geostatistik - variogramme und kriging · fortgeschrittene lineare geostatistik nichtlineare...
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ZufallsfelderVariographie
Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik
Nichtlineare Geostatistik
GeostatistikVariogramme und Kriging
Prof. van den Boogaart
Prof. van den Boogaart Geostatistik
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ZufallsfelderVariographie
Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik
Nichtlineare 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
Prof. van den Boogaart Geostatistik
-
ZufallsfelderVariographie
Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik
Nichtlineare Geostatistik
Regionalisierte VariablenAbhängigkeitStationarit”atVariogramm
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
Prof. van den Boogaart Geostatistik
-
ZufallsfelderVariographie
Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik
Nichtlineare Geostatistik
Regionalisierte VariablenAbhängigkeitStationarit”atVariogramm
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
Prof. van den Boogaart Geostatistik
-
ZufallsfelderVariographie
Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik
Nichtlineare Geostatistik
Regionalisierte VariablenAbhängigkeitStationarit”atVariogramm
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
Prof. van den Boogaart Geostatistik
-
ZufallsfelderVariographie
Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik
Nichtlineare Geostatistik
Regionalisierte VariablenAbhängigkeitStationarit”atVariogramm
h-Scatterplot
X YZ (s1) Z (s1)Z (s2) Z (s1)
......
Z (s1) Z (s2)...
...mit ‖s1 − s2‖ ≈ h = 5000
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0 100 200 300 400 500 600
010
030
050
0
cor= 0.847013453748368
xi − xj = 5000Z(xj)
Z(x
j)
Prof. van den Boogaart Geostatistik
-
ZufallsfelderVariographie
Gewöhnliches KrigingFortgeschrittene Lineare Geostatistik
Nichtlineare Geostatistik
Regionalisierte VariablenAbhängigkeitStationarit”atVariogramm
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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