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

The problems related to the characterization of mining and environmental georesources are many, such as eg.
• the selection of the useful part of a field to be exploited;
• the definition of a polluted area;
• the cartography of the spatial and temporal distributions of substances;
• the optimization of a sampling.
All these problems are based on the processing of quantities which are Regionalized Variables and which are normally known only in certain points, where samples are available. The variety of these quantities is very wide, and ranges from spatial-temporal concentrations in land / aquifers / air; the porosity / density / permeability, temperatures, heights / depths / thicknesses, the color of the surface of ornamental rock slabs. The sectors involved are also many, such as eg. mining and oil engineering, agriculture and fishing, life sciences.
Geostatistics allows to define and quantitatively characterize the spatial, temporal and space-time variability of these quantities. The study of the variability is necessary for getting a correct solution of the problem which is not normally of a deterministic 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 preparation to face and solve problems based on Regionalized Variables, that is, of all the quantities that characterize georesources and the environment. In particular, the various models necessary for the solution of the problems will be developed.
Program
INTRODUCTION TO GEOSTATISTICS
- The problems, the variables at stake.
- Regionalized Variables (VR) and probabilistic approach to problem solving
- Reminders of probability
- Introduction to Random Functions (FA)
STATIONARY MONOVARIATE GEOSTATISTICS
- The "stationary" problems
- Experimental Variogram and model
- Linear estimation: Ordinary and Simple Kriging
- The regularization, the variogram, the estimation and the variances (extension, estimation, dispersion) of quantities with non-point support
NON-STATIONARY MONOVARIED GEOSTATISTICS
- The "non-stationary" problems
- Non-stationary random functions (FANSt)
- The drift and the variogram of fluctuations
- The Universal Kriging
- Intrinsic FA of order k (FAI-k)
- Kriging of FAI-k
MULTIVARIATE GEOSTATISTICS
- The "multivariate" problems
- Multivariate analysis
- Cross Variograms and Covariances
- The Cokriging
- The External Drift and Krigings review.
SELECTION
- Problems involving selection
- Objective function and sample optimization

Readings/Bibliography

• Bruno, Roberto APPUNTI delle LEZIONI (power point)

• Bruno, R.; Raspa G. La pratica della geostatistica lineare:il trattamento dei dati spaziali, Guarini Studio, 1994

• Chiles, J.P. & Delfiner, Pierre (1999) - Geostatistics - Wiley Series in Probability and Statistics, - John Wiley and sons, Inc., 687 pp.
• Emery, X.; Séguret S.A. Geostatistics for the Mining Industry, CRC Press, Taylor & Francis Group, 2023

Teaching methods

In module I the lessons will deal with the introduction to geostatistics and stationary geostatistics.

In module II the program of non-stationary and multivariate geostatistics will be carried out,

Each lesson begins with an introduction to a type of real problem related to georesources. These problems will be discussed and the necessary approach to obtain solutions will be identified.
Subsequently, the lesson develops the specific theory to obtain the tools necessary to solve the problem.
The exercises will train students to develop simple calculation tools on spreadsheet and to use commercial software.

Carrying out of individual work.
Each student will have to carry out a "case-study", choosing a problem to be solved and collecting the necessary data.
The analysis of the problem and the solutions will be developed collectively.
Students will have to apply the theoretical notions and develop specific operational tools to obtain the solution to their problem.
The discussion of the individual work will be the subject of the exam.

Assessment methods

The exam consists of:

• the discussion of the individual work at the end of both modules.
  

The individual work consists in the solution of a practical problem to be solved by putting into practice the theoretical teachings and the calculation tools suitable for solving the problems. Moreover, during the discussion the knowledge of theory, useful to perform the practical part, will be verified

Teaching tools

Lessons are based on power-point presentations supported by blackboard developments.
The exercises are carried out at the Didactic-informatic Laboratory and will carry out practical numerical applications on EXCEL spreadsheets, where elementary programs in VBA will also be developed.

Office hours

See the website of Roberto Bruno

See the website of Francesco Tinti