Abstract
A practical solution for nonlinear geostatistical estimation is presented as Gaussian kriging and Riemann Sums (KRS). KRS is an association of Gaussian kriging with numerical Riemann integration for a nonlinear kriging solution. The approach returns unbiased nonlinear conditional moments, including heteroscedastic conditional variances that are typical of skewed random variables. KRS is generally applicable to either point or block estimates. Block Gaussian KRS is a new solution for ensemble upscaling of nonlinearly averaging parameter fields.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Deutsch, C. V., & Journel, A. G. (1998). GSLIB geostatistical software library and user’s guide (p. 369). Oxford: Oxford University Press.
Armstrong, M., & Matheron, G. (1986). Disjunctive kriging revisited—Part I. Mathematical Geology, 18(8), 711–728.
Ortiz, J., Oz, B., & Deutsch, C. V. (2005). A step by step guide to bi-Gaussian disjunctive kriging. In O. L. Leuangthong & C. V. Deutsch (Eds.), Geostatistics Banff 2004 (pp. 1097–1102). Netherlands: Springer.
Vargas-Guzmán, J. A. (2004). Geostatistics for power models of Gaussian fields. Mathematical Geology, 36(3), 307–322.
Vargas-Guzmán, J. A. (2005). Change of support of transformations: Conservation of lognormality revisted. Mathematical Geology, 37(6), 551–567.
Wackernagel, H. (2003). Multivariate geostatistics (p. 387). Berlin: Springer.
Journel, A. G. (1999). Conditioning geostatistical operations to nonlinear volume averages. Mathematical Geology, 31(8), 931–953.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khan, K.D. (2014). Nonlinear Estimation with Gaussian Kriging and Riemann Sums. In: Pardo-Igúzquiza, E., Guardiola-Albert, C., Heredia, J., Moreno-Merino, L., Durán, J., Vargas-Guzmán, J. (eds) Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32408-6_184
Download citation
DOI: https://doi.org/10.1007/978-3-642-32408-6_184
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32407-9
Online ISBN: 978-3-642-32408-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)