Characterization and quantification of uncertainty in coregionalization analysis

Mathematical Geology

Volumn 39, Issue 3, 2007, Pages 263-288

  Larocque, Guillaume ^a   Dutilleul, Pierre ^a   Pelletier, Bernard ^a   Fyles, James W ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Direct and cross variograms; Ergodic, estimation and fluctuation variances; Least squares estimators of sills; Multi scale analysis; Positive semidefiniteness; Structural correlations and coefficients of determination

Indexed keywords

CORE ANALYSIS; COVARIANCE MATRIX; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MULTIVARIANT ANALYSIS; PARAMETER ESTIMATION; UNCERTAINTY ANALYSIS;

COVARIANCE ANALYSIS; GEOSTATISTICS; LEAST SQUARES METHOD; MULTIVARIATE ANALYSIS; UNCERTAINTY ANALYSIS; VARIANCE ANALYSIS; VARIOGRAM;

EID: 34447344041     PISSN: 08828121     EISSN: 15738868     Source Type: Journal    
DOI: 10.1007/s11004-007-9086-8     Document Type: Article

References (35)

1. Bocchi, S., Castrignanò, A., Fornaro, F., and Maggiore, T., 2000, Application of factorial kriging for mapping soil variation at field scale: Eur. J. Agron., v. 13, no. 4, p. 295-308.
2. Bourennane, H., Salvador-Blanes, S., Cornu, S., and King, D., 2003, Scale of spatial dependence between chemical properties of topsoil and subsoil over a geologically contrasted area (Massif central, France): Geoderma, v. 112, no. 3-4, p. 235-251.
3. Castrignanò, A., Giugliarini, L., Risaliti, R., and Martinelli, N., 2000a, Study of spatial relationships among some soil physico-chemical properties of a field in central Italy using multivariate geostatistics: Geoderma, v. 97, no. 1-2, p. 39-60.
4. Castrignanò, A., Goovaerts, P., Lulli, L., and Bragato, G., 2000b, A geostatistical approach to estimate probability of occurrence of Tuber melanosporum in relation to some soil properties: Geoderma, v. 98, no. 3-4, p. 95-113.
5. Chilès, J.-P., and Delfiner, P., 1999, Geostatistics: Modeling Spatial Uncertainty: Wiley, New York, 695 p.
6. Cressie, N. A. C., 1993, Statistics for Spatial Data: Wiley, New York, 900 p.
7. Dobermann, A., Goovaerts, P., and Neue, H. U., 1997, Scale-dependent correlations among soil properties in two tropical lowland rice fields: Soil Sci. Soc. Am. J., v. 61, no. 5, p. 1483-1496.
8. Goovaerts, P., 1992, Factorial kriging analysis: A useful tool for exploring the structure of multivariate s patial soil information: J. Soil Sci., v. 43, p. 597-619.
9. Goovaerts, P., 1994, Study of spatial relationships between 2 sets of variables using multivariate geostatistics: Geoderma, v. 62, no. 1-3, p. 93-107.
10. Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation: Oxford University Press, New York, 483 p.
11. Goovaerts, P., and Webster, R., 1994, Scale-dependent correlation between topsoil copper ad cobalt concentrations in Scotland: Eur. J. Soil Sci., v. 45, no. 1, p. 79-95.
12. Goovaerts, P., Sonnet, P., and Navarre, A., 1993, Factorial kriging analysis of springwater contents in the Dyle River basin, Belgium: Water Resour. Res., v. 29, no. 7, p. 2115-2125.
13. Goulard, M., 1989, Inference in a regionalization model, in Armstrong, M., ed., Geostatistics, vol. 1: Kluwer Academic, Dordrecht, pp. 397-408.
14. Goulard, M., and Voltz, M., 1992, Linear coregionalization model: Tools for estimation and choice of cross-variogram matrix: Math. Geol., v. 24, no. 3, p. 269-286.
15. Isaaks, E. H., and Srivastava, R. M., 1989, Applied Geostatistics: Oxford University Press, New York, 561 p.
16. Journel, A. G., and Huijbregts, C. J., 1978, Mining geostatistics: Academic, London, 600 p.
17. Larocque, G., Dutilleul, P., Pelletier, B., and Fyles, J. W., 2006, Conditional Gaussian co-simulation of regionalized components of soil variation: Geoderma, v. 134, no. 1, p. 1-16.
18. Lin, Y.P., 2002, Multivariate geostatistical methods to identify and map spatial variations of soil heavy metals: Environ. Geol., v. 42, p. 1-10.
19. Marchant, B. P., and Lark, R. M., 2004, Estimating variogram uncertainty: Math. Geol., v. 36, no. 8, p. 867-898.
20. Matheron, G., 1965, Les Variables Régionalisées et Leur Estimation, une Application de la Théorie des Fonctions Aléatoires aux Sciences de la Nature: Masson, Paris, 305 p.
21. Matheron, G., 1978, Estimer et Choisir: Un Essai sur la Pratique des Probabilités, Les Cahiers du Centre de Morphologie Mathématique, fasc. 7: Centre de Géostatistique, Fontainebleau, 175 p.
22. Matheron, G., 1982, Pour une analyse krigeante des données régionalisées: Rapport N-732, Centre de Géostatistique, Fontainebleau
23. Matheron, G., 1989, Estimating and Choosing: An Essay on Probability in Practice: Springer, Berlin, 141 p.
24. Müller, W. G., and Zimmerman, D. L., 1999, Optimal designs for variogram estimation: Environmetrics, v. 10, no. 1, p. 23-37.
25. Ortiz, C. J., and Deutsch, C. V., 2002, Calculation of uncertainty in the variogram: Math. Geol., v. 34, no. 2, p. 169-183.
26. Pardo-Igúzquiza, E., and Dowd, P., 2001, Variance-covariance matrix of the experimental variogram: Assessing variogram uncertainty: Math. Geol., v. 33, no. 4, p. 397-419.
27. Pardo-Igúzquiza, E., and Dowd, P., 2003, Assessment of the uncertainty of spatial covariance parameters of soil properties and its use in applications: Soil Sci., v. 168, no. 11, p. 769-781.
28. Pelletier, B., Dutilleul, P., Larocque, G., and Fyles, J. W., 2004, Fitting the linear model of coregionalization by generalized least squares: Math. Geol., v. 36, no. 3, p. 323-343.
29. Pettitt, A. N., and McBratney, A. B., 1993, Sampling designs for estimating spatial variance components: Appl. Stat. J. Roy. Stat. C, v. 42, no. 1, p. 185-209.
30. Searle, S. R., 1971, Linear Models: Wiley, New York, 532 p.
31. Vargas-Guzman, J. A., Warrick, A. W., and Myers, D. E., 2002, Coregionalization by linear combination of nonorthogonal components: Math. Geol., v. 34, no. 4, p. 401-415.
32. Wackernagel, H., 2003, Multivariate Geostatistics: An Introduction with Applications Springer, Berlin, 387 p.
33. Warrick, A. W., and Myers, D., 1987, Optimization of sampling locations for variogram calculations: Water Resour. Res., v. 23, no. 3, p. 496-500.
34. Webster, R., and Oliver, M. A., 1992, Sample adequately to estimate variograms of soil properties: J. Soil Sci., v. 43, no. 1, p. 177-192.
35. Webster, R., Atteia, O., and Dubois, J. P., 1994, Coregionalization of trace metals in the soil in the Swiss Jura: Eur. J. Soil Sci., v. 45, no. 2, p. 205-218.