Geostatistics

Keywords: spatial variability, variogram, estimation, uncertainties
Prerequisites: probabilities

Many phenomena studied in geosciences or in environment present a spatial (or spatio-temporal) correlation, which makes the usual statistics inappropriate. The course presents modelling methods from data to variable mapping, and quantifying the associated uncertainty: exploratory and variographic analysis to understand and quantify the spatial (or spatio-temporal) structure, concept of “support”, optimal linear estimation (kriging, co-kriging and their variants), consequences of estimation error for the comparison of the map to a quality threshold (selection).

Lectures, TD (directed exercises) and TP (computer practice; softwares: R, Rgeostats).

Module Content: Presentation of the basics of geostatistics, showing the importance of exploratory data analysis to identify the spatial (or spatio-temporal) structure of the studied variable. Linear estimation and modelling of the estimation uncertainty for comparison to a quality threshold. Concept of support (volume to which a value relates) and consequences on spatial variability and selection.
Awareness of the dangers of indiscriminate use of (statistical or geostatistical) software, which may lead to nonsense, if the properties of the variables or the assumptions on which the methods are based are not taken into account.

• Quality criteria of a map (grades, depth of the top or thickness of the geological formation…). What is needed for linear estimation?
• Notion of Random Function. The variogram to characterize and quantify the spatial variability.
• Variance of Estimation error, kriging and properties.
• Multivariate modeling: cross-covariances and variograms, cokriging and its variants (factorial kriging, external drift).
• The notion of support and its consequences on spatial variability and selection.
• Consequences of the estimation error. Introduction to non-linear estimation.
• Introduction to simulations.
• Examples: case studies (air quality, soil pollution, rivers and water tables, etc.)
• TD: exercises, using basic probabilistic concepts in order to “equate” a simple problem