusingaweightedleastsquaresfitwithdatawithinthegridnode'ssearchellipse.
2.4径向基函数方法
径向基函数法属于人工神经网络方法,该方法所拟合的表面都必须经过所有样本数据。
径向基函数以某个已知点为中心按一定距离变化的函数,因此在每个数据点都会形成径向基函数,即每个基函数的中心落在某一个数据点上。
径向基函数适合于非常平滑的表面,要求样本数据量大,如果数据点少,则内插效果不佳[3]。
同时,径向基函数难以对误差进行估计,也是其缺点之一。
常用的径向基函数法,它们分别是:
薄盘样条函数(thin-platespline):
张力样条函数(splinewithtension):
规则样条函数(completelyregularizedspline):
高次曲面样条函数(multiquadricspline):
反高次曲面样条函数(inversemultiquadricspline):
各式子中h为表示由点(x,y)到第i个数据点的距离,R参数是用户指定的平滑因子,
为修正贝塞尔函数,
为指数积分函数,
为Euler常数,其值约为0.577215。
RadialBasisFunctioninterpolationisadiversegroupofdatainterpolationmethods.Intermsoftheabilitytofityourdataandtoproduceasmoothsurface,theMultiquadricmethodisconsideredbymanytobethebest.AlloftheRadialBasisFunctionmethodsareexactinterpolators,sotheyattempttohonoryourdata.Youcanintroduceasmoothingfactortoallthemethodsinanattempttoproduceasmoothersurface.
FunctionTypes
ThebasiskernelfunctionsareanalogoustovariogramsinKriging.Thebasiskernelfunctionsdefinetheoptimalsetofweightstoapplytothedatapointswheninterpolatingagridnode.TheavailablebasiskernelfunctionsarelistedintheTypedrop-downlistintheRadialBasisFunctionOptionsdialog.
InverseMultiquadric
Multilog
Multiquadratic
NaturalCubicSpline
ThinPlateSpline
where:
h istheanisotropicallyrescaled,relativedistancefromthepointtothenode
R2 isthesmoothingfactorspecifiedbytheuser
DefaultR2Value
ThedefaultvalueforR2intheRadialBasisFunctiongriddingalgorithmiscalculatedasfollows:
(lengthofdiagonalofthedataextent)2/(25*numberofdatapoints)
SpecifyingRadialBasisFunctionAdvancedOptions
1. ClickonGrid|Data.
2. IntheOpendialog,selectadatafileandthenclicktheOpenbutton.
3. IntheGridDatadialog,chooseRadialBasisFunctionintheGriddingMethodgroup.
4. ClicktheAdvancedOptionsbuttontodisplaytheRadialBasisAdvancedOptionsdialog.
5. IntheGeneralpage,youcanspecifythefunctionparametersforthegriddingoperation.
▪TheBasisFunctionlistspecifiesthebasiskernelfunctiontouseduringgridding.Thisdefinestheoptimalweightsappliedtothedatapointsduringtheinterpolation.TheBasisFunctionisanalogoustothevariograminKriging.ExperienceindicatesthattheMultiquadricbasisfunctionworksquitewellinmostcases.SuccessfuluseoftheThinPlateSplinebasisfunctionisalsoreportedregularlyinthetechnicalliterature.
▪TheR2Parameterisashapingorsmoothingfactor.ThelargertheR2Parametershapingfactor,therounderthemountaintopsandthesmootherthecontourlines.Thereisnouniversallyacceptedmethodforcomputinganoptimalvalueforthisfactor.AreasonabletrialvalueforR2Parameterisbetweentheaveragesamplespacingandone-halftheaveragesamplespacing.
TriangulationwithLinearInterpolation
TheTriangulationwithLinearInterpolationmethodinSurferusestheoptimalDelaunaytriangulation.Thealgorithmcreatestrianglesbydrawinglinesbetweendatapoints.Theoriginalpointsareconnectedinsuchawaythatnotriangleedgesareintersectedbyothertriangles.Theresultisapatchworkoftriangularfacesovertheextentofthegrid.Thismethodisanexactinterpolator.
Eachtriangledefinesaplaneoverthegridnodeslyingwithinthetriangle,withthetiltandelevationofthetriangledeterminedbythethreeoriginaldatapointsdefiningthetriangle.Allgridnodeswithinagiventrianglearedefinedbythetriangularsurface.Becausetheoriginaldataareusedtodefinethetriangles,thedataarehonoredveryclosely.
TriangulationwithLinearInterpolationworksbestwhenyourdataareevenlydistributedoverthegridarea.Datasetsthatcontainsparseareasresultindistincttriangularfacetsonthemap.
2.5最小曲率法
MinimumCurvatureiswidelyusedintheearthsciences.TheinterpolatedsurfacegeneratedbyMinimumCurvatureisanalogoustoathin,linearlyelasticplatepassingthrougheachofthedatavalueswithaminimumamountofbending.
TheMinimumCurvaturegriddingalgorithmissolvesthespecifiedpartialdifferentialequationusingasuccessiveover-relaxationalgorithm.Theinteriorisupdatedusinga"chessboard"strategy,asdiscussedinPress,etal.(1988,p.868).Theonlydifferenceisthatthebiharmonicequationmusthaveninedifferent"colors,"ratherthanjustblackandwhite.
MinimumCurvaturegeneratesthesmoothestpossiblesurfacewhileattemptingtohonoryourdataascloselyaspossible.MinimumCurvatureisnotanexactinterpolator,however.Thismeansthatyourdataarenotalwayshonoredexactly.
MinimumCurvatureproducesagridbyrepeatedlyapplyinganequationoverthegridinanattempttosmooththegrid.Eachpassoverthegridiscountedasoneiteration.ThegridnodevaluesarerecalculateduntilsuccessivechangesinthevaluesarelessthantheMaximumResidualsvalue,orthemaximumnumberofiterationsisreached(MaximumIterationfield).
TheMaximumResidualparameterhasthesameunitsasthedata,andanappropriatevalueisapproximately10%ofthedataprecision.Ifdatavaluesaremeasuredtothenearest1.0units,theMaximumResidualvalueshouldbesetat0.1.TheiterationscontinueuntilthemaximumgridnodecorrectionfortheentireiterationislessthantheMaximumResidualvalue.ThedefaultMaximumResidualvalueisgivenby:
DefaultMaxResidual=0.001(Zmax-Zmin)
TheMaximumIterationparametershouldbesetatonetotwotimesthenumberofgridnodesgeneratedinthegridfile.Forexample,whengeneratinga50by50gridusingMinimumCurvature,theMaximumIterationvalueshouldbesetbetween2,500and5,000.
TheInternalTensionandBoundaryTension,Qualitatively,theMinimumCurvaturegriddingalgorithmisattemptingtofitapieceofsheetmetalthroughalloftheobservationswithoutputtinganycreasesorkinksinthesurface.Betweenthefixedobservationpoints,thesheetbowsabit.TheInternalTensionisusedtocontroltheamountofthisbowingontheinterior:
thehigherthetension,thelessthebowing.Forexample,ahightensionmakesareasbetweenobservationslooklikefacetsofagemstone.TheBoundaryTensioncontrolstheamountofbowingontheedges.TherangeofvaluesforInternalTensionandBoundaryTensionare0to1.Bydefault,theInternalTensionandtheBoundaryTensionaresetto0.
theRelaxationFactor,
TheRelaxationFactorisasdescribedinPressetal.(1988).Ingeneral,theRelaxationFactorshouldnotbealtered.Thedefaultvalue(1.0)isagoodgenericvalue.Roughly,thehighertheRelaxationFactor(closertotwo)thefastertheMinimumCurvaturealgorithmconverges,butthemorelikelyitwillnotconvergeatall.ThelowertheRelaxationFactor(closertozero)themorelikelytheMinimumCurvaturealgorithmwillconverge,butthealgorithmisslower.TheoptimalRelaxationFactorisderivedthroughtrialanderror.
2.6近邻法
TheNaturalNeighborgriddingmethodisquitepopularinsomefields.WhatisNaturalNeighborinterpolation?
ConsiderasetofThiessenpolygons(thedualofaDelaunaytriangulation).Ifanewpoint(target)wereaddedtothedataset,theseThiessenpolygonswouldbemodified.Infact,someofthepolygonswouldshrinkinsize,whilenonewouldincreaseinsize.Theareaassociatedwiththetarget'sThiessenpolygonthatwastakenfromanexistingpolygoniscalledthe"borrowedar
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 地质 数据处理 方法