Interpolación geoestadística de datos...
15
objetivo datos estrategia resumen Interpolaci ´ on geoestad´ ıstica de datos composicionales V. Pawlowsky-Glahn [email protected] (Universidad de Girona) Jornadas I+D+iGME: Nuevas Aplicaciones de las Geomatem ´ aticas en las Ciencias de la Tierra 26 de Marzo de 2010, Madrid, Espa˜ na
Transcript of Interpolación geoestadística de datos...
objetivo datos estrategia resumen
Interpolacion geoestadıstica dedatos composicionales
V. Pawlowsky-Glahn
[email protected] (Universidad de Girona)
Jornadas I+D+iGME: Nuevas Aplicaciones de lasGeomatematicas en las Ciencias de la Tierra
26 de Marzo de 2010, Madrid, Espana
objetivo datos estrategia resumen
referencias
Tolosana-Delgado, Pawlowsky-Glahn, Egozcue (2008). Indicator Kriging without OrderRelation Violations. Math. Geo.. DOI 10.1007/s11004-008-9146-8
Tolosana-Delgado, Pawlowsky-Glahn (2007). Kriging regionalized positive variablesrevisited: sample space and scale considerations. Math. Geo. 39(6), 529-558.
Tolosana-Delgado (2006). Geostatistics for constrained variables: positive data,compositions and probabilities. Applications to environmental hazard monitoring. Ph.D.dissertation. University of Girona. (Available online)
Tolosana-Delgado, van den Boogaart, Pawlowsky-Glahn, V. (2009). Estimating andmodeling variograms of compositional data with occasional missing variables in R. In:StatGIS’09, Geoinformatics for environmental surveillance Workshop, Milos (Greece).
Tolosana-Delgado, (2007). Geostatistics for vectors from Euclidean spaces: revisitingcokriging of compositions and indicator functions, In: Zhao et al. (Eds.) Proceedings ofIAMG’07: Geomathematics and GIS Analysis of Resources, Environment and Hazards.China University of Geosciences. Beijing, China. (Vistelius award keynote lecture)
Tolosana-Delgado, Egozcue, Pawlowsky-Glahn (2008). Cokriging of compositions:log-ratios and unbiasedness. In: Proceedings of Geostats’08, VIII th InternationalGeostatistics Conference, Santiago (Chile).
objetivo datos estrategia resumen
CoDa-kriging (kriging of compositional data)
propiedades:
atiende al caracter composicional de los datos
calcula intervalos de incertidumbre para la prediccion
es un estimador BLU (Best Linear Unbiased)
integra datos irregulares: datos faltantes, datosrecogidos por distintos laboratorios/operadores
objetivo datos estrategia resumen
datos
Grazer Palaozoikum, Graz (Austria): regionhistoricamente activa en minerıa
datos: 601 muestras de sedimentos fluviales
7 partes (de 34): K, Na, Ca, P, Fe, Mg, Mn
contexto geologico: 70% pizarras paleozoicas, calizasy dolomitas, 15% subsuelo cristalino, 15%sedimentos clasticos cenozoicos
Weber & Davis (1990): estudio geostadıstico de 7componentes principales (raw data)
objetivo datos estrategia resumen
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Ca
X
Y0.0 0.2 0.4 0.6 0.8 1.0
proportion
objetivo datos estrategia resumen
datos composicionales: espacio muestral restringido
observaciones = partes de un todo
valores siempre positivos
satisfacen alguna restriccion(generalmente suma constante)
vectores proporcionales sonequivalentes (tanto por 1, por 100, ppm)
objetivo datos estrategia resumen
estrategia: trabajar en coordenadas
estructura Euclıdea del espacio muestral (sımplex)
Na K
Ca
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perturbacion (⇐⇒ traslacion;operacion conmutativa de grupo)
potenciacion (⇐⇒ escalado;producto por un escalar)
producto escalar (⇐⇒ proyeccion)
balances (coordenadas ortonormales)
paso 1: particion (balances)
agrupar partes en grupos con interpretacion geologicaagrupar partes con datos faltantes/irregularesmaximizar el numero de log-cocientes computables
objetivo datos estrategia resumen
paso 1: representacion – CoDa-dendrogram
estructura jerarquicade gruposbalances entre paresde grupos(transformacion ilr)varianza de cada balance
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0.0
0.5
1.0
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Mn P
Mg Fe
Ca
Na K
log−
ratio
var
ianc
e
coord.1
coord.3
coord.5
coord.2
coord.4
coord.6
p.ej., coord.3 =
√3 · 23 + 2
ln2√
Mg · Fe3√Ca · Na · K
objetivo datos estrategia resumen
paso 2: analisis estructural de los balances
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modelo lineal de coregionalizacion:
γ(h) = C0 + C1Exp(r = 8000
3
)+ C2Gau
(r = 10000√
3
)
objetivo datos estrategia resumen
paso 3: cokriging de balances (coordenadas ilr)
no-observados: cokriging “completo”observaciones parciales: “collocated” cokrigingesperanza condicional multivariante: ilr(X) ∼ N (x, Σk )⇒ ±2σ intervalos de confianza
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valizacion cruzada: 60 valores de P y/o Mn eliminados al azar; cokriging de coord.1 y coord.2
objetivo datos estrategia resumen
paso 4: transformacion inversa
ilr(X) ∼ N (x, Σk )⇒ simulacion⇒ transformacion inversa⇒composicion con 7-partes⇒ intervalos (95% de lassimulaciones)
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objetivo datos estrategia resumen
resumen: geoestadıstica para datos composicionales
datos composicionales CoDa-kriging
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interpolation
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map of Na
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Na proportion
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map of Ca
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