“Geostatistics”的意思、由来-开放百科全书

Geostatistics is intimately related to interpolation methods, but extends far beyond simple interpolation problems. Geostatistical techniques rely on statistical models that are based on random function (or random variable) theory to model the uncertainty associated with spatial estimation and simulation.

A number of simpler interpolation methods/algorithms, such as inverse distance weighting, bilinear interpolation and nearest-neighbor interpolation, were already well known before geostatistics.^[3] Geostatistics goes beyond the interpolation problem by considering the studied phenomenon at unknown locations as a set of correlated random variables.

Let {{math|Z(x)}} be the value of the variable of interest at a certain location {{math|x}}. This value is unknown (e.g. temperature, rainfall, piezometric level, geological facies, etc.). Although there exists a value at location {{math|x}} that could be measured, geostatistics considers this value as random since it was not measured, or has not been measured yet. However, the randomness of {{math|Z(x)}} is not complete, but defined by a cumulative distribution function (CDF) that depends on certain information that is known about the value {{math|Z(x)}}:

Typically, if the value of {{math|Z}} is known at locations close to {{math|x}} (or in the neighborhood of {{math|x}}) one can constrain the CDF of {{math|Z(x)}} by this neighborhood: if a high spatial continuity is assumed, {{math|Z(x)}} can only have values similar to the ones found in the neighborhood. Conversely, in the absence of spatial continuity {{math|Z(x)}} can take any value. The spatial continuity of the random variables is described by a model of spatial continuity that can be either a parametric function in the case of variogram-based geostatistics, or have a non-parametric form when using other methods such as multiple-point simulation^[4] or pseudo-genetic techniques.

By applying a single spatial model on an entire domain, one makes the assumption that {{math|Z}} is a stationary process. It means that the same statistical properties are applicable on the entire domain. Several geostatistical methods provide ways of relaxing this stationarity assumption.

A number of methods exist for both geostatistical estimation and multiple realizations approaches. Several reference books provide a comprehensive overview of the discipline.^[7]^[3]^[8]^[9]^[10]^[11]^[12]^[13]^[14]^[15]^[16]

Methods

Estimation

Kriging

Kriging is a group of geostatistical techniques to interpolate the value of a random field (e.g., the elevation, z, of the landscape as a function of the geographic location) at an unobserved location from observations of its value at nearby locations.

Indicator kriging

Multiple-indicator kriging (MIK) is a recent advance on other techniques for mineral deposit modeling and resource block model estimation, such as ordinary kriging. Initially, MIK showed considerable promise as a new method that could more accurately estimate overall global mineral deposit concentrations or grades.

Simulation

Definitions and tools

Main scientific journals related to geostatistics

Scientific organisations related to geostatistics

Related software

See also

Notes

1. ^Krige, Danie G. (1951). "A statistical approach to some basic mine valuation problems on the Witwatersrand". J. of the Chem., Metal. and Mining Soc. of South Africa 52 (6): 119–139
2. ^Hemakumara, GPTS, & Rainis, Ruslan. (2015). Geo-statistical modeling to evaluate the socio-economic impacts of households in the context of low-lying areas conversion in Colombo metropolitan region-Sri Lanka. Paper presented at the AIP Conference Proceedings.
3. ^¹Isaaks, E. H. and Srivastava, R. M. (1989), An Introduction to Applied Geostatistics, Oxford University Press, New York, USA.
4. ^Mariethoz, Gregoire, Caers, Jef (2014). Multiple-point geostatistics: modeling with training images. Wiley-Blackwell, Chichester, UK, 364 p.
5. ^Hansen, T.M., Journel, A.G., Tarantola, A. and Mosegaard, K. (2006). "Linear inverse Gaussian theory and geostatistics", Geophysics 71
6. ^Kitanidis, P.K. and Vomvoris, E.G. (1983). "A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations", Water Resources Research 19(3):677-690
7. ^Remy, N., et al. (2009), Applied Geostatistics with SGeMS: A User's Guide, 284 pp., Cambridge University Press, Cambridge.
8. ^Deutsch, C.V., Journel, A.G, (1997). GSLIB: Geostatistical Software Library and User's Guide (Applied Geostatistics Series), Second Edition, Oxford University Press, 369 pp., http://www.gslib.com/
9. ^Chilès, J.-P., and P. Delfiner (1999), Geostatistics - Modeling Spatial Uncertainty, John Wiley & Sons, Inc., New York, USA.
10. ^Lantuéjoul, C. (2002), Geostatistical simulation: Models and algorithms, 232 pp., Springer, Berlin.
11. ^Journel, A. G. and Huijbregts, C.J. (1978) Mining Geostatistics, Academic Press. {{ISBN|0-12-391050-1}}
12. ^Kitanidis, P.K. (1997) Introduction to Geostatistics: Applications in Hydrogeology, Cambridge University Press.
13. ^Wackernagel, H. (2003). Multivariate geostatistics, Third edition, Springer-Verlag, Berlin, 387 pp.
14. ^Pyrcz, M. J. and Deutsch, C.V., (2014). Geostatistical Reservoir Modeling, 2nd Edition, Oxford University Press, 448 pp.
15. ^Tahmasebi, P., Hezarkhani, A., Sahimi, M., 2012, Multiple-point geostatistical modeling based on the cross-correlation functions, Computational Geosciences, 16(3):779-79742,
16. ^{{cite web|url=http://www.statios.com/WinGslib/index.html|title=Statios - WinGslib|first=Manu|last=Schnetzler|publisher=}}
17. ^Finazzi, F. and Fassò, A. (2014). "D-STEM: A Software for the Analysis and Mapping of Environmental Space-Time Variables", Journal of Statistical Software 62(6)

Background