CFSG Module C: Simulation of Continuous and Categorical Variables for Uncertainty Analysis and Domain Modeling

Content

This module is the third and last one of the CFSG series. At the end, you will be able to generate simulation realizations for quantified uncertainty analysis and geological modeling.

Simulations for continuous variables

Introduction
– Why resort to the Gaussian Model?
– Transform from Raw to Gaussian quantities: Normal score and Anamorphosis.
– Gibbs Sampler and Zero-Effect management.

Simulation algorithms
– Sequential Gaussian Simulations (SIS).
– Turning Bands Simulations (TBS).
– Direct Block Simulations for integrated support change.
– Stochastic Partial Differential Equations (SPDE) for handling local anisotropies.

Multivariate methods
– Gaussian Mixture Model (GMM) for completing missing data while preserving statistical relationships
– Projection Pursuit Multivariate Transform (PPMT) for decorrelating data with complex correlations to generate a coherent block model (correlations, ratios, chemical balance)

Simulations for categorical variables

Boundary analysis
– Comparison between soft and hard boundaries.

Theory of Indicators
– From geology to indicators.
– Indicator statistical properties.
– Indicator variogram (modeling).

Indicator Kriging

Sequential Indicator Simulations (SIS)

Truncated and Plurigaussian Simulations (TGS – PGS)
– Reminders: the Gaussian Simulation approach for continuous variables (e.g. Turning Bands)
– Ingredients: Indicators, dimension of the latent Gaussian field (mono-gaussian or pluri-gaussian), truncation rules
– Modeling: Facies proportions and variograms of the underlying Gaussian Random Function
– Non-conditional simulations
– Conditional simulations:
. Gibbs sampler for translating categorical constraints into Gaussian values
. Conditional Gaussian simulations

Introduction to other methods for modeling categorical variables
– Bi-PGS
– Multiple-point Statistics (MPS)
– Potential methods for implicit modeling
– Generative models

Practice

Several exercises to learn how to run simulation variants and post-processing (probabilistic resource estimation and facies modeling, statistics, simulation reduction, grade-tonnage curves, facies proportions modeling) using Isatis.neo.