2023-2024 / GEOL0097-2



30h Th, 30h Labo.

Number of credits

 Master of Science (MSc) in Geological and Mining Engineering, professional focus in geometallurgy (EMERALD) (Erasmus mundus)5 crédits 
 Master of Science (MSc) in Geological and Mining Engineering5 crédits 
 Master of Science (MSc) in Geological and Mining Engineering (joint-degree programme with the "Université polytechnique de Madrid")5 crédits 


Eric Pirard

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

1. Computers and Geosciences
2. Statistical terminology and data typology
3. Principles of geological monitoring and spatial sampling
4. Exploratory Data Analysis
Univariate Visualisation (histograms, box plot)
Univariate analysis (percentiles, mean, variance,...)
Identification of outliers
Principles of data levelling
Bivariate Visualisation (scatterplots)
Bivariate Analysis (covariance, correlation,...)
5. Spatial Exploratory Data Analysis
Terminology and Notations
Data posting
Local Analysis - Moving window
Spatial Correlation Analysis
The experimental variogram
Variogram Modeling
6. General principles of spatial modeling
Probabilistic vs. Deterministic Modelling
Validation of a model
Spatial deterministic inference

7.  Introduction to regionalized variables
Random variable, random function and regionalized variable
Joint random variables
The covariance and variogram function
The theoretical and the experimental variogram   8. Kriging
The kriging problem
Ordinary Kriging equations
An intuitive look at ordinary kriging weights
Spatial contuinity model influence on kriging weight
Properties of the kriging estimate
Simple kriging
Kriging with trend
9. Change of support and block kriging
Importance of the support on statistics
Effect of the support on estimates
Affine and indirect lognormal corrections
Total variance and variance within block
Block kriging
10. Estimation with secondary data
Secondary information
Kriging within strata
Kriging with local varying mean
Kriging with external drift
Cross-covariance and cross-variogram
11. Uncertainty of the estimation
Uncertainty of the local estimate
Confidence interval
Multi-Gaussian approach
Indicator kriging
12. Simulations
Kriging limitations
Simulations and spatial uncertainty
Sequential simulation algorithm
Sequential Gaussian simulations
Sequential Indicator simulations

Learning outcomes of the learning unit

1) To present the main geostatistical inference tools (advantages and drawbacks)

2) To acquire a good mastership of the most utilised concepts

3) To provide the basis for understanding the most advanced papers on spatial inference

4) To learn about the most common professional geostatistical applications

This course contributes to the learning outcomes III.1, IV.3, IV.5 of the MSc in geological and mining engineering.

Prerequisite knowledge and skills

Probability and Statistics (basic course)

Planned learning activities and teaching methods

Practical sessions will use R software

Mode of delivery (face to face, distance learning, hybrid learning)

2h theory followed by 2h of supervised (or non-) practice

Recommended or required readings

Copy of all PPT used for teaching.
Main reference :
Applied Spatial Data Analysis with R. Roger S. Bivand, Edzer Pebesma and V. Gómez-Rubio UseR! Series, Springer. 2nd ed. 2013, xviii+405 pp., Softcover ISBN: 978-1-4614-7617-7
Goovaerts P., 1997, Geostatistics for natural resources estimation, Oxford Univ. Press
Recommended Lectures : Isaaks E. & Srivastava M., 1989, Introduction to applied geostatistics, Oxford Univ. Press Cressie N., 1993, Statistics for Spatial Data, Wiley

Exam(s) in session

Any session

- In-person

oral exam

Written work / report

Additional information:

Evaluation will bear on a personal project performed by the student and an oral examination.

Each student will receive a set of data and will have to characterize and spatially model the data set with the tools seen during the course.

The written work will be submitted before the oral examination and will be subject to additional questions/oral presentation during the exam.

The oral examination will bear on the theoretical principles.
The final notation will be a weighted average : 75% (oral examination) + 25% (personal work).

Work placement(s)

Organisational remarks and main changes to the course

Full English



Teaching & Research assistant

Sart Tilman B52

e-mail : mcabidoche@uliege.be

Association of one or more MOOCs