Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T15:43:54.805Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic indicator analysis of contaminated sites

Part of: Applications Decision theory Geophysics (general) Geophysics Survival analysis and censored data Stochastic processes

Published online by Cambridge University Press:  14 July 2016

George Christakos  and
Dionissios T. Hristopulos
George Christakos*
Affiliation:
University of North Carolina
Dionissios T. Hristopulos*
Affiliation:
University of North Carolina
*
∗Postal address: Department of Environmental Sciences and Engineering, University of North Carolina, CB#7400, Chapel Hill, NC 27599–7400, USA.
∗Postal address: Department of Environmental Sciences and Engineering, University of North Carolina, CB#7400, Chapel Hill, NC 27599–7400, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We formulate stochastic indicator parameters that characterize pollution levels in geographical regions with heterogeneous contaminant distributions. The indicator parameters are expressed in terms of the random fields representing the contaminant distributions and the critical threshold level specified by health and environmental standards. Certain theoretical results are proven regarding univariate and bivariate indicator parameters. The analytical expressions obtained are general and can be used in practice for various types of contaminant distributions. A test of ergodicity-breaking is suggested for scientific and engineering applications in terms of the indicator parameters. Fractal characteristics of the indicator parameters are discussed. The effects of modelling and observation scale on exceedance contamination analysis are examined. Indicator random field parameters are studied on both continuum and lattice domains using analytical means and numerical simulations.

Keywords

RANDOM FIELDSINDICATORSLEVEL-CROSSINGLATTICE

MSC classification

Primary: 60G60: Random fields 62C99: None of the above, but in this section 62N99: None of the above, but in this section 62P99: None of the above, but in this section
Secondary: 86A05: Hydrology, hydrography, oceanography 86A32: Geostatistics
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 988 - 1008
Copyright
Copyright © Applied Probability Trust 1997 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adler, R. J. (1981) The Geometry of Random Fields. Wiley, New York.Google Scholar
Alfsen, G. M. (1971) Compact Convex Sets and Boundary Integrals. Springer, Berlin.CrossRefGoogle Scholar
Christakos, G. (1992) Random Field Models in Earth Sciences. Academic Press, San Diego.Google Scholar
Christakos, G. and Hristopulos, D. T. (1995) Contaminant characterization in terms of stochastic indicator parameters. Research Report SM/12.95. University of North Carolina.Google Scholar
Christakos, G. and Killam, B. R. (1993) Sampling design for classifying contaminant level using annealing search algorithms. Water Resource Res. 29, 4063–4076.CrossRefGoogle Scholar
Cramer, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
Deutsch, C. V. and Journel, A. G. (1992) Geostatistical Software Library and User's Guide. Oxford University Press, Oxford.Google Scholar
Dzombak, D. A., Labienec, P. A. and Siegrist, R. L. (1993) The need for uniform soil clean-up goals. Environ. Sci. Technol. 27, 765–766.Google Scholar
Journel, A. G. (1983) Non-parametric estimation of spatial distributions. Math. Geol. 15, 445–468.Google Scholar
Loeve, M. (1953) Probability Theory. Van Nostrand, Princeton, NJ.Google Scholar
Longuet-Higgins, M. S. (1957) The statistical analysis of a random moving surface. Phil. Trans. R. Soc. A 249, 321–387.Google Scholar
Mandelbrot, B. B. (1983) The Fractal Geometry of Nature. Freeman, San Francisco.Google Scholar
Swerling, P. (1962) Statistical properties of the contours of random surfaces. IRE Trans. Inf. Theory , 315–321.Google Scholar
Wentz, C. A. (1989) Hazardous Waste Management. McGraw-Hill, New York.Google Scholar
Wolfram, S. (1991) Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley, Reading, MA.Google Scholar