Skip to main content
SpringerLink
Log in

Geostatistical Space–Time Models: A Review

  • Published:
Mathematical Geology Aims and scope Submit manuscript

Abstract

Geostatistical space–time models are used increasingly for addressing environmental problems, such as monitoring acid deposition or global warming, and forecasting precipitation or stream flow. Each discipline approaches the problem of joint space–time modeling from its own perspective, a fact leading to a significant amount of overlapping models and, possibly, confusion. This paper attempts an annotated survey of models proposed in the literature, stating contributions and pinpointing shortcomings. Stochastic models that extend spatial statistics (geostatistics) to include the additional time dimension are presented with a common notation to facilitate comparison. Two conceptual viewpoints are distinguished: (1) approaches involving a single spatiotemporal random function model, and (2) approaches involving vectors of space random functions or vectors of time series. Links between these two viewpoints are then revealed; advantages and shortcomings are highlighted. Inference from space–time data is revisited, and assessment of joint space–time uncertainty via stochastic imaging is suggested.

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

Similar content being viewed by others

REFERENCES

  • Almeida, A., and Journel, A. G., 1994, Joint simulation of multiple variables with a Markov-type coregionalization model: Math. Geology, v. 26, no. 5, p. 565–588.

    Google Scholar 

  • Armstrong, M., Chetboun, G., and Hubert, P., 1993, Kriging the rainfall in Lesotho, in A. Soares, ed., Geostatistics Tróia' 92, Vol. 2: Kluwer Academic Publ., Dordrecht, p. 661–672.

    Google Scholar 

  • Bacchi, B., and Kottegoda, N. T., 1995, Identification and calibration of spatial correlation patterns of rainfall: Jour. Hydrology, v. 165, p. 311–348.

    Google Scholar 

  • Bennett, R. J., 1979, Spatial time series: Analysis-forecasting-control: Pion, London, 674 p.

    Google Scholar 

  • Bilonick, R. A., 1985, The space-time distribution of sulfate deposition in the northeastern United States: Atmosph. Environment, v. 19, no. 11, p. 1829–1845.

    Google Scholar 

  • Bilonick, R. A., 1988, Monthly hydrogen ion deposition maps for the northeastern U.S. from July 1982 to September 1984: Atmosph. Environment, v. 22, no. 9, p. 1909–1924.

    Google Scholar 

  • Bogaert, P., 1996, Comparison of kriging techniques in a space-time context: Math. Geology, v. 28, no. 1, p. 73–86.

    Google Scholar 

  • Bogaert, P., and Christakos, G., 1997a, Spatiotemporal analysis and processing of thermometric data over Belgium: Jour. Geoph. Res., v. 102, no. D22, p. 25831–25846.

    Google Scholar 

  • Bogaert, P., and Christakos, G., 1997b, Stochastic analysis of spatiotemporal solute content measurements using a regression model: Stoch. Hydrol. Hydraulics, v. 11, no. 4, p. 267–295.

    Google Scholar 

  • Boulanger, F., 1989, Géostatistique et methods autorégressifs: Une nouvelle méthode de modélisation, in M. Armstrong, ed., Geostatistics, Vol. 1: Kluwer Academic Publ., Dordrecht, p. 259–271.

    Google Scholar 

  • Box, G. E. P., Jenkins, G. M., and Reinsel, G. C., 1994, Time series analysis, forecasting and control: Prentice-Hall, Englewood Cliffs, NJ, 3rd ed., 598 p.

    Google Scholar 

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

    Google Scholar 

  • Bras, R. L., and Rodrígues-Iturbe, I., 1984, Random functions and hydrology: Addison-Wesley, Reading, MA, 559 p.

    Google Scholar 

  • Brown, P. J., Le, N. D., and Zidek, J. V., 1994, Multivariate spatial interpolation and exposure to air pollutants: Can. Jour. Statistics, v. 22, no. 4, p. 489–509.

    Google Scholar 

  • Buxton, B. E., and Plate, A. D., 1994, Joint temporal-spatial modeling of concentrations of hazardous pollutants in urban air, in R. Dimitrakopoulos, ed., Geostatistics for the next century: Kluwer Academic Publ., Dordrecht, p. 75–87.

    Google Scholar 

  • Carroll, R. J., Chen, R., George, E. I., Li, T. H., Newton, H. J., Schmiediche, H., and Wang, N., 1997, Ozone exposure and population density in Harris county, Texas (with discussion): Jour. Amer. Statistical Assoc., v. 92, no. 438, p. 392–415.

    Google Scholar 

  • Carroll, S. S., and Cressie, N., 1997, Spatial modeling of snow water equivalent using covariances estimated from spatial and geomorphic attributes: Jour. Hydrology, v. 190, p. 42–59.

    Google Scholar 

  • Chirlin, G. R., and Wood, E. F., 1982, On the relationship between kriging and state estimation: Water Resources Res., v. 18, no. 2, p. 432–438.

    Google Scholar 

  • Christakos, G., 1992, Random field models in earth sciences: Academic Press, San Diego, CA, 474 p.

    Google Scholar 

  • Christakos, G., and Bogaert, P., 1996, Spatiotemporal analysis of spring water ion processes derived from measurements at the Dyle basin in Belgium: IEEE Transactions on Geoscience and Remote Sensing, v. 34, no. 3, p. 626–642.

    Google Scholar 

  • Christakos, G., and Hristopulos, D. T., 1998, Spatiotemporal environmental health modelling: A tractatus stochasticus: Kluwer Academic Publ., Boston, 424 p.

    Google Scholar 

  • Christakos, G., and Lai, J., 1997, A study of breast cancer dynamics in North Carolina: Social Sci. Medicine, v. 45, no. 10, p. 1503–1517.

    Google Scholar 

  • Christakos, G., and Raghu, R., 1996, Dynamic stochastic estimation of physical variables: Math. Geology, v. 28, no. 3, p. 341–365.

    Google Scholar 

  • Cleveland, W., and Devlin, S., 1988, Locally weighted regression: An approach to regression analysis by local fitting: Jour. Amer. Statistical Assoc., v. 83, no. 403, p. 596–610.

    Google Scholar 

  • Cliff, A. D., Haggett, P., Ord, J. K., and Bassett, K. A., 1975, Elements of spatial structure: A quantitative approach: Cambridge University Press, New York, 258 p.

    Google Scholar 

  • Cressie, N. A. C., 1993, Statistics for spatial data: John Wiley & Sons, New York, rev. ed., 900 p.

    Google Scholar 

  • Creutin, J. D., and Obled, C., 1982, Objective analyses and mapping techniques for rainfall fields: An objective comparison: Water Resources Res., v. 18, no. 2, p. 413–431.

    Google Scholar 

  • De Cesare, L., Myers, D. E., and Posa, D., 1997, Spatio-temporal modeling of SO 2 in Milan district, in Baaffi, E., and Schofield, N., eds., Geostatistics Wollongong'96, Vol. 2: Kluwer Academic Publ., Dordrecht, p. 1310–1042.

    Google Scholar 

  • Delfiner, P., 1976, Linear estimation of non-stationary spatial phenomena, in Guarascio, M., David M., and Huijbregts Ch. J., eds., Advanced Geostatistics in the Mining Industry: Reidel, Dordrecht, The Netherlands, p. 49–68.

    Google Scholar 

  • Deutsch, C. V., and Journel, A. G., 1998, GSLIB: Geostatistical software library and user's guide: Oxford University Press, New York, 2nd ed., 368 p.

    Google Scholar 

  • Dimitrakopoulos, R., and Luo, X., 1994, Spatiotemporal modeling: Covariances and ordinary kriging systems, in R. Dimitrakopoulos, ed., Geostatistics for the next century: Kluwer Academic Publ., Dordrecht, p. 88–93.

    Google Scholar 

  • Dimitrakopoulos, R., and Luo, X., 1997, Joint space-time modeling in the presence of trends, in Baaffi, E., and Schofield, N., eds., Geostatistics Wollongong'96, Vol. 1: Kluwer Academic Publ., Dordrecht, p. 138–149.

    Google Scholar 

  • Egbert, G. D., and Lettenmaier, D. P., 1986, Stochastic modeling of the space-time structure of atmospheric chemical deposition: Water Resources Res., v. 22, no. 2, p. 165–179.

    Google Scholar 

  • Eynon, B. P., 1988, Statistical analysis of precipitation chemistry measurements over the eastern United States. Part II: Kriging analysis of regional patterns and trends: Jour. Appl. Meteorology, v. 27, p. 1334–1343.

    Google Scholar 

  • Eynon, B. P., and Switzer, P., 1983, The variability of rainfall acidity: Can. Jour. Statistics, v. 11, no. 1, p. 11–24.

    Google Scholar 

  • Gandin, L., 1963, Objective Analysis of Meteorological Fields: Gidrometeorologicheskoe Izdatel'stvo (GIMEZ), Leningrad. Reprinted by Israel Program for Scientific Translations, Jerusalem, 1965.

    Google Scholar 

  • Gelb, A., 1974, Applied optimal estimation: MIT Press, Cambridge, MA, 374 p.

    Google Scholar 

  • Goovaerts, P., 1997, Geostatistics for natural resources evaluation: Oxford University Press, New York, 483 p.

    Google Scholar 

  • Goovaerts, P., and Chiang, C., 1993, Temporal persistence of spatial patterns for mineralizable nitrogen and selected soil properties: Soil Sci. Soc. America Jour., v. 57, no. 2, p. 372–381.

    Google Scholar 

  • Goovaerts, P., and Sonnet, P., 1993, Study of spatial and temporal variations of hydrogeochemical variables using factorial kriging analysis, in A. Soares, ed., Geostatistics Tróia '92, Vol. 2: Kluwer Academic Publ., Dordrecht, p. 745–756.

    Google Scholar 

  • Goulard, M., and Voltz, M., 1992, Linear coregionalization model: Tools for estimation and choice of cross-variogram matrix: Math. Geology, v. 24, no. 3, p. 269–286.

    Google Scholar 

  • Guttorp, P., and Sampson, P., 1994, Methods for estimating heterogeneous spatial covariance functions with environmental applications, in Patil, G. P., and Rao, C. R., eds., Handbook of statistics, Vol. 12: Elsevier Science, North-Holland, Amsterdam, p. 661–689.

    Google Scholar 

  • Guttorp, P., Sampson, P. D., and Newman, K., 1992, Non-parametric estimation of spatial covariance with application to monitoring network evaluation, in Walden, A. T., and Guttorp, P., eds., Statistics in environmental and earth sciences: Edward Arnold, London, p. 39–51.

    Google Scholar 

  • Haas, T. C., 1995, Local prediction of a spatio-temporal process with an application to wet sulfate deposition: Jour. Am. Statistical Assoc., v. 90, no. 432, p. 1189–1199.

    Google Scholar 

  • Haas, T. C., 1998, Statistical assessment of spatio-temporal pollutant trends and meteorological transport models: Atmosph. Environment, v. 32, no. 11, p. 1865–1879.

    Google Scholar 

  • Handcock, M. S., and Wallis, J. R., 1994, An approach to statistical spatial-temporal modeling of meteorological fields (with discussion): Jour. Am. Statistical Assoc., v. 89, no. 426, p. 368–390.

    Google Scholar 

  • Haslett, J., 1989, Space time modeling in meteorology: A review, Proceedings of the 47th Session: International Statistical Institute, Paris, p. 229–246.

    Google Scholar 

  • Haslett, J., and Raftery, A. E., 1989, Space-time modeling with long-memory dependence: Assessing Ireland's wind power resource (with discussion): Appl. Statistics, v. 38, no. 1, p. 1–50.

    Google Scholar 

  • Heuvelink, G. B. M., Musters, P., and Pebesma, E. J., 1997, Spatio-temporal kriging of soil water content, in Baaffi, E., and Schofield, N., eds., Geostatistics Wollongong '96, Vol. 2: Kluwer Academic Publ., Dordrecht, p. 1020–1030.

    Google Scholar 

  • Hohn, M. E., Liebhold, A. M., and Gribko, L. S., 1993, Geostatistical model for forecasting spatial dynamics of defoliation caused by the gypsy moth (Lepidoptera: Lymantriidae): Environmental Entomology, v. 22, no. 5, p. 1066–1075.

    Google Scholar 

  • Høst, G., Omre, H., and Switzer, P., 1995, Spatial interpolation errors for monitoring data: Jour. Am. Statistical Assoc., v. 90, no. 431, p. 853–861.

    Google Scholar 

  • Hudson, G., and Wackernagel, H., 1994, Mapping temperature using kriging with external drift: Theory and an example from Scotland: Int. Jour. Climatology, v. 14, no. 1, p. 77–91.

    Google Scholar 

  • Jones, R. H., and Vecchia, A. V., 1993, Fitting continuous ARMA models to unequally spaced spatial data: Jour. Am. Statistical Assoc., v. 88, no. 423, p. 947–954.

    Google Scholar 

  • Jones, R. H., and Zhang, Y., 1997, Models for continuous stationary space-time processes, in Gregoire, T. G., Brillinger, D. R., Diggle, P. J., Russek-Cohen, E., Warren, W. G., and Wolfinger, R. D., eds., Modelling longitudinal and spatially correlated data, Lecture Notes in Statistics, Vol. 122: Springer-Verlag, New York, p. 289–298.

    Google Scholar 

  • Journel, A. G., 1986, Geostatistics: Models and tools for the earth sciences: Math. Geology, v. 18, no. 1, p. 119–140.

    Google Scholar 

  • Journel, A. G., 1989, Fundamentals of geostatistics in five lessons, Volume 8 Short Course in Geology: American Geophysical Union, Washington, DC, 40 p.

    Google Scholar 

  • Journel, A. G., 1993, Modeling uncertainty: Some conceptual thoughts, in R. Dimitrakopoulos, ed., Geostatistics for the Next Century: Kluwer Academic Publ., Dordrecht, p. 30–43.

    Google Scholar 

  • Journel, A. G., and Huijbregts, Ch. J., 1972, Estimation of lateritic-type orebodies, Proceedings of the 10th International APCOM Symposium: Society of Mining Engineers, Johannesburg, p. 202–212.

    Google Scholar 

  • Journel, A. G., and Huijbregts, Ch. J., 1978, Mining geostatistics: Academic Press, New York, 600 p.

    Google Scholar 

  • Journel, A. G., and Rossi, M., 1989, When do we need a trend model in kriging?: Math. Geology, v. 21, no. 7, p. 715–739.

    Google Scholar 

  • Kyriakidis, P. C., 1998, Stochastic models for spatiotemporal distributions: Application to sulphate deposition over Europe, Rep. 11, Vol. 2: Stanford Center for Reservoir Forecasting, Stanford University, Stanford, CA.

    Google Scholar 

  • Kyriakidis, P. C., 1999, Stochastic Simulation of Spatiotemporal Phenomena: Unpublished doctorate dissertation: Stanford University, Stanford, CA, 221 p.

    Google Scholar 

  • Loader, C., and Switzer, P., 1992, Spatial covariance estimation for monitoring data, in Walden, A. T., and Guttorp, P., eds., Statistics in Environmental and Earth Sciences: Edward Arnold, London, p. 52–70.

    Google Scholar 

  • Mardia, K. V., and Goodall, C. R., 1993, Spatial-temporal analysis of multivariate environmental data, in Patil, G. P., and Rao, C. R., eds., Multivariate environmental statistics: Elsevier, Amsterdam, p. 347–386.

    Google Scholar 

  • Matérn, B. 1980, Spatial Variation, Lecture Notes in Statistics, Vol. 36: Springer Verlag, New York, 2nd ed., 151 p. First edition published in Meddelanden fran Statens Skogsforskningsinstitut, Band 49, No. 5, 1960.

    Google Scholar 

  • Matheron, G., 1962, Traitéde géostatistique appliquée, Tome I: Mémoires du Bureau de Recherches Géologiques et Miniéres, Editions Technip, Paris, 333 p.

    Google Scholar 

  • Matheron, G., 1973, The intrinsic random functions and their applications: Adv. Appl. Probab., v. 5, p. 439–468.

    Google Scholar 

  • Meiring, W., Guttorp, P., and Sampson, P. D., 1998, Space-time estimation of grid-cell hourly ozone levels for assessment of a deterministic model: Environmental and Ecological Statistics, v. 5, in press.

  • Meiring, W., Monestiez, P., Sampson, P. D., and Guttorp, P., 1997, Developments in the modeling of nonstationary spatial covariance structure from space-time monitoring data, in Baaffi, E., and Schofield, N., eds., Geostatistics Wollongong '96, Vol. 1: Kluwer Academic Publ., Dordrecht, p. 162–173.

    Google Scholar 

  • Myers, D. E., and Journel, A. G., 1990, Variograms with zonal anisotropies and noninvertible kriging systems: Math. Geology, v. 22, no. 7, p. 779–785.

    Google Scholar 

  • Obled, C., and Creutin, J. D., 1986, Some developments in the use of Empirical Orthogonal Functions for mapping meteorological fields: Jour. Climate Appl. Meteorology, v. 25, no. 9, p. 1189–1204.

    Google Scholar 

  • Oehlert, G. W., 1993, Regional trends in sulfate wet deposition: Jour. Am. Statistical Assoc., v. 88, no. 422, p. 390–399.

    Google Scholar 

  • Papritz, A., and Flühler, H., 1994, Temporal change of spatially autocorrelated soil properties: Optimal estimation by cokriging: Geoderma, v. 62, p. 29–43.

    Google Scholar 

  • Pereira, M. J., Soares, A., and Branquinho, C., 1997, Stochastic simulation of fugitive dust emissions, in Baaffi, E., and Schofield, N., eds., Geostatistics Wollongong '96, Vol. 2: Kluwer Academic Publ., Dordrecht, p. 1055–1065.

    Google Scholar 

  • Rao, A. R., and Hsieh, C. H., 1991, Estimation of variables at ungaged locations by Empirical Orthogonal Functions: Jour. Hydrology, v. 123, p. 51–67.

    Google Scholar 

  • Rehman, S. U., 1995, Semiparametric Modeling of Cross-Semivariograms: Unpublished doctorate dissertation, Georgia Institute of Technology, Athens, GA, 143 p.

    Google Scholar 

  • Reichenbach, H., 1958, The philosophy of space & time: Dover, New York, 295 p.

    Google Scholar 

  • Rodríguez-Iturbe, I., and Mejía, J. M., 1974, The design of rainfall networks in time and space: Water Resources Res., v. 10, no. 4, p. 713–728.

    Google Scholar 

  • Rouhani, S., Ebrahimpour, R. M., Yaqub, I., and Gianella, E., 1992, Multivariate geostatistical trend detection and network evaluation of space-time acid deposition data–I. Methodology: Atmosph. Environment, v. 26, no. 14, p. 2603–2614.

    Google Scholar 

  • Rouhani, S., and Hall, T. J., 1989, Space-time kriging of groundwater data, in M. Armstrong, ed., Geostatistics, Vol. 2: Kluwer Academic Publ., Dordrecht, p. 639–650.

    Google Scholar 

  • Rouhani, S., and Myers, D. E., 1990, Problems in space-time kriging of geohydrological data: Math. Geology, v. 22, no. 5, p. 611–623.

    Google Scholar 

  • Rouhani, S., and Wackernagel, H., 1990, Multivariate geostatistical approach to space-time data analysis: Water Resources Res., v. 26, no. 4, p. 585–591.

    Google Scholar 

  • Salas, J. D., 1993, Analysis and modeling of hydrologic time series, in D. R. Maidment, ed., Handbook of hydrology: McGraw-Hill, New York, p. 19.1–19.71.

    Google Scholar 

  • Sampson, P., and Guttorp, P., 1992, Non parametric estimation of nonstationary spatial structure: Jour. Am. Statistical Assoc., v. 87, no. 417, p. 108–119.

    Google Scholar 

  • Séguret, S. A., 1989, Filtering periodic noise by using trigonometric kriging, in M. Armstrong, ed., Geostatistics, Vol. 1: Kluwer Academic Publ., Dordrecht, p. 481–491.

    Google Scholar 

  • Séguret, S., and Huchon, P., 1990, Trigonometric kriging: A new method for removing the diurnal variation fom geomagnetic data, Jour. Geophys. Res., v. 95, no. B13, p. 21383–21397.

    Google Scholar 

  • Simard, Y., and Marcotte, D., 1993, Assessing similarities and differences among maps: A study of temporal changes in distribution of northern shrimp (pandalus borealis) in the gulf of St. Lawrence, in A. Soares, ed., Geostatistics Tróia '92, Vol. 2: Kluwer Academic Publ., Dordrecht, p. 865–874.

    Google Scholar 

  • Soares, A., Patinha, P. J., and Pereira, M. J., 1996, Stochastic simulation of space-time series: Application to a river water quality modeling, in Srivastava, R. M., Rouhani, S., Cromer, M. V., Johnson, A. I., and Desbarats, A. J., eds., Geostatistics for environmental and geotechnical applications: American Society for Testing and Materials, West Conshohocken, PA, p. 146–161.

    Google Scholar 

  • Sølna, K., and Switzer, P., 1996, Time trend estimation for a geographic region: Jour. Am. Statistical Assoc., v. 91, no. 434, p. 577–589.

    Google Scholar 

  • Solow, A. R., 1984, The analysis of second-order stationary processes: Time series analysis, spectral analysis, harmonic analysis, and geostatistics, in Verly, G., David, M., Journel, A. G., and Marechal, A., eds., Geostatistics for Natural Resources Characterization, Vol. 1: Reidel, Dordrecht, The Netherlands, p. 573–585.

    Google Scholar 

  • Solow, A. R., and Gorelick, S. M., 1986, Estimating monthly streamflow values by cokriging: Math. Geology, v. 18, no. 8, p. 785–809.

    Google Scholar 

  • Srivastava, R., 1992, Reservoir characterization with probability field simulation, SPE Annual Conference and Exhibition, Washington, DC: Society of Petroleum Engineers, Washington, DC, p. 927–938. SPE paper number 24753, preprint.

    Google Scholar 

  • Stein, M., 1986, A simple model for spatial-temporal processes: Water Resources Res., v. 22, no. 13, p. 2107–2110.

    Google Scholar 

  • Switzer, P., 1979, Statistical considerations in network design: Water Resources Res., v. 15, no. 6, p. 1712–1716.

    Google Scholar 

  • Switzer, P., 1989, Non-stationary spatial covariances estimated from monitoring data, in M. Armstrong, ed., Geostatistics, Vol. 1: Kluwer Academic Publ., Dordrecht, p. 127–138.

    Google Scholar 

  • Tabios, G., and Salas, J., 1985, A comparative analysis of techniques for spatial interpolation of precipitation: Water Resources Bull., v. 21, no. 3, p. 365–380.

    Google Scholar 

  • Venkatram, A., 1988, On the use of kriging in the spatial analysis of acid precipitation data: Atmosph. Environment, v. 22, no. 9, p. 1963–1975.

    Google Scholar 

  • Voltz, M., and Goulard, M., 1994, Spatial interpolation of soil moisture retention curves: Geoderma, v. 62, p. 109–123.

    Google Scholar 

  • Vyas, V., and Christakos, G., 1997, Spatiotemporal analysis and mapping of sulfate deposition data over eastern U.S.A.: Atmosph. Environment, v. 31, no. 21, p. 3623–3633.

    Google Scholar 

  • Wackernagel, H., 1995, Multivariate Geostatistic: Springer, Berlin, 256 p.

    Google Scholar 

  • Weyl, H., 1952, Space-time-matter: Dover, New York, 330 p.

    Google Scholar 

  • Wikle, C., Berliner, L. M., and Cressie, N., 1998, Hierarchical Bayesian space-time models: Environmental and Ecological Statistics, v. 5, in press.

  • Wikle, C. K., and Cressie, N., 1997, A dimension reduction approach to space-time Kalman filtering, Technical Report Preprint No. 97–24: Statistical Laboratory, Department of Statistics, Iowa State University, Ames, IA.

    Google Scholar 

  • Xu, W., and Journel, A. G., 1994, Dssim: A general sequential simulation algorithm, Report. 7: Stanford Center for Reservoir Forecasting, Stanford University, Stanford, CA.

    Google Scholar 

  • Yao, T., 1996, Hole effect or not?, Rep. 9: Stanford Center for Reservoir Forecasting, Stanford University, Stanford, CA.

    Google Scholar 

  • Yao, T., 1998. Conditional spectral simulation with phase identification: Math. Geology, v. 30, no. 3, p. 285–308.

    Google Scholar 

  • Yao, T., and Journel, A. G., 1998, Automatic modeling of covariance tables with Fast Fourier Transform: Math. Geology, v. 30, no. 6, p. 589–615.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geological and Environmental Sciences, Stanford University, Stanford, California, 94305-2115

    Phaedon C. Kyriakidis

  2. Department of Petroleum Engineering, Stanford University, Stanford, California, 94305-2220

    André G. Journel

Authors
  1. Phaedon C. Kyriakidis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. André G. Journel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kyriakidis, P.C., Journel, A.G. Geostatistical Space–Time Models: A Review. Mathematical Geology 31, 651–684 (1999). https://doi.org/10.1023/A:1007528426688

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007528426688

Search

Navigation