This document proposes a new approach called implicit boundary simulation (IBS) for stochastic geological modelling that combines implicit and stochastic modelling. IBS simulates the distance function to geological boundaries using geostatistical algorithms rather than interpolating distances. The approach is applied to a deposit, showing IBS better reproduces indicator variograms and interval lengths compared to sequential indicator simulation. IBS provides distances to boundaries, conveying information about mineral zone configuration unlike other methods.

1. 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

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

3. Introduction
Main issues with geological modelling
• Hard or soft boundary? contact analysis

4. Introduction
• Uncertainty in boundary position
Boundary 1 Boundary 3
Boundary 2

5. Current modelling approaches
Deterministic modelling
• Hand contouring, wireframing

6. 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

7. Current modelling approaches
Stochastic modelling
Main geostatistical approaches
• Sequential indicator simulation
• Truncated Gaussian simulation
• Plurigaussian simulation
• Multiple-point simulation

8. 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 geostatistical
algorithms

9. 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

10. Proposed approach

11. 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]

12. 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

13. Application
• Presentation of the data
– Rosario Oeste deposit
– 53,735 diamond drill hole samples with information on mineral
zones: pyritic primary / sulphide zone

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

15. Application
– Examples of conditional realisations

16. 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.

17. Application
• Reproduction of the proportion of sulphide zone

18. Application
• Match percentage between simulation and sample data

19. Application
• Reproduction of down-the-hole indicator variogram

20. Application
• Reproduction of sulphide interval length distribution

21. 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.

22. Acknowledgements
• Compañia minera Doña Inés de Collahuasi
• Geoinnova
• ALGES Laboratory at University of Chile