90029 - Geostatistics and Environmental Modelling

Learning outcomes

The course aims to provide the elements needed to characterize and model a georesource for exploitation and environmental rehabilitation projects.

Course contents

Objectives

The problems related to mining and environmental geo-resources are manifold, such as eg.:

• the selection of the useful part of a mining deposit;
• the identification of a polluted area;
• the mapping of spatial and temporal distributions of substances;
• the optimization of a sampling.

All these problems are based on the elaboration of quantities which are Regionalized Variables and which are normally known only in some points, where the samples are available. The variety of these quantities is very wide, ranging from space-time concentrations in soils / groundwater / air; to porosity / density / permeability; to temperatures; to heights / depths / thicknesses; to the surface color of ornamental rock slabs. Many sectors are involved , eg. mining and oil engineering; agriculture and fishing; life sciences.

The Geostatistics allows to define and quantitatively characterize the spatial, temporal and spatio-temporal variability of these quantities. The study of variability is necessary to arrive at a correct solution to the problem that is not normally deterministic in nature and requires the calculation of the reliability of the solution itself. A correct analysis allows to optimize the results in economic terms.

The course aims to provide a basic notion on how to tackle and solve problems based on Regionalised Variables, that is of all the quantities that characterize georesources and the environment. In particular, an overview of the various models necessary for solving problems will be done.

Program

Module I

INTRODUCTION TO GEOSTATISTICS
- The problems and the variables at hand
- Regionalized Variables and the probabilistic approach to problem solving
- Recall of probability
- Introduction to Random Functions

STATIONARY MONOVARIATE GEOSTATISTICS
- "Stationary" problems and the StRF (Stationary Random Functions)
- Spatial variability, experimental variograms and modeling
- Linear estimation: Ordinary and Simple Kriging
- The regularization, the variogram, the estimation and the variances (extension, estimation, dispersion) of quantities with non-punctual support

Module II

NON-STATIONARY MONOVARIATE GEOSTATISTICS
- "Non-stationary" problems
- Non-stationary Random Functions
- The drift and the variogram of fluctuations
- The Universal Kriging
- Intrinsic Random Function of order k (IRF-k)
- Kriging of IRF-k

MULTIVARIATE GEOSTATISTICS
- "Multivariate" problems
- Multivariate analysis
- Cross-Variograms
- The Co-kriging
- The External Drift and Kriging revision.

SELECTION
- Problems involving selection
- Objective function and sampling optimization

Readings/Bibliography

• Bruno, Roberto Lecture notes (power point)

• Raspa, G. & Bruno, R. APPUNTI di GEOSTATISTICA (pdf)

• Chiles, J.P. & Delfiner, Pierre (1999) - Geostatistics - Wiley Series in Probability and Statistics, - John Wiley and sons, Inc., 687 pp.

Teaching methods

• Each lesson begins with the introduction to a type of real problem related to geo-resources. These problems will be discussed and the approach necessary to obtain solutions will be identified.
• Subsequently, the lesson develops the specific theory to obtain the tools necessary for solving the problem.

The exercises will train students in the development on a spreadsheet of simple calculation tools and in the use of commercial software.

with reference to the individual final work

• Each student will have the possibility to do a practical work, choosing a problem to solve and collecting the necessary data.
• The analysis of the problem and the solutions will be discusses collectively.
• Students will have to apply the theoretical notions and develop specific operational tools to get the solution.

The discussion of the work will be the main subject of the exam.

Assessment methods

The exam consists of:

• an oral test over the theory, with reference to Stationary Geostatistics;
• the discussion of the final work.

The test: verify the cognition of the theory of Stationary Random Functions with simple numerical applications.

The final work: proposes a concrete problem to be solved, forces the student to put into practice the theoretical teachings and the appropriate calculation tools to solve the problems.

Teaching tools

Teaching tools

• The lessons are presented with projection of power-point files supported by developments on the board.
• The exercises are carried out by Excel worksheets, by developing specific macros in "visual basic"
• Some basics of open source softwares are taught, to provide tools to manage large quantities of data
  

Office hours

See the website of Roberto Bruno

See the website of Francesco Tinti