93276 - GEOSTATISTICA MINERARIA M

Learning outcomes

At the end of the course, the student will possess the knowledge for the characterization of the natural variability of the main regionalized quantities of interest for Mining, Georesources and Environmental Engineering.

The student will therefore learn how to build geostatistical models allowing to produce reliable estimates of the variables of interest.

Specifically, the student will be able to:

• calculate and model variograms, spatial covariances, trends and generalized covariances, for both stationary and non-stationary regionalized variables;
• perform estimates, by kriging, of space-time quantities, together with their precision, used for the realization of maps;
• design optimal sampling grids;
• perform optimal selections, considering sampling support and available information, by optimizing an objective function
• realize simulations of the regionalized variables, used for further data processing.

Course contents

The course aims to provide the basic information to solve the main problems related to Regionalized Variables (RV), those georeferenced natural variables whose variability, together with the limited knowledge of sampling, prevents the use of deterministic models. The sectors of interest refer to 1D, 2D, 3D space and time.The Theory of Random Function (RF) is the reference probabilistic domain.

The problems to be addressed may refer to one or more variables, for which the modeling methods of monovariate and multivariate RFs are developed.

Furthermore, RVs can show the presence of space-time trends, making necessary to approach the problems in the context of non-stationary RF.

The basic tools for the study of RF are spatial covariances and variograms, which will be calculated experimentally and modeled with positive definite functions.

Through the analysis and use of the model, it will be possible to perform estimates and simulations of RV in the space-time domain. Typical geostatistical problems are: estimation of the resources, selection of recoverable reserves, optimization of sampling, mapping, realizations of sensitivity and risk analyses.

The course is divided in two modules:

Module 1 - Introduction: Linear Stationary Monovariate Geostatistics

Module 2 - Deepening: non-Linear, non-Stationary and Multivariate Geostatistics

Module 1

• The use of geostatistics for the characterization of georesources
• Recall on Probability and Statistics
• Regionalized Variables
• Experimental Variogram
• Variogram Model
• Recall on traditional estimators
• Linear Stationary Monovariate geostatistical estimation tools

Module 2

• Regularization and Dispersion
• Support and Information Effect
• Selection
• Multivariate Geostatistics
• Non-Stationary Geostatistics
• Non-Linear Geostatistics
  

Readings/Bibliography

• Bruno, R.; Tinti, F. - Lecture notes
• Matheron, G. The Theory of Regionalized Variables and Its Application; École Nationale Supérieure des Mines de
  Paris: Paris, France, 1971
• Chiles, J.P.; Delfiner, P. Geostatistics Modeling Spatial Uncertainty, 2nd ed.; WILEY: Hoboken, NJ, USA, 2012
• Armstrong M.; Basic Linear Geostatistics, Springer Berlin, Heidelberg, 1998
• Bruno, R.; Raspa G. La pratica della geostatistica lineare: il trattamento dei dati spaziali Guarini Studio, 1994
  
• Remy, N.; Boucer, A. and Wu J. Applied Geostatistics with SGeMS, Cambridget University press 2009
• Emery, X.; Séguret S.A. Geostatistics for the Mining Industry, CRC Press, Taylor & Francis Group, 2023

Teaching methods

The course is made by lectures, with the support of dedicated presentations.

Specific exercises, mainly over spreadsheets, will train students to develop geostatistical methodologies for the solution of practical problems.

Moreover, some time will be dedicated to open source softwares, to give students tools for managing manage large datasets.

Assessment methods

The exam consists in the drafting and discussion of an essay, agreed with the student, addrssing a specific problem to be solved by the use of geostatistical tecniques.

Besides the discussion of the essay, an oral test will evaluate the knowledge of theory and specifically its key and basic concepts.

Higher grades will be awarded to students who demonstrate, through the exposition of the essay, to know and understand the theory and to correctly apply it into practice, with high ability of critical exposure.

Passing grades will be given to students who correctly realize the essay, but are not sufficiently able to link the fundamentals of theory to the practical application.

Failing grades will be communicated to students who provide an incomplete essay and show prominent gaps in the knowledge of the subject.

Teaching tools

The exercises will make use of electronic spreadsheets and specific geostatistical softwares, mainly open source

Office hours

See the website of Francesco Tinti

See the website of Roberto Bruno