CFSG 2022 Module 1: Geostatistics Fundamentals

Learn the fundamentals of mining geostatistics for resource estimation and build your first block model.

Objectives

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 ParisTech 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 2022 edition of CFSG is delivered online in 6 modules over 10 weeks starting from February 2022. 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.

Outlines

  • 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 ParisTech professors and are scheduled in order to match the time zone of the audience. For more convenience, these courses are recorded and made available to participants.
    The practical sessions will be driven by Geovariances’ consultants, 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 2022 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 giving official recognition to 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 to actually take place.

Who should attend

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

Content

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 (live remote session). Learn how to manage a project and various types of data sets.
  • Working in batch with Isatis.neo (recorded video)
  • Working with Python in Isatis.neo (recorded video)

 

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.

Prerequisites

Some background in basic mathematics and statistics is strongly recommended. This course is ideal for newcomers to mining geostatistics.

We recall that CFSG 2022 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: Handling big data sets

Please note that Module 1 is mandatory. Modules 2 to 6 can be attended à la carte, according to your needs, independently from each other.

We offer a 25% discount on the purchase of all 6 modules.

CONTACT US

training@geovariances.com
Europe - Middle East - Africa - USA - Canada: +33 1 6074 9090
Asia-Pacific: +61 8 9321 3877
Latin America - The Carribean: +61 8 9321 3877