Geostatistics for Mineral Resource Estimation

Mineral Resource Estimation (in-situ and recoverable)

Estimating mineral resources is performed at all stages of the mine life cycle. Geostatistics will ensure you get the maximum value out of the available information: investigate data quality, focus on the reliable data, discount unreliable, erroneous data and produce accurate resource estimates. Maximise the return on your data investment and then use the results to optimise future data collection.

Statistical and Geostatistical skills can be used in all aspects of resource estimation:

• DATA QC

The relevance of any resource estimate is directly dependent upon the quality of your input data. Statistical and Geostatistical analyses provide quantitative inputs for:
– Assessing the validity of your different data sources
– Rejecting imprecise or biased information
– Combining different data sources

• GEOLOGICAL DOMAIN VALIDATION

The definition of robust geological envelopes is paramount for ensuring the quality of your mineral resource estimation. The envelopes must be relevant (i.e. as detailed as the data allows them to be) and robust (to changes in the local geological rationales). Geostatistics can help assuring they are fit for the purpose of producing a MRE you can trust by focusing on:
– Statistical Homogeneity
– Boundary Analysis and Boundary Treatment
– Domain Combination or Sub-division

• CHARACTERIZATION OF SPATIAL VARIABILITY

This is the only way you can ensure the estimation methodology you use will be completely adapted to the deposit you are modeling:
– Exploratory Data Analysis
– Experimental Variography
– Data transforms
– Variogram Modeling
– Cross-Validation

• IN SITU ESTIMATION AT ALL STAGES

– Exploration
– Feasibility
– Grade Control

• RECOVERABLE RESOURCE ESTIMATION

A sound evaluation of Recoverable Resources is a pre-requisite for Reserve Calculation. They help determine the portion of the deposit that is technically recoverable when one applies a cut-off to selective mining units (SMU’s) to be mined at production stage. They are usually much smaller than the Panels that can safely be estimated from exploration data. Linear Interpolation is thus no longer applicable and one needs to resort to non-linear geostatistics to estimate these recoverable resources.

– Testing grade architecture to inform the choice of an adapted Change of Support Model
– Global or Local recoverable resource estimation
– Characterization of uncertainty of the recovery functions (link with simulation)
– Localization of models to facilitate communication to mine planning engineers
– Validation and reporting.

Mineral Resource Classification

Resource classification categories provide a global assessment of confidence levels that can be placed in different aspects of a mining project.
Geostatistics allows you to objectively characterize the confidence of your resource estimates by integrating corporate risk profiles and reporting code guidelines through quantitative inputs.

Resource classification focuses on the categorisation of the mineral resource. Geostatistics can produce quantitative inputs to characterise the confidence placed in each element having a bearing on the resource classification. More importantly geostatistics offers a coherent and objective framework that can help you maintain a global approach to classification.A variety of geostatistical inputs can be used to fully characterize the level of confidence in the resource estimates of your key elements:

– Kriging variance and other kriging quality statistics;
– Optimal neighborhood search parameters; and
– Assessments of geological uncertainty.

Geostatistics also offers an unparalleled ability to generate:
– Local and global confidence intervals to fully characterize how resource confidence will vary in space. These confidence intervals can be based on the use of conditional simulation which can be processed to produce indicators of the variability of the resource for different confidence levels; and
– Coherent volumes corresponding to the various categories by using adapted geostatistical post-processing tools that help smooth the definition of the different categories.

Risk analysis and uncertainty characterization

Risk analysis of mineral resources is crucial at all levels:
– Company level – optimisation of your portfolio of projects;
– Project by project – identifying and characterising geological and grade uncertainty; and
– At mining stage – inform ore/waste allocation decisions on risk profiles, characterise product variability, help near mine development.

Risk analysis for mineral resource estimates generally relies on the use of conditional simulation.

Conditional simulation offers the perfect platform to tackle issues related to risk analysis. Conditional simulation, by characterizing spatial variability and producing multiple equi-probable realizations of the orebody, allows you to characterize uncertainty in a way single resource estimates cannot. They pave the way for:
– Quantitative assessment of uncertainties;
– Production of probability based indicators and maps;
– Supporting Monte Carlo risk analysis;
– Reproducing the orebody heterogeneities; and
– Capturing and reducing the space of uncertainty via scenario reduction, allowing effective multiple scenario analysis,

For scenario reduction, Isatis Simulation Reduction module offers a quick way to identify grade realizations which best represent the whole space of uncertainty. This approach is easy to set up in an industrial context and the selected scenarios are more manageable, which means it can be readily implemented to characterise the risk attached to a project due to the uncertainty on the resource for:
– Open pit optimization and mine scheduling;
– Evaluation of projects when taking financial and technical uncertainties into account; and
– Mine optimization for a portfolio of deposits.

Conditional simulation can also be used for:
– Recoverable resource estimation particularly when additivity is an issue; and to characterise the precision of recoverable estimates.
– Sampling optimisation; and
– Resource classification.

Drill Hole Spacing Analysis and Drilling Optimization

Drill Hole Spacing Analysis (DHSA) is optimal method to use to:
– Optimize drilling budgets;
– Prioritize drilling targets in terms of value to the resource model;
– Derive robust and objective resource classification schemes;
– Characterize product variability; and
– Minimize risks attached to the mine plan.

Drill hole spacing should be optimized at all stages of a mining project on the basis of detailed cost/benefit analyses.

Geostatistics provides the most robust and objective framework to carry out such drill hole spacing analyses. Geostatistics allows you to quantify the value of acquiring more information in terms of uncertainty reduction. The cost of acquiring information can then be benchmarked against the gains in precision it provides.

The value of information can be assessed and optimised on both global and local scales:

Globally, global estimation techniques are used to carry out DHSA studies for coal, iron ore, bauxite and a wide variety of bulk commodities. DHSA enables you to attach a level of precision to the estimation of global quantities (e.g. average value over a 5 yr period) and provide relevant inputs to:
– Derive robust resource classification schemes (link with Res Class.);
– Optimize drilling budgets; and
– Maximise the ground covered for fixed drilling costs.

Locally, conditional simulation can be used to assess:
– The local impact of acquiring additional information (offering the ability to optimise pre-exploitation or grade control drilling grids); and
– The response of the mine plan to resource uncertainty and thus optimize the density and location of new information to minimize identified risks.

Model Validation and Reconciliation

Checking the validity and robustness of any resource estimate is a mandatory step to ensure models remain current and useful. Key avenues for validation and reconciliation are:
– Geostatistical inspection of resource estimates and benchmarking against data inputs; and
– Reconciliation of production outcomes with grade control models and exploration resource estimates (e.g. using past and current production information to improve the predictive performance of your models).

Geostatistics is particularly well-suited to test and check:

1/ The internal consistency of the model (check hypotheses, reproduction of input parameters):
– Grade architecture: helps you chose the change of support models adapted to your deposit; and
– Compare grade tonnage curves produced by your estimates (OK, UC, CS…) with theoretical curves based on samples and change of support model.

2/ The statistical compatibility of the estimates with input parameters:
– Global checks: statistics, histograms, variograms; and
– Local checks: scatter plots, q-q plots, swathplots, boxplots.

3/ The validity of the estimation domains used:
– Border effect and contact analysis (samples/models):
these two complementary tools are used to qualify how domains should be treated at estimation (i.e. hard/soft boundary, definition of transition domains etc.);
– Response of estimates to combination/sub-division of domains; and
– Uncertainty on estimation volumes/tonnages.

4/ The use of production dig line to reconcile models at different scales with actual production data and propose mediatory actions;

5/ Time-sampling and reconciliation at the mill; and

6/ QAQC points, control charts