Skip to main content
Log in

Infill sampling criteria to locate extremes

  • Published:
Mathematical Geology Aims and scope Submit manuscript

Abstract

Three problem-dependent meanings for engineering “extremes” are motivated, established, and translated into formal geostatistical (model-based) criteria for designing infill sample networks. (1) Locate an area within the domain of interest where a specified threshold is exceeded, if such areas exist. (2) Locate the maximum value in the domain of interest. (3) Minimize the chance of areas where values are significantly different from predicted values. An example application on a simulated dataset demonstrates how such purposive design criteria might affect practice.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Armstrong, M., and Matheron, G., 1986a, Disjunctive kriging revisited: part I: Math. Geology, v. 18. no. 8. p. 711–728.

    Google Scholar 

  • Armstrong, M., and Matheron, G., 1986b, Disjunctive kriging revisited: part II: Math. Geology, v. 18, no. 8, p. 729–742.

    Google Scholar 

  • Aspie, D., and Barnes, R. J., 1990, Infill-sampling design and the cost of classification errors: Math. Geology, v. 22. no. 8, p. 915–932.

    Google Scholar 

  • Attanasi, E. D., and Karlinger, M. R., 1979. Worth of data and natural disaster insurance: Water Resources Research, v. 15, no. 6, p. 1763–1766.

    Google Scholar 

  • Barnes, R. J., 1989. Sample design for geologic site characterization,in Armstrong, M., ed., Geostatistics, Vol. 2: Kluwer, Dordrecht, p. 809–822.

    Google Scholar 

  • Barnes, R. J., and Watson, A. G., 1992, Efficient updating of kriging estimates and variances: Math. Geology, v. 24. no. 1. p. 129–134.

    Google Scholar 

  • Bras, R. L.. and Colon, R., 1978, Time-averaged areal mean of precipitation: estimation and network design: Water Resources Research, v. 14, no. 5, p. 878–888.

    Google Scholar 

  • Bras, R. L., and Rodríguez-Iturbe, I., 1976a. Network design for the estimation of areal mean of rainfall events: Water Resources Research, v. 12, no. 6, p. 1185–1195.

    Google Scholar 

  • Bras, R. L., and Rodríguez-Iturbe, I., 1976b, Rainfall network design for runoff prediction: Water Resources Research, v. 12. no. 6, p. 1197–1208.

    Google Scholar 

  • Burgess, T. M., Webster, R., and McBratney, A. B., 1981. Optimal interpolation and isarithmic mapping of soil properties: IV. Sampling Strategy: Jour. Soil Science, v. 32, no. 4.

  • Cressie, N. A. C., 1991. Statistics for spatial data: John Wiley & Sons. New York, 900 p.

    Google Scholar 

  • Davis, D. R., Duckstein, L., and Krysztofowicz, R.. 1979. The worth of hydrologie data for nonoptimal decision making: Water Resources Research, v. 15, no. 6, p. 1733–1742.

    Google Scholar 

  • Davis, D. R., and Dvoranchik, W. M., 1971, Evaluation of the worth of additional data: Water Resources Bull., v. 7. no. 4, p. 700–707.

    Google Scholar 

  • Dawdy, D. R., 1979, The worth of hydrologic data: Water Resources Research, v. 15, no. 6, p. 1726–1732.

    Google Scholar 

  • Deutsch, C. V., and Journel, A. G., 1992, GSLIB: Geostatistical Software Library and user's guide: Oxford Univ. Press, New York. 340 p.

    Google Scholar 

  • Duckstein, L., and Kisiel, C. C., 1971. Efficiency of hydrologic data collection systems: role of Type I and Type II Errors: Water Resources Bull., v. 7, no. 3. p. 592–604.

    Google Scholar 

  • Gershon, M., 1983, Optimal drillhole location using geostatistics: Soc. Mining Engineers preprint 83-63, Littleton, Colorado, unpaginated.

  • Journel, A. G., 1983, Nonparametric estimation of spatial distributions: Math. Geology, v. 15, no. 3, p. 445–468.

    Google Scholar 

  • Journel, A. G., and Alabert, F., 1988, Non-gaussian data expansion in the earth sciences: Terra Review, v. 1, no. 2, p. 123–134.

    Google Scholar 

  • Journel, A. G., and Huijbregts, C., 1978, Mining geostatistics: Academic Press. London, 600 p.

    Google Scholar 

  • Manoukian, E. B., 1986, Modem concepts and theorems of mathematical statistics: Springer-Verlag, New York, 156 p.

    Google Scholar 

  • Naylor, T. H., Baintfy, J. L., Burdick, D. S., and Chu, K., 1966, Computer simulation techniques: John Wiley & Sons, New York, 352 p.

    Google Scholar 

  • Rodríguez-Iturbe, I., and Mejia, J. M., 1974, The design of rainfall networks in time and space: Water Resources Research, v. 10, no. 4, p. 1185–1195.

    Google Scholar 

  • Rouhani, S., 1985, Variance reduction analysis: Water Resources Research, v. 21, no. 6, p. 837–846.

    Google Scholar 

  • Thompson, S. K., 1992, Sampling: John Wiley & Sons, Inc., New York, 343 p.

    Google Scholar 

  • Veneziano, D., and Kitanidis, P. K., 1982, Sequential sampling to contour an uncertain function: Math. Geology, v. 14, no. 5, p. 387–404.

    Google Scholar 

  • Verly, G., 1983. The multigaussian approach and it applications to the estimation of local reserves: Math. Geology, v. 15, no. 3. p. 263–290.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Watson, A.G., Barnes, R.J. Infill sampling criteria to locate extremes. Math Geol 27, 589–608 (1995). https://doi.org/10.1007/BF02093902

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02093902

Key words

Navigation