CFSG EMEA | Training course

PART 1 – STATISTICS FOR MINERAL RESOURCES

THEORY

• The different types of quantities
  – Quantitative (i.e., grade or petrophysical properties) or categorical (i.e., geological facies and rock types)
  – Missing information, limit of detection (LOD), limit of quantification (LOQ)
  – Additive variables
  – Variables defined on a space (i.e., drillholes, maps, and block models)
  – Support of information (size and shape) and volume of selection (i.e., Selective Mining Unit)
• Univariate statistics
  – Histograms
  – Summary statistics:  mean, median, mode to capture the centrality, variance, inter-quartile interval, coefficient of variation to capture the dispersion, minimum, maximum, quantiles, box plots to capture the extremes
  – Base maps and swath plots
  – Transform of the variable: logarithm, log, indicator, capping, ranking, proportional effect
  – Continuous and discrete distributions: Gaussian, lognormal, uniform, triangular, exponential, gamma, Bernoulli, Binomial, Poisson
• Multivariate statistics
  – Scatter plots
  – Marginal and conditional distributions
  – Linear and empirical regression
  – Transformations (linear combinations, i.e., Principal Component Analysis)
• Selectivity curves
  – Rules for selection: cutoff and support (sample vs. Selective Mining Unit)
  – Tonnage, Average Grade, Metal, and Conventional benefit
  – Support effect
  – Information effect

PRACTICE

Introduction to Isatis.neo Mining Edition to learn how to manage a project and various types of data sets. You will learn how to manage the statistical concept presented in theory in the software.

PART 2 – MODELING THE SPATIAL CONTINUITY

THEORY

• Sampling for spatialized variables
  – Clustered and preferential sampling
  – Sampling geometry: scattered, seismic lines, drill holes, regular grids
  – Declustering and weighted statistics
• Measuring the spatial continuity
  – Spatial covariance and variograms
  – Variogram cloud, variogram map
  – Calculations in one, two, and three-dimensional spaces. The particular case of regular, gridded data.
  – Other empirical structural tools: robust variogram, madogram, rodogram
• Variogram model
  – The basic models: Nugget Effect, Exponential, Spherical, Gaussian, Cubic, Linear
  – Parameters and properties
  – The nested model and its multi-scale interpretation
  – Anisotropies: geometric, zonal, separable
  – Fitting strategy

PRACTICE

Several exercises to learn to import data, achieve exploratory data analysis, compute experimental variograms, and adjust variogram models with Isatis.neo Mining Edition.

PART 3 – IN-SITU RESOURCE ESTIMATION

THEORY

• Estimator
  – Examples: Moving Mean, Nearest Neighbor, Inverse Distances
  – Precision vs. accuracy
  – Dichotomy between (deterministic) Drift and (stochastic) Residuals: (strictly) stationary, intrinsic, or non-stationary
  – Linear, Unbiased, Optimal
  – Estimation and quality of estimation (estimation error)
• Kriging (Best Linear Unbiased Estimation)
  – Simple Kriging with known mean
  – Ordinary Kriging in intrinsic cases
  – Universal Kriging in more general cases
• Parameters
  – The Variogram Model
  – The Neighborhood: Moving vs. Global
• Properties of kriging
  – Support of the sample (different sizes)
  – Support of the target: block, convolution, gradient
• Cross-validation (leave-one-out, K-fold) and Kriging validation
• Extensions: Kriging with Variance of Measurement Errors, Filtering

PRACTICE

Several exercises to learn to build block models with Isatis.neo Mining Edition using Ordinary and Simple Kriging and to validate the model with cross-validation.

PART 4 – ADVANCED IN-SITU RESOURCE ESTIMATION AND SIMULATION

THEORY

• Multivariate modeling
  – Experimental statistics: scatter plots, correlation table, regressions (linear and non-linear)
  – Transforms: Principal Component Analysis (PCA) and Multiple Factor Analysis (MAF), Indicator Residuals
  – Simple and cross variograms
  – Modeling: Linear Model of Coregionalization
• Multivariate estimation
  – Cokriging: Simple and Ordinary. Simplifications
  – Collocated Co-kriging
  – Factorial Kriging Analysis
• Selectivity curves for recoverable resources
  – Reminders:
  . Rules for selection: cutoff and support (sample vs. Selective Mining Unit)
  . Tonnage, Average Grade, Metal, and Conventional Benefit
  . Support effect of the variable
  . Information effect
  – Limitations of Linear Kriging
  – Non-linear estimation vs. simulations
• Gaussian Simulations
  – Why resort to the Gaussian Model?
  – Transform from Raw to Gaussian quantities: Normal score and Anamorphosis
  – Properties (univariate, multivariate), covariance function
  – Simulation techniques: Sequential Gaussian Simulations, Turning Bands Simulations, Conditioning Kriging

PRACTICE

Several exercises to learn how to analyze contacts between domains, compute and adjust multivariate variograms, and run point and block simulations,  Direct Block Simulations, and post-processing (statistics, simulation reduction, grade-tonnage curves) with Isatis.neo Mining Edition.

“The CFSG training covered a wide range of geostatistical concepts during the theory sessions. I then had the ability to put these concepts into practice using Isatis.neo, allowing me to confirm my understanding and ask any further questions. I now have a deeper understanding of EDA, estimation, and validation, which will aid me in my current role. My geostatistical tool set has been greatly boosted since completing the CFSG program.”

Marlies Barden – CFSG 2023
Senior Resource Geologist – Mineral Resources Limited

“As an exploration/resource development geologist, the CFSG training program has not only allowed me to understand better geostatistics and resource estimation concepts (EDA, IDW, OK, MIK…), but it has also bridged my career path from a resource development geologist to a resource estimation geologist. Thanks to the Center of Geostatistics of Mines Paris and Geovariances and their very comprehensive CFSG program, I was able to learn and reach my career goal without leaving my job.”

Lassana Sanogo – CFSG 2023
Senior Exploration and Resource Development Geologist – Resolute Mining (Syama Gold Mine)

“Doing the Master of Geostatistics CFSG has not only boosted my career in so many ways, but it has also opened my social and professional network to a whole new level, giving me job opportunities I never thought possible. So don’t miss the chance to solve a Kriging matrix by hand and get in-depth knowledge of what happens behind a few Isatis clicks!”

Flavie Isatelle – CFSG 2018
Senior Resource Geologist/Geostatistician – Cube Consulting

“The CFSG Program allowed me to dive deep into the World of Geostatistics for the first time. In addition to understanding the theoretical principle, I also enjoyed the opportunity to apply the learned theories to practical examples, giving me insight into my daily activities as a Specialist in Resource Estimation. Having a connection with great teachers from the CFSG Centre and Geovariances, I could say,  I had a splendid and wonderful time! Thank you, CFSG Post Graduate Diplome – Mines Paris!”

Ufi Ma’rufianty – CFSG 2010
Mineral Resource Specialist – Harita Group