Geostatistik - Variogramme und Kriging · Fortgeschrittene Lineare Geostatistik Nichtlineare...

ZufallsfelderVariographie

Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik

Nichtlineare Geostatistik

GeostatistikVariogramme und Kriging

Prof. van den Boogaart

[email protected]

Prof. van den Boogaart Geostatistik




Gliederung1 Zufallsfelder

Regionalisierte VariablenAbhängigkeitStationarit”atVariogramm

2 VariographieEmpirisches VariogrammNugget, Sill und RangeVariogrammodelle

3 Gewöhnliches KrigingKriging AufgabeKriging GleichungssystemKriging VorhersageKriging KarteKriging FehlerKriging GainVorhersageintervallKriging EigenschaftenKreuzvalidation

4 Fortgeschrittene Lineare GeostatistikAndere Lineare Kriging ArtenGeostatistische SimulationFortgeschrittene VariographieVorgehen bei der linearen Geostatistik

5 Nichtlineare GeostatistikVectorielles KrigingCompositionales KrigingMutliple Point Statistics (MPS)Stochastische Optimierung






Gliederung1 Zufallsfelder


2 VariographieEmpirisches VariogrammNugget, Sill und RangeVariogrammodelle

3 Gewöhnliches KrigingKriging AufgabeKriging GleichungssystemKriging VorhersageKriging KarteKriging FehlerKriging GainVorhersageintervallKriging EigenschaftenKreuzvalidation

4 Fortgeschrittene Lineare GeostatistikAndere Lineare Kriging ArtenGeostatistische SimulationFortgeschrittene VariographieVorgehen bei der linearen Geostatistik

5 Nichtlineare GeostatistikVectorielles KrigingCompositionales KrigingMutliple Point Statistics (MPS)Stochastische Optimierung






Regionalisierte Variablen

Z (s) = Messwert an Stelle s

s ∈ R2, Ort

Eine regionalisierte Variable(Zufallsfeld) hat überall einenWert.Toblers erstes Gesetz der Geo-graphie: Alles ist abhängig.Nahes ist stärker abhängig.

−150000 −50000 50000 150000

−1e

+05

0e+

001e

+05






Geostatistische Daten

x y Z

((xy

))x1 y1 z1x2 y2 z2...

......

Messorte:

si , i = 1, . . . , n

Beobachtungen / Messwerte

zi = Z (si )

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−150000 −50000 50000 150000

−1e

+05

0e+

001e

+05






h-Scatterplot

X YZ (s1) Z (s1)Z (s2) Z (s1)

......

Z (s1) Z (s2)...

...mit ‖s1 − s2‖ ≈ h = 5000

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010

030

050

0

cor= 0.847013453748368

xi − xj = 5000Z(xj)

Z(x

j)






h-Scatterplot

X YZ (s1) Z (s1)Z (s2) Z (s1)

......

Z (s1) Z (s2)...

...mit ‖s1 − s2‖ ≈ h = 55000Kovarianzfunktion:

c(s1, s2) = cov(Z (s1),Z (s2))

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Geostatistik - Variogramme und Kriging · Fortgeschrittene Lineare Geostatistik Nichtlineare...

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