Skip to main content
SpringerLink
Log in

Multivariate grid-free geostatistical simulation with point or block scale secondary data

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

A novel grid-free geostatistical simulation method (GFS) allows representing coregionalized variables as an analytical function of the coordinates of the simulation locations. Simulation on unstructured grids, regridding and refinement of available realizations of natural phenomena including, but not limited to, environmental systems are possible with GFS in a consistent manner. The unconditional realizations are generated by utilizing the linear model of coregionalization and Fourier series-based decomposition of the covariance function. The conditioning to data is performed by kriging. The data can be measured at scattered point-scale locations or sampled at a block scale. Secondary data are usually used in conjunction with primary data for the improved modeling. Satellite imaging is an example of exhaustively sampled secondary data. Improvements and recommendations are made to the implementation of GFS to properly assimilate secondary exhaustive data sets in a grid-free manner. Intrinsic cokriging (ICK) is utilized to reduce computational time and preserve the overall quality of the simulation. To further reduce the computational cost of ICK, a block matrix inversion is implemented in the calculation of the kriging weights. A projection approach to ICK is proposed to avoid artifacts in the realizations around the edges of the exhaustive data region when the data do not cover the entire modeling domain. The point-scale block value representation of the block-scale data is developed as an alternative to block cokriging to integrate block-scale data into realizations within the GFS framework. Several case studies support the proposed enhancements.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  • Babak O (2008) Theoretical and practical improvements to geostatistical estimation and simulation. PhD Thesis, University of Alberta

  • Babak O, Machuca-Mory DF, Deutsch CV (2010) An approximate method for joint sequential simulation of multiple spatial variables. Stoch Environ Res and Risk Assess 24:327–336

    Article  Google Scholar 

  • Barnett RM, Deutsch CV (2015) Multivariate imputation of unequally sampled geological variables. Math Geosci. (online publication)

  • Barnett RM, Manchuk JG, Deutsch CV (2014) Projection Pursuit Multivariate Transform. Math Geosci 46(3):337–359

    Article  Google Scholar 

  • Bellin A, Rubin Y (1996) HYDRO_GEN: a spatially distributed random field generator for correlated properties. Stoch Hydrol Hydraul 10:253–278

    Article  Google Scholar 

  • Capilla JE, Rodrigo J, Gómez-Hernández JJ (1998) Worth of secondary data compared to piezometric data for the probabilistic assessment of radionuclide migration. Stoch Hydrol and Hydraul 12:171–190

    Article  Google Scholar 

  • Chiles JP, Delfiner P (2012) Geostatistics: modeling spatial uncertainty, 2nd edn. Wiley, New York

    Book  Google Scholar 

  • Deutsch CV, Journel AG (1998) GSLIB: Geostatistical Software Library and User’s Guide, 2nd edn. Oxford University Press, New York

    Google Scholar 

  • Emery X (2010) Multi-Gaussian Kriging and simulation in the presence of an uncertain mean value. Stoch Environ Res Risk Assess 24:211–219

    Article  Google Scholar 

  • Goldberger AS (1964) Econometric theory. Wiley, New York

    Google Scholar 

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York

    Google Scholar 

  • Gutjahr B, Bullard B, Hatch S, Hughson L (1994) Joint conditional simulations and the spectral approach for flow modeling. Stoch Hydrol Hydraul 8:79–108

    Article  Google Scholar 

  • Hughson DL, Yeh TCJ (1998) A geostatistically based inverse model for three-dimensional variability saturated flow. Stoch Hydrol Hydraul 12:285–298

    Article  Google Scholar 

  • Journel AG (1974) Geostatistics for conditional simulation of ore bodies. Econ Geolog 69(50):673–687

    Article  Google Scholar 

  • Journel AG, Huijbregts CJ (1978) Mining Geostatistics. Academic Press, New York

    Google Scholar 

  • Leuangthong O, Deutsch CV (2003) Stepwise conditional transformation for simulation of multiple variables. Math Geol 35(2):155–173

    Article  Google Scholar 

  • Ostrouchov G, Doll WE, Beard LP, Morris MD, Wolf DA (2009) Multiscale structure of UXO site characterization: spatial estimation and uncertainty quantification. Stoch Environ Res Risk Assess 23:215–225

    Article  Google Scholar 

  • Pyrcz MJ, Deutsch CV (2014) Geostatistical reservoir modeling, 2nd edn. Oxford University Press, New York

    Google Scholar 

  • Roberts BL, McKenna SA (2009) The Use of secondary information in geostastical target area identification. Stoch Environ Res Risk Assess 23:227–236

    Article  Google Scholar 

  • van de Kassteele J, Koelemeijer BA, Dekkers ALM, Schaap M, Homan CD, Stein A (2006) Statistical mapping of PM10 concentrations over Western Europe using secondary information from dispersion modeling and MODIS satellite observations. Stoch Environ Res Risk Assess 21:183–194

    Article  Google Scholar 

  • Vargas-Guzman JA (2003) Conditional components for simulation of vector random fields. Stoch Environ Res Risk Assess 17:260–271

    Article  Google Scholar 

  • Wackernagel H (2003) Multivariate geostatistics: an introduction with applications, 3rd edn. Springer, Berlin

    Book  Google Scholar 

  • Xu H, Xu CY, Sælthun NR, Zhou B, Xu Y (2014) Evaluation of Reanalysis and Satellite-based Precipitation Datasets in Driving Hydrological Models in a Humid Region of Southern China. Stoch Environ Res Risk Assess (online)

  • Zagayevskiy Y, Deutsch CV (2015) Multivariate geostatistical grid-free simulation of natural phenomena. Math Geosci (under review)

Download references

Acknowledgments

The authors would like to express gratitude to the sponsoring companies of the Centre for Computational Geostatistics (CCG) for their financial support.

Author information

Authors and Affiliations

  1. Markin/CNRL Natural Resources Engineering Facility, University of Alberta, 9105 116th St, Edmonton, AB, T6G 2W2, Canada

    Yevgeniy Zagayevskiy & Clayton V. Deutsch

Authors
  1. Yevgeniy Zagayevskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Clayton V. Deutsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yevgeniy Zagayevskiy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zagayevskiy, Y., Deutsch, C.V. Multivariate grid-free geostatistical simulation with point or block scale secondary data. Stoch Environ Res Risk Assess 30, 1613–1633 (2016). https://doi.org/10.1007/s00477-015-1154-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-015-1154-x

Keywords

Search

Navigation