CFSG Module 1: Geostatistics Fundamentals | Training course

The Specialized Training Cycle in Geostatistics, known as CFSG, is a high-level training program in mining geostatistics delivered by the Geostatistics Team from Mines Paris and Geovariances. Its objective is to give you a comprehensive and deep knowledge of geostatistics for mineral resource estimation so that, when you return to work, you will be able to build the block models that your company needs for confident mine planning. By attending the program, you learn the theory behind the techniques presented to you and practice them through numerous exercises and a real-life project.

The 2023 edition of CFSG is delivered online in 6 modules over 10 weeks starting end of January 2023. This module is the first one of the series. At the end of it, you will be able to analyze and model the spatial variability of grades, build your first block model through various techniques, and compute grade-tonnage curves.

• Half of the training program is devoted to methodological presentations, the other half to practical exercises to deepen the understanding of concepts.
  – The methodological courses are given by Mines Paris professors and are scheduled to match the audience’s time zone. For more convenience, these courses are recorded and made available to participants.
  – Geovariances’ consultants will drive the practical sessions, either from our French office (for those whose time zone is compatible with the French one) or from our Australian and Brazilian offices for the other participants.
• A typical training week would then be:
  – Monday, Tuesday, and Wednesday: theoretical course (on a half-day) and hands-on practice with Isatis.neo Mining Edition (on the half-day following the theoretical course).
  – Thursday or Friday: Homework using Isatis.neo Mining Edition with compulsory rendering at the end of the day.
  – Friday: Live correction and comments from the teaching team. Validation of prior learning.
• CFSG is a full-time training. You are required to be present for the duration of the sessions.
• CFSG is a certification training. The knowledge acquired in each module is validated through an examination. At the end of each module, you will get a training certificate with a distinction that officially recognizes the full completion of the module.
• Course material and a temporary software license are provided.
• A minimum number of 5 participants is required for a module actually to take place.

Note that sessions scheduled at AWST Perth time are designed for people from the Asia-Pacific region, as sessions scheduled at CET/CEST Paris time are meant for people from Africa, the Americas, and Europe. Practical sessions are planned to adapt to the Americas, the whole of Europe, and the Asia-Pacific.

CFSG training program is meant for mining geologists and engineers who are willing to achieve a high level in geostatistics.

WEEK 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.

WEEK 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.

WEEK 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 (developed in Module 2)
• 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.

This course is ideal for newcomers to mining geostatistics.

The course is delivered in English and requires a good level of this language. Good notions of mathematics are also recommended.

We recall that the CFSG program is made of 6 modules:
– Module 1: Geostatistics Fundamentals
– Module 2: Advanced in-situ resources
– Module 3: Recoverable resources
– Module 4: Facies simulations
– Module 5: Domaining
– Module 6: Coupling Machine-Learning and geostatistical techniques using Python

Modules can be attended à la carte, according to your needs, independently from each other. Module 1 is mandatory if you have never used Isatis.neo or have no prior experience in geostatistics.

We offer a 25% discount on the purchase of all six modules and a 15% discount on the purchase of the four modules 1, 2, 3, and 4.