|SCIENTIFIC DISCIPLINARY SECTOR||GEO/08|
Geostatistics, called also spatial statistics, is the implementation of the statistics applied to the to geospatial dataset, main sources of data for GIS.
The tools of Geostatistics enable the user to understand the spatial relations and to estimates the magnitudes of some variables where are unknown in a regular, random or clustered sampling grid in mono- bi or tridimensional space.
That introduction to Geostatistics for natural resources enable the student to use safely the tools that feature the exploratory data analysis and the Geostatistics. The practical section of the Course in particular will be the opportunity for the student to play with dataset that as geologist or environmental technician will explore in the future professional activity. Thus time-series, chemical analysis or permeability dataset will be used to understand how we can start from an incomplete dataset to fill the unknown. Recently some basic concepts presented here are implemented in some documents used in Policy.
The Course is conceived to be useful to interpret geospatial dataset that a professional can acquire directly or indirectly in the field. The student in particular will be able to:
- carry out the exploratory data analysis;
- define from dataset some linear model, parametric or non-parametric;
- depict the features of a geospatial dataset, avoiding unphysical results although numerically possible, ie concentrations outside a range, often negative values;
- obtain with some geostatistical tool informations about the spatial law to be used in interpolation or extrapolation;
- obtain spatial model of a variable on a structured isotropic grid;
Some final hours of the Course will be devoted to a stochastic processing of some data with the estimation of an average distribution of a variable and the consistent spatial uncertainty.
The course is developed in two sections: the first one will be devoted to present in a practical way some basic concept of statistics and probability using basic maths skills and the second one will be devoted to applications.
Visualization and feature of uni- and multi-variate variable
Features of environmental datasets. Continuous and categorical variables. Probability and conditional probability. Statistical inference. Statistical moments of a univariate variable: mean, median, mode, variance and standard deviation. Random variable and random function. Gaussian and lognormal distributions. Quantiles and percentiles of a distribution. Stationarity conditions of a variable: strong and weak condition.
Bivariate plot and regression linear models. Classification of continuous variable. Q-Q and P-P plots. Proportional effects. Detrending of a variable with a drift. Normalization of a non normal distribution. Zero, missing values or below detection limits. Meaning and processing of outliers in environmental sciences.
Linear geostatistics tools
Regionalized variable. Interpolation and extrapolation. Covariance, correlogram and variogram. Variography of a geospatial variable. Experimental variogram and variogram model: range, sill and nugget. Nugget effect. Additivity of variograms. Variogam modeling.
Local approximation: simple kriging and ordinary kriging. Co-kriging: kriging of colocated variable.
Regional approximation: multigaussianity, stochastic gaussian simulations.
Practical activity based on environmental dataset devoted to reconstruct incomplete time-series, distribution od geochemical data in 2D or describe a tridimensional geological model starting from logs.
Applied geostatistics - Isaaks, Edward H ; Srivastava, R. Mohan (presso BTM)
Geostatistics for Natural Resources Evaluation - Pierre Goovaerts - Oxford University
MARINO VETUSCHI ZUCCOLINI (President)
DANIELE SPALLAROSSA (President Substitute)
GABRIELE FERRETTI (Substitute)
The student will receive on request via email an examination text to be developed in complete self-sufficiency and presented during the examination session.
Details about the examinations will be furnished during the first lesson jointly with the syllabus, thus the examination will be based on the discussion of the results of the test recalling the theory of the tools used. It is considered of great value the use of consistent terminology.
The constant participation to the lessons is greatly wished, although not mandatory, to have great continuity between theory and practice.