Geostatistic is a sound framework for modeling any kind of spatial/temporal data. It aims at providing accurate estimates of phenomenea at unsampled locations together with a quantification of the related uncertainty.
A powerful tool for characterizing data spatial correlation
The application of probabilistic methods to regionalized variables
Geostatistics has been defined by Georges Matheron as the application of probabilistic methods to regionalized variables, which designates any function distributed in a real space. At the difference of conventional statistics, whatever the complexity and irregularity of the real phenomenon, geostatistics search to unveil a structure of spatial correlation. This accounts for the intuitive idea that closely separated points in space should be accordingly close in values.
Geostatistics is powerful for mapping and uncertainty quantification
What makes geostatistics powerful is its ability to characterize spatial variability through a consistent probabilistic model. Therefore, the predictions made using the geostatistical methods are tailored to the intrinsic structure of the variable and not only to the sampling quantity or geometric pattern. This spatial structure is characterized by the variogram.
Because of its probabilistic framework, geostatistics quantifies the uncertainty related to the description of the reality and provides efficient decision tools for practitioners and managers.
A virtually unlimited field of application
Each time data are acquired and positioned in space( i.e. data with coordinates and values), a geostatistical approach may be explored.
Because of the large variety of domains and the specificity of related issues, many geostatistical methods are available.
Geostatistics involves different types of algorithms. Two main classes of algorithms are usually distinguished:
Estimation or kriging-like techniques
These techniques are dedicated to the mapping of the phenomenon in between data locations. The variogram is used to provide a safe path between data points. Safety comes at a price: the estimated profile is usually smoother than the unknown real one.
These techniques are used to characterize the uncertainty on estimates (oil volumes, grade above cut-off, pollution risk). Simulations reproduce the variability captured by the variogram. They offer a more realistic representation of the unknown reality. Realism comes at a price: safety. Each realization in the simulated model is a riskier estimate than the Kriged one above.
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