Geostatistics Course

Lesson 1 • Probability Review for Spatial Analysis

Reviews random variables, distributions, and expectation in a spatial context. Provides the probabilistic language used throughout the course.

Lesson 2 • Regionalized Variable Theory

Introduces Matheron's regionalized variable concept as the theoretical basis for geostatistics. Links spatial continuity to statistical inference.

Lesson 3 • Spatial Data and Its Properties

Introduces spatial data types, coordinate systems, and attribute structures. Establishes the vocabulary needed for all subsequent geostatistical operations.

Lesson 4 • Exploratory Spatial Data Analysis

Covers histograms, scatter plots, and spatial maps for initial data inspection. Identifies outliers and data quality issues before modelling.

Lesson 1 • Concept of Spatial Continuity

Defines spatial autocorrelation and explains why nearby samples are more similar than distant ones. Motivates the variogram as a continuity measure.

Lesson 2 • Variogram Model Fitting

Introduces authorised variogram models and weighted least-squares fitting. Ensures positive-definiteness required for valid kriging systems.

Lesson 3 • Computing the Experimental Variogram

Covers lag distance, tolerance, and direction parameters for variogram calculation. Students compute omnidirectional and directional variograms from sample data.

Lesson 4 • Anisotropy Modelling

Extends variogram modelling to handle geometric and zonal anisotropy in 2D and 3D. Produces anisotropy ratios and rotation angles for kriging.

Lesson 1 • Simple and Ordinary Kriging

Derives simple kriging with known mean and ordinary kriging with unknown local mean. Highlights when each method is appropriate.

Lesson 2 • Search Strategy and Neighbourhood Design

Covers octant search, maximum sample counts, and search ellipse parameters. Demonstrates how neighbourhood choices affect kriging results.

Lesson 3 • Optimal Linear Estimation Principles

Establishes unbiasedness and minimum variance as criteria for optimal estimation. Connects these criteria to the kriging system derivation.

Lesson 4 • Cross-Validation of Kriging Models

Uses leave-one-out cross-validation to assess variogram model and search parameter quality. Interprets standardised error statistics for model refinement.

Lesson 1 • Universal and Trend Kriging

Incorporates deterministic trend functions into the kriging system for non-stationary data. Separates trend and residual components for accurate estimation.

Lesson 2 • Cokriging with Secondary Variables

Extends kriging to jointly estimate primary and secondary correlated variables. Builds cross-variograms and solves the cokriging system.

Lesson 3 • Indicator Kriging for Categorical Data

Applies kriging to binary indicator transforms to estimate local probability distributions. Handles categorical variables and threshold-based uncertainty.

Lesson 4 • Block Kriging and Change of Support

Estimates average values over blocks rather than points to support resource decisions. Addresses variance reduction when upscaling from point to block support.

Lesson 1 • Compositional Data in Geostatistics

Handles proportions and percentages that sum to a constant using log-ratio transforms. Prevents spurious correlations and closure effects in multivariate modelling.

Lesson 2 • Linear Model of Coregionalisation

Fits a valid joint variogram model ensuring positive-definiteness across all variable pairs. Decomposes spatial variability into independent spatial factors.

Lesson 3 • Multivariate spatial correlation

Quantifies cross-correlations between variables as functions of lag distance and direction. Builds the foundation for joint spatial modelling.

Lesson 4 • Multivariate sequential simulation

Extends SGS to jointly simulate correlated variables while honouring cross-variogram models. Maintains spatial and inter-variable correlations across realisations.

Lesson 1 • Turning bands and LU decomposition

Covers alternative simulation algorithms including turning bands and LU decomposition. Compares computational efficiency and applicability of each method.

Lesson 2 • Sequential Gaussian simulation

Implements SGS by visiting random nodes and drawing from conditional Gaussian distributions. Covers the random path, conditioning data, and kriging within SGS.

Lesson 3 • Sequential indicator simulation

Applies sequential simulation to categorical or threshold-based variables using indicator kriging. Produces facies or lithology realisations honouring proportions.

Lesson 4 • Validating and post-processing simulations

Checks that realisations reproduce input statistics, variograms, and conditioning data. Summarises ensembles using E-type means, variances, and probability maps.

Lesson 1 • Probability maps and risk indicators

Creates maps of exceedance probability for contamination, grade, or other thresholds. Links spatial probability maps to remediation or extraction decisions.

Lesson 2 • Communicating uncertainty to stakeholders

Translates probabilistic outputs into clear visual and narrative formats for non-technical audiences. Avoids overconfidence and misrepresentation of model limitations.

Lesson 3 • Loss functions and decision theory

Applies symmetric and asymmetric loss functions to choose optimal estimates under uncertainty. Connects geostatistical outputs to economic decision frameworks.

Lesson 4 • Global uncertainty from simulation ensembles

Aggregates local uncertainties across realisations to produce global resource distributions. Demonstrates the difference between local and global uncertainty.

Lesson 1 • Model validation and quality control

Applies cross-validation, swath plots, and global bias checks to verify model performance. Iterates on parameters until validation criteria are met.

Lesson 2 • Domain and population definition

Segments the study area into stationary domains with distinct spatial statistics. Ensures that variogram models and kriging parameters are domain-specific.

Lesson 3 • Project scoping and data audit

Defines study objectives, data requirements, and quality criteria before modelling begins. Prevents downstream errors by resolving data issues at the outset.

Lesson 4 • Reporting and peer review standards

Structures technical reports to meet professional and regulatory reporting expectations. Prepares students for independent peer review of geostatistical studies.