Geostatistical Approach

  • Vikenti Gorokhovski
Part of the SpringerBriefs in Earth Sciences book series (BRIEFSEARTH)


The situation with the deterministic approach to predictive simulations is transparent. It can provide evaluations of the uncertainty of the simulation results in some typical circumstances for which engineering experience exists. These evaluations are of statistical nature. They are based on observed successes and failures of decisions made based on results of the corresponding simulations. However, if such experience does not exist, the engineering approach fails to provide provable estimates for the uncertainty of the simulation results. The situation seems more complicated with the geostatistical approach.


Hydraulic Conductivity Representative Elementary Volume Hydraulic Head Random Function Regional Trend 
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  1. Bear J (1972) Dynamics of fluid in porous media. Elsevier, New York, p 764Google Scholar
  2. Beven K (1989) Changing ideas in hydrology—the case of physically-based models. J Hydrol 105:157–172 (Amsterdam)CrossRefGoogle Scholar
  3. Beven K (2005) On the concept of model structural error. Water Sci Technol 52(6):167–175 IWA PublishingGoogle Scholar
  4. Beven K, Freer J (2001) Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology. J Hydrol 249:11–29CrossRefGoogle Scholar
  5. Bolotin VV (1969) Statistical methods in structural mechanics. Holden-Day, SanFrancisco, p 240Google Scholar
  6. Bondarik GK (1974) Fundamentals of the theory of variability of geological-engineering properties of rocks (Ocнoвы Teopии Измeнчивocти Инжeнepнo-Гeoлoгичecкиx Cвoйcтв Гopныx Пopoд). Nedra, Moscow, p 272 (in Russian)Google Scholar
  7. Borevsky BV, Samsonov BG, Yazvin LS (1973) Methodology of evaluating parameters of aquifers by pumping tests (Meтoдикa Oпpeдeлeния Пapaмeтepoв Boдoнocныx Гopизoнтoв пo Дaнным Oткaчeк). Nedra, Moscow, p 304 (in Russian)Google Scholar
  8. Brown GO, Hsieh HT, Lucero DA (2000) Evaluation of laboratory dolomite core sample size using representative elementary volume concepts. WWR 36(5):1199–1207CrossRefGoogle Scholar
  9. Cooley RL (2004) A theory for modeling ground-water flow in heterogeneous media: Reston VA, U.S. Geological survey, Professional paper, 1679, p 220Google Scholar
  10. Dagan G (1986) Statistical theory laboratory to formation, and formation to regional scale. WRR 22(9):109S–134SCrossRefGoogle Scholar
  11. Fisher RA (1935) The design of experiments. Oliver and Boyd, EdinburghGoogle Scholar
  12. Gentle JE (1985) Monte Carlo methods. In: Kots Samuel, Johnson Norman L (eds) Encyclopedia of statistical sciences, Vol 5. New York, Wiley, pp 612–617 Google Scholar
  13. Gnedenko BV (1963) The theory of probability. Chelsea, New York, p 471Google Scholar
  14. Gomez-Hernandez JJ, Gorelick SM (1989) Effective groundwater model parameter values: influence of spatial variability of hydraulic conductivity, leakance, and recharge. WRR 25(3):405–419CrossRefGoogle Scholar
  15. Gorokhovski VM (1977) Mathematical methods and reliability of hydrogeological and engineering geological predictions (Maтeмaтичecкиe мeтoды и дocтoвepнocть гидpoгeoлoгичecкиx и инжeнepнo-гeoлoгичecкиx пpoгнoзoв). Nedra, Moscow, p 77 (in Russian)Google Scholar
  16. Graham W, McLaughlin D (1989) Stochastic analysis of nonstationary subsurface solute transport. 1. Unconditional moments. WWR 25(2):215–232CrossRefGoogle Scholar
  17. Hornung U (1990) Parameter identification, In: Proceedings of the international symposium on water quality modeling of agricultural non-point sources, part 2, June 19–23 1988, U.S. department of agriculture, agriculture research service, ARS-81, pp 755–764Google Scholar
  18. Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics. Oxford University Press, New York, 561 pGoogle Scholar
  19. Kitandis PK (1997) Introduction to geostatistics: applications in hydrogeology. Cambridge University Press, Cambridge, p 249CrossRefGoogle Scholar
  20. Kolomensky NV, Komarov IS (1964) Geological engineering (Инжeнepнaя Гeoлoгия). Moscow, Vyshaja Shkola, p 489 in RussianGoogle Scholar
  21. McLaughlin D, Townley LR (1996) A reassessment of the groundwater inverse problem. WWR 32(5):1131–1161Google Scholar
  22. Moore C, Doherty J (2006) The cost of uniqueness in groundwater model calibration. Adv Water Res 29(4):605–623CrossRefGoogle Scholar
  23. Morton A (1993) Mathematical models: questions of trustworthiness. Br J Phil Sci 44:659–674CrossRefGoogle Scholar
  24. Neuman SP, Orr S (1993) Prediction of steady state flow in nonuniform geologic media by conditional moments: exact nonlocal formalism, effective conductivities, and weak approximation. WWR 29(2):341–364CrossRefGoogle Scholar
  25. NRC (1990) National resource council, groundwater models: scientific and regulatory applications. National Academy Press, Washington, DC, p 320Google Scholar
  26. Rats MV (1968) Heterogeneity of rocks and their physical properties (Heoднopoднocть Гopныx Пopoд и Иx Физичecкиe Cвoйcтвa). Nauka, Moscow, p 108 (in Russian)Google Scholar
  27. Review (1990) Review of geostatistics in geohydrology I: Basic Concepts. ASCE task committee on geostatistical techniques in hydrogeology, J Hydraulic Eng, vol 116, No. 5, 612–632, p 615Google Scholar
  28. Rozovsky LB, Zelenin IP (1975) Geological-engineering predictions and modeling (Розовский Л.Б. и Зеленин И.П, Инженерно-Геологические Прогнозы и Моделирование, Одесский Государственный Университет, Одесса) (in Russian)Google Scholar
  29. Shvidler MI (1964) Filtration flows in heterogeneous media (A statistical approach), consultants bureau enterprises, Inc., New York, USA, p 104 (Translation from Russian, see Shvidler, 1963)Google Scholar
  30. Shvidler MИ (1963) Фильтpaциoнныe Teчeния в Heoднopoдныx Cpeдax, Гocтexиздaт, Гocyдaтcтвeннoe Издaтeльcтвo Hayчнoй и Texничecкoй Литepaтypы пo Heфти и Mинepaльнoй Toпливнoй Пpoмышлeннocти, Mocквa, 110 c. (in Russian)Google Scholar
  31. van Genuchten M Th, Gorelick SM, Yeh WW-G (1990) Application of parameter estimation technique to solute transport studies, In: Proceedings of the international symposium on water quality modeling of agricultural non-point sources, part 2, June 19–23 1988, U.S. Department of agriculture, agriculture research service, ARS-81, 731–753Google Scholar
  32. Yeh WW-G (1986) Review of parameter identification procedures in ground water hydrology: the inverse problem. WWR 22(2):95–108CrossRefGoogle Scholar
  33. Yeh WW-G, Yoon YS (1981) Aquifer parameter identification with optimum dimension in parameterization. WRR 17(3):664–672CrossRefGoogle Scholar
  34. Yule GU, Kendall MG (1950) An introduction to the theory of statistics, 14th edn. New York, Hafner, p 701Google Scholar
  35. Zimmermann DA, de Marsily G, Gotway CA, Marrietta MG, Axness CL, Beauheim RL, Bras RL, Carrera J, Dagan G, Davies PB, Gallegos DP, Gally A, Gomez-Hernandez J, Grindrod P, Gutjahr AL, Kitanidis PK, Lavenue AM, McLaughlin D, Neuman SP, RamaRao BS, Ravenne C, Rubin Y (1998) A comparison of seven geostatistically based inverse approaches to estimate transmissivity for modeling adjective transport by groundwater flow. WRR 34(6):1373–1413CrossRefGoogle Scholar

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© The Author(s) 2012

Authors and Affiliations

  1. 1.AthensUSA

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