Skip to main content

Geostatistical Approach

  • Chapter
  • First Online:
  • 522 Accesses

Part of the book series: SpringerBriefs in Earth Sciences ((BRIEFSEARTH))

Abstract

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.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Bear J (1972) Dynamics of fluid in porous media. Elsevier, New York, p 764

    Google Scholar 

  • Beven K (1989) Changing ideas in hydrology—the case of physically-based models. J Hydrol 105:157–172 (Amsterdam)

    Article  Google Scholar 

  • Beven K (2005) On the concept of model structural error. Water Sci Technol 52(6):167–175 IWA Publishing

    Google Scholar 

  • Beven K, Freer J (2001) Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology. J Hydrol 249:11–29

    Article  Google Scholar 

  • Bolotin VV (1969) Statistical methods in structural mechanics. Holden-Day, SanFrancisco, p 240

    Google Scholar 

  • 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 

  • 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 

  • Brown GO, Hsieh HT, Lucero DA (2000) Evaluation of laboratory dolomite core sample size using representative elementary volume concepts. WWR 36(5):1199–1207

    Article  Google Scholar 

  • Cooley RL (2004) A theory for modeling ground-water flow in heterogeneous media: Reston VA, U.S. Geological survey, Professional paper, 1679, p 220

    Google Scholar 

  • Dagan G (1986) Statistical theory laboratory to formation, and formation to regional scale. WRR 22(9):109S–134S

    Article  Google Scholar 

  • Fisher RA (1935) The design of experiments. Oliver and Boyd, Edinburgh

    Google Scholar 

  • 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 

  • Gnedenko BV (1963) The theory of probability. Chelsea, New York, p 471

    Google Scholar 

  • Gomez-Hernandez JJ, Gorelick SM (1989) Effective groundwater model parameter values: influence of spatial variability of hydraulic conductivity, leakance, and recharge. WRR 25(3):405–419

    Article  Google Scholar 

  • 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 

  • Graham W, McLaughlin D (1989) Stochastic analysis of nonstationary subsurface solute transport. 1. Unconditional moments. WWR 25(2):215–232

    Article  Google Scholar 

  • 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 755–764

    Google Scholar 

  • Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics. Oxford University Press, New York, 561 p

    Google Scholar 

  • Kitandis PK (1997) Introduction to geostatistics: applications in hydrogeology. Cambridge University Press, Cambridge, p 249

    Book  Google Scholar 

  • Kolomensky NV, Komarov IS (1964) Geological engineering (Инжeнepнaя Гeoлoгия). Moscow, Vyshaja Shkola, p 489 in Russian

    Google Scholar 

  • McLaughlin D, Townley LR (1996) A reassessment of the groundwater inverse problem. WWR 32(5):1131–1161

    Google Scholar 

  • Moore C, Doherty J (2006) The cost of uniqueness in groundwater model calibration. Adv Water Res 29(4):605–623

    Article  Google Scholar 

  • Morton A (1993) Mathematical models: questions of trustworthiness. Br J Phil Sci 44:659–674

    Article  Google Scholar 

  • 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):341–364

    Article  Google Scholar 

  • NRC (1990) National resource council, groundwater models: scientific and regulatory applications. National Academy Press, Washington, DC, p 320

    Google Scholar 

  • 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 

  • 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 615

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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, 731–753

    Google Scholar 

  • Yeh WW-G (1986) Review of parameter identification procedures in ground water hydrology: the inverse problem. WWR 22(2):95–108

    Article  Google Scholar 

  • Yeh WW-G, Yoon YS (1981) Aquifer parameter identification with optimum dimension in parameterization. WRR 17(3):664–672

    Article  Google Scholar 

  • Yule GU, Kendall MG (1950) An introduction to the theory of statistics, 14th edn. New York, Hafner, p 701

    Google Scholar 

  • 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):1373–1413

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vikenti Gorokhovski .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 The Author(s)

About this chapter

Cite this chapter

Gorokhovski, V. (2012). Geostatistical Approach. In: Effective Parameters of Hydrogeological Models. SpringerBriefs in Earth Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23722-5_3

Download citation

Publish with us

Policies and ethics