Summary
There is little to guide the geostatistical practitioner on the size of sample needed to estimate the variogram adequately. It is often estimated from few data, but because confidence limits cannot be determined analytically from a single set of data its precision is unknown. Approximate confidence intervals can be found numerically by Monte Carlo simulation. A large field of values is created using a plausible model of the variogram. It is then sampled many times, and the observed variogram of each sample is computed. An experimental sampling distribution of the variogram is constructed from which percentiles and confidence limits can be obtained. Our experiments suggest that variograms computed on fewer than 50 data are of little worth and that at least 100 data are needed. For a normally distributed isotropic variable 150 data should suffice, while one derived from 225 data will usually be reliable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cressie, N. & Hawkins, D. M. 1980. Fitting variogram models by weighted least squares. Mathematical Geology 17, 563–586.
Jenkins, G. M. & Watts, D. G. 1968. Spectral Analysis and its Applications. Holden-Day, Oakland, California.
Journel, A. G. & Huijbregts, C. J. 1978. Mining Geostatistics. Academic Press, London.
Lantuéjoul, C. 1991. Ergodicity and integral range. Journal of Microscopy 161, 387–403.
Matheron, G. 1965. Les variables régionalisées et leur estimation. Masson, Paris.
Matheron, G. 1989. Estimating and Choosing. Springer Verlag, Berlin.
Mcbratney, A. B. & Webster, R. 1986. Choosing functions for semivari-ograms of soil properties and fitting them to sampling estimates. Journal of Soil Science 37, 617–639.
Müñoz-Pardo, J. F. 1987. Approche géostatistique de la variablité spatiale des milieux géophysiques. Thèse Docteur-Ingénieur, Université de Grenoble et l’Institut National Polytechnique de Grenoble.
Shafer, J. M. & Varljen, M. D. 1990. Approximation of confidence limits on sample semivariograms from single realizations of spatially correlated random fields. Water Resources Research 26, 1787–1802.
Taylor, C. C. & Burrough, P. A. 1986. Multiscale sources of spatial variation in soil. III Improved methods for fitting the nested model to one-dimensional semi-variograms. Mathematical Geology 18, 811–821.
Webster, R. & Oliver, M. A. 1992. Confidence intervals on variograms for samples of different sizes. In Proceedings of the 2nd Codata Conference on Geomathematics and Geostatistics, eds P. A. Dowd and J. J. Royer. Sciences de la Terre, Série Informatique Géologique 31, 11–23.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Kluwer Academic Publishers
About this chapter
Cite this chapter
Webster, R., Oliver, M.A. (1993). How large a sample is needed to estimate the regional variogram adequately?. In: Soares, A. (eds) Geostatistics Tróia ’92. Quantitative Geology and Geostatistics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1739-5_14
Download citation
DOI: https://doi.org/10.1007/978-94-011-1739-5_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-2157-6
Online ISBN: 978-94-011-1739-5
eBook Packages: Springer Book Archive