5 GEOLOGICAL RISK (SLICE & PRISM)
The most common method of defining geological risk is to simulate the uncertainty associated with estimation of grade into a model cell. There are two geostatistical methods currently handles by the SSO. They are "Conditional Simulation" or "Multiple Indicator Kriging" (MIK). The SSO geological risk techniques enable either stope-shapes to be designed to a geological confidence level (i.e. maximising optimisation field value while meeting confidence criteria) or evaluated to ascertain their geological confidence level (maximising optimisation field value and reporting the confidence level). An example of this second approach is depicted in Figure 5-1 using a visual representation of the stope grade confidence level.
Figure 5 ‑ 1Stope-Shapes with Geological Risk ConfidencePercentage
5.1 Accuracy vs Precision in Estimation and Simulation
The key difference between estimation and simulation is that:
·Estimationaims to provide the best local grade estimate, which has the effect of smoothing the grade variance, while
·Simulationis specifically designed to reproduce the grade variability and examine its effects.
As a consequence, the results of this type of analysis may be very challenging because the level of confidence associated with stope designs may be significantly different to the resource classification. The differences however may often be attributed to categorisation limitations and/or practicalities (such as avoidance of "spotted dog" classification or QA/QC issues that require re-classification). If however provides an independent alternative view regarding the certainty of the resource modelling.
5.2 Conditional Simulation
The “Conditional Simulation” method typically provides 20-50 equi-probable realisations of the cell grades within the block model. The maximum number of realisation is currently 50.
If making comparison regarding the appropriate number of realisations, it should be noted that if alternate models are used, they must have the same starting seed position. It is therefore preferable when making such comparisons that the model with largest number of realisations is used and other sub-sets extracted in lowest sequential order to make correct comparisons.
5.3 Multiple Indicator Kriging
The MIK method provides the frequency distribution of the grades in a block (expressed as the percentage of material above cut-off and the head-grade of this material for typically 10-20 cut-off values), but is not able to identify the location of the grades. The SSO internally manipulates the MIK model to produce “conditional simulation like” outputs using a technique calledPfield Simulation, which is documented in the Stanford University GSLIB package ( http://www.gslib.com/ ).
There are several alternatives for conditioning the MIK data to a series of simulations:
(1) Provide a series of unconditioned [0, 1] fields.
(2) Provide a set of fields with absent data and default of -1.0 (which is the value recognised by GSLIB) for UNSET data, and a random distribution of [0, 1] values will be generated.
(3) Provide no fields and a random distribution of [0, 1] values will be assigned to the maximum number of conditional fields that can he handled (currently 50).
Option (1) is preferred, and the benefit of supplying the field names in the model file is that the stope grades based on the simulations generated can be reported.
5.4 Risk Evaluation
One approach to risk evaluation is to generate stope inventories for each of the simulation fields (often referred to as realisations), and to report the distribution of grade and tonnes across all the realisations. The approach to using these inventories is to do a mine design for a small subset of the inventories - ideally selecting a subset that has the median
While this approach can be undertaken with the Stope Shape Optimiser, another method is to analyse all the simulations concurrently. The criterion for each run is that the final stope-shapes must satisfy the selected cut-off/head-grade at a selected level of confidence, and produce the optimal set of stopes to maximise value/metal.
The single set of stope-shapes that return maximum value is reported at the requested level of confidence, rather than reporting a stope optimisation on each and every realisation. At 100% confidence the stope-shape will satisfy the cut-off value for every realisation. At 80% confidence the stope-shape will satisfy the cut-off in 80% of the realisations. The trade-off between risk and return is found by graphing the stope tonnage and value against confidence, and is a way to generate a "nested" set of stopes.
For either method, conditional simulation or multiple indicator kriging, a complete set of realisations is analysed in a single run of the SSO, with a single set of stope-shapes output. All the stope grades for each realisation can be reported at that confidence level.
5.4.1 Comparison with Pit Optimisation Techniques
An approach to risk evaluation in Pit Optimisation is to complete a pit optimisation for each realisation, and then produce a set of nested pits based on the number of times that a block reports within the optimised pit for each realisation. This works well in that context because the pit optimisation works with a regularised model grid. This approach however is less appropriate for underground stope-shape optimisation.
5.5 Optimisation Field
For either method it is necessary to supply an optimisation field that is the primary grade field reported. This field is typically the Kriged value. A proxy for this optimisation field could be the average of the realisations - termed the "E-type" value. The confidence level for a stope is found by evaluating the stope-shape against all the realisations, and finding the proportion of the reported realisations above cut-off.
5.6 Reporting
For any nominated confidence level, the output stope report file will provide the following four statistics from evaluating all realisations:
i. CONF-PER the confidence level for the stope-shape as a percentage
ii. CONF-MED the median value (using the Excel definition for median)
iii. CONF-MIN the minimum value
iv. CONF-MAX the maximum value
5.7 Using CONF-PER in Post-SSO Activities
There are many ways that stope design risk measures could be integrated into post SSO activities.
An interesting possibility of applying Geological Risk in production planning may be applied as follows:
1. Apply 0% Confidence criteria in SSO and export the “CONF-PER” values for various Kriged fields. This would be the optimised grade (say Au, Cu, EgV,... etc.) but could also be for elements which effect process recovery or other elements which may affect process throughout, and perhaps even a geotechnical parameter like RMR (which may potentially be used for dilution/stope failure estimation). This would be the optimised grade (say Au, Cu, EqV,... etc.) but could also be for elements which effect process recovery or other elements which may affect process throughout, and perhaps even a geotechnical parameter like RMR (which may potentially be used for dilution/stope failure estimation).
2. Run schedule based on optimising project goals.
