Mini-Max Joint Simulation Flashcards
Name the (3) impacts of having outliers.
- Increase variance
- Increase mean
- Highly right-skewed grade distribution (high grades with low frequencies)
Name the impacts of removing outliers from grade distribution.
We observe a decrease of the mean and a decrease of the variance. This results in the underestimation of the deposit and we have smoothing.
Why was MAF method developed.
- Common joint simulation methods are too computationally intensive.
- This is a source of complexity = inference of modelling of cross-variograms, and computational inefficiency due to increasing # of variables being co-simulated.
-A potential solution is the decorrelation of variables using PCA.
-Hoever, PCA ignores cross-correlations at distances other than 0 (a limitation).
Therefore need Minimum/Maximum Autocorrelation Factors (MAF).
What does the PCA type factorization method allow?
The preservation of the correlation between elements
What does PCA stand for?
Principal Component Analysis
What is a limitation of PCA and its solution?
PCA ignores cross-correlations at distances other than 0 (a limitation) therefore it’s a limitation in the presence of spatial cross-correlations. Solution: Min/Max Autocorrelation Factors (MAF) in the context of spatial simulation
Describe the MAF method in 3 steps.
It is an approach based of PCA,
(1) spatially decorrelates the variables involved to non-correlated factors
(2) independent factors are then individually simulated
(3) back-transformed to the conditional simulations of the correlated deposit attributes
What does MAF stand for.
Min/Max Autocorrelation Factors
Describe the MAF algorithmin 8 steps
- Normalize the variables to be simulated.
- Use MAF to generate the MAF non-correlated factors.
- Produce variograms for each MAF.
- Conditionally simulate each MAF using any Gaussian simulation method.
- Validate the simulation of factors.
- Back-transform simulated MAF to variables and denormalize.
- Validate the final results.
- Generate additional simulations, as needed.
What is the following case study about: Assessing risk in Grade-tonnage curves in a complex copper deposit, northern Brazil.
Its a mine with a multi-mineral deposit which includes Cu, Fe, and K. They decided to do joint simulation of Cu, Fe and K to:
1. Determine recoverable Cu: copper solubility is controlled by K and Fe content, in addition to Cu grade (aka you can’t feasibly process ore with too much K and Fe)
2. Quantify Risk: generate grade-tonnage curves based on a range of Cu, Fe, and K grades
Why did the Brazil mine decide to complete a Joint Simulation with MAF? State all the reasons
- It was for the pre-feasibility study
The joint simulation with MAF was used because: - Allows for Multiple elements (3) within the deposit
- Traditional methods for jointly simulating correlated variables are impractical and heavy (cross-variance, cross-variograms, cross-correlation à gigantic matrices)
- MAF allows decorrelation of elements
- MAF can be simulated independently, and the cross-correlations re-appear when MAFs are back-transformed to elements
How many and which units were studied in the Brazil Case study?
2 units: sector 11 and 12
Describe the simulation process step-by-step for the Brazil case study.
- Normal-score transformation: normal score transformation performed on the Cu, Fe, and K composites of sectors 11 and 12
- MAF transformation: generate the 3 min/max autocorrelation factors (As many MAF as there are elements looked at)
- Variography of MAF: almost no correlation (line around 0) means that the data is not correlated anymore with the factors (variance at approximately)
- Conditional simulation of MAF: generalized gaussian simulation method, 20 simulations
- Back-transformations (rotations) of MAFs
- Validation of the joint Cu-Fe-K simulation results: histograms, experimental variograms and cross-variograms to ensure reproduction of original data characteristics (reproduction is excellent)
a. Reproduction of data statistics through histograms
b. Reproduction of spatial correlation through varigorams
c. Reproduction of correlation coefficients through scatter plots
What are the results from the Brazil case study? More precisely about the grade tonnage curves.
Recoverable copper results and risk quantification were derived from metallurgical tests results and from the simulations. From the grade tonnage curves we have a very high change in tonnages as the Cu content increases, a very low change in tonnages as the K content increases, and a very high change in tonnages as the Fe content increases. There is also low variability lines for Fe graph, the lines are closer together than the lines in the Cu graph for a higher grade content.
What are the main takeaways from the Brazil case study?
-Recoverable copper tonnage variability is more clearly related to the in-situ copper and potassium content than to iron content. That means for Fe rich ores, no wide variability in copper output is apparent in the grade-tonnage curves.
-Variability in recoverable copper grade is, however, mainly dependent on the in-situ copper content.
What is a drilling program?
infill drilling + step-out drilling
What is the goal of step out drilling
aim to expand the mineralization zone
What is the goal of infill drilling
confirm the presence of mineralization between step-out drill holes
What is the concept of Infill drilling
Critical information collection process: ability to assess the performance of potential drilling schemes, prior to drilling is important
What are the realted: ‘‘enjeux’’ xd
reducing drilling can enhance the profitability of an operation if misclassification cost does not exceed the saving in drilling.