93276 - GEOSTATISTICA MINERARIA M

Learning outcomes

At the end of the course, the student possesses the knowledge for the characterization of the natural variability of the main regionalized quantities at the basis of the curriculum.

It also possesses the theoretical tools and software to build numerical models that allow you to qualify the design and management of the various activities of the production cycle and to solve the main problems related to mining and environmental engineering.

In particular, the student is able to:

• calculate and model variograms, spatial covariances, trends and generalized covariances, of stationary and non-stationary regionalized variables;
• perform estimates by krigaggio of space-time quantities, determining their reliability, and feeding activities such as the production of the related maps;
• designing optimal sampling designs for achieving the objectives of the sampling itself;
• performing the optimal selection in relation to the selection support and available information, optimizing an objective function;
• build simulated numerical models of the regionalized variables, of input for specific downstream 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. Georeferencing and problems refer to 1D, 2D, 3D space and time.

Thus arises the need to study these variables in a probabilistic framework, the Theory of Random Functions (RF). 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, a situation in which it is 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, to be calculated experimentally and modeled with positive definite functions.

The numerical models that can be built are estimates and simulations, each with its own characteristics that make them necessary to solve typical problems such as the estimation of resources and the selection of recoverable reserves, the optimization of a sampling, mapping, the elements for a sensitivity and risk analysis.

Readings/Bibliography

• Bruno, Roberto - 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

Teaching methods

The lessons are presented with a slide show.

The exercises will train students to develop numerical methodologies on a spreadsheet for the solution of specific problems.

Moreover, open source softwares will be shown to give students the possibility to manage large sets of data

Assessment methods

The exam consists in the drafting and discussion of an essay agreed with the student, which addresses a specific problem to be solved.

Besides the discussion of the essays, an oral test will evaluate the knowledge of theory, with main reference to Stationary Geostatistics

Teaching tools

The exercises, carried out at the Didactic-Computer Laboratory, will make use of Microsoft Office programs (EXCEL) and other software, mainly open source

Office hours

See the website of Francesco Tinti

See the website of Roberto Bruno