Stochastic geological modelling using implicit boundary simulation

Alejandro Cáceres, Xavier Emery, Luis Aedo, Osvaldo Gálvez

Geoinnova Consultores Ltda

Department of Mining Engineering, University of Chile

Advanced Mining Technology Centre, University of Chile

Compañía Minera Doña Inés de Collahuasi

Introduction

• Geological modelling for mineral resources evaluation: definition of homogeneous domains (“geological units”)

Introduction

Main issues with geological modelling

• Hard or soft boundary? contact analysis

Introduction

• Uncertainty in boundary position

Boundary 3

Boundary 2

Boundary 1

Current modelling approaches

Deterministic modelling

• Hand contouring, wireframing

Current modelling approaches

• Implicit modelling

Example of two geological

units:

─ For each sample, calculate a signed distance to the nearest boundary

─ Interpolate the signed distance over the domain of interest.

─ Extract the zero-distance iso-surface as the boundary of the target geological unit

Current modelling approaches

Stochastic modelling

Main geostatistical approaches

• Sequential indicator simulation

• Truncated Gaussian simulation

• Plurigaussian simulation

• Multiple-point simulation

Proposed approach

• Implicit boundary simulation

Principle: A combination of implicit and stochastic

modelling. Instead of interpolating the signed distance function, one can simulate this function using geostatisticalalgorithms

Proposed approach

• Implicit boundary simulation from available data

– Calculate the distance of each sample to the nearest boundary

– Transform the calculated distances into normal scores

– Perform variogram analysis of the transformed distances

– Simulate the transformed distances

– Truncate the resulting realisations to the zero distance

Proposed approach

Proposed approach

• Implicit boundary simulation using a reference model

– In the reference model, calculate the distance Dtrue of each node to the nearest boubdary. Transform the calculated distances into normal scores and perform variogram analysis of the transformed distances

– In the sample data base, calculate the distance Dsample of each sample to the nearest boundary. The true distance to the boundary (Dtrue) belongs to the interval [0,Dsample]

Proposed approach

– Using the transformation function and variogram determined with the reference model, simulate Dtrue conditionally to the previous interval constraint, at the data locations first (Gibbs sampler), then over the domain of interest

– Truncate the realisations to obtain the simulated geological units

Application

• Presentation of the data

– Rosario Oeste deposit

– 53,735 diamond drill hole samples with information on mineral zones: pyritic primary / sulphide zone

Application

• Implicit boundary simulation

– Distances to the nearest boundary are calculated from available data. Their normal score variogram shows a smooth behaviour in space.

Application

– Examples of conditional realisations

Application

• Geological Cross validation

– Two approaches are validated: • implicit boundary simulation (IBS)

• sequential indicator simulation (SIS)

– At each drill hole sample, the mineral zone is simulated 25 times conditionally to the remaining drill hole data.

Application

• Reproduction of the proportion of sulphide zone

Application

• Match percentage between simulation and sample data

Application

• Reproduction of down-the-hole indicator variogram

Application

• Reproduction of sulphide interval length distribution

Conclusions

Implicit boundary simulation (IBS) better reproduces sulphide indicator variogram and interval length distribution. It is able to reproduce regular boundaries and connected patterns

Unlike sequential indicator simulation, IBS also provides the distance to the nearest boundary, which conveys information about the configuration of the mineral zones.

Acknowledgements

• Compañia minera Doña Inés de Collahuasi

• Geoinnova

• ALGES Laboratory at University of Chile