Midterm Flashcards
What are the important formulas for simple kriging?
Name the steps and substeps of SGS
- Normalize Data (Normal Score)
- Model Variogram, Covariance, Correlogram
- Define a random visit path for each nodes
- For each nodes:
4.1 Solve kriging system to get mean, variance
4.2 Sample form N(mean, variance)
4.3 Add new node value to simulation and conditionning data - Back transform
What is a random variable? What are the types of RV?
A variable whose value is not known can take on a series of values according to some probability distribution.
- Continuous,
- Indicator (0 or 1)
- Categorical (0, 1, 2, 3 ….)
Draw a cumulative distribution function.
What is a random function (RF)
is a set of random variables defined over an area (domain) of interest
Comment on the search ellipsoid
The ellipsoid acts as a spatial filter, determining which surrounding observed points will be considered (those within the ellipsoid) and which will be ignored (those outside the ellipsoid) when estimating values at unobserved locations using kriging
What affects Variation of sample weights and estimation variance
- Nugget effect
- Range
- Anisotropy
- Block size
- Position of samples around block
What is a random number generator?
Responsible for creating a sequence of random numbers which follow the characteristics of a specified distribution (most common distribution is the uniform distribution)
What makes a random number?
- Generated by chance
- Independent from previous values
- Associated probability of occurring
What makes a good random number generator?
- long period
- ability to reproduce sequences
- speed and simplicity
- agreeance of statistical properties of uniform distribution
Give the Linear Congruential Generator formula and variables
Give the coeffient of variation formula.
Why do we use the coeffient of variation formula?
For ability to provide a normalized measure of dispersion, which can be particularly valuable when dealing with variables of different units or scales. Remove bias by scaling the value.
Why variance increases overtime in this forecast.
Variance increases overtime as we are moving to block with higher variance. So, if we observe the variance increasing over production periods, it can indeed suggest that the mining operation is progressing from more certain to less certain areas
What is Sequential Gaussian Simulation with Screen-Effect Approximation?
Advantage?
Considering a fixed-size neighborhood around a node where the posterior probability density function is approximated using only the data within this nearby region.
limiting calculations to localized neighborhoods around. Better for computer
What is a selective mining unit?
The selected block size basically.
Comment on the SMU size and the grade tonnage curve.
As block size decreases, there is less dilution and reduced smoothing of the data (more variability), resulting in higher recorded tonnages for the superior grades due to the availability of a greater number of high-grade blocks (or tonnes).
In essence, smaller blocks capture more detailed variability in grade, thus presenting a more accurate representation of high-grade zones in the data, leading to higher tonnages at those high grades.
Give the main LU Method formulas.
Give the full covariance matrix
Give the formulas to compute the values of the L matrix.
Give the steps of GSGS.
- Define a path visiting each of the k groups
- Define a path visiting each of the v nodes inside each of the k group
- Find a neighbourhood for nodes inside visited group
- Compute conditional mean and variance for nodes inside visited group
- Generate simulated values of the current group nodes
- Add simulated values into the data set
- Loop until all groups are simulated
Explain loss of accuracy in GSGS.
As the size of the local neighbourhood increases the loss decreases. Takes more data point into account leads to overlapping grid points and less loss.
Give the O notation for runtime and all intergrated variables for GSGS, SGS and LU.
N is number of points
vmax is the neighborhood size
v is the group size
What does the dispersion variance do?
The dispersion variance evaluates the difference in variability within the values of the small block compared to the entire large block.
Give the F1 factor intent, formula and interprétations.
Intent:
F1 calculates accuracy in estimating reserves
Formula:
F1 = Actual In Situ Quantities / Estimated In Situ Quantities
- If F1 > 1.0 in situ reserves are underestimated
- If F1 < 1.0 in situ reserves are overestimated
What are the factors for F1 to be different from 1.
- Data problems
- Poor estimation method
- Over smoothing of estimated block grades
- Change of support corrections
Give the F2 factor intent, formula and interprétations.
Intent:
F2 calculates ability to select ore from waste
Formula:
F2 = Run-of-Mine Quantities / Actual In Situ Quantities
If F2 > 1.0 for tonnage, waste is mined as ore
If F2 < 1.0 for tonnage, ore is sent to waste
What are the factors for F2 to be different from 1.
Reasons for F2 to be different than unity:
1. Assaying or sampling problems in blast holes or RC
2. Highly variable mineralization
3. Operational constraints leading to ore loss & dilution
4. Change of support
Give the F3 factor intent, formula and interprétations.
F3
Intent:
* The F3 factor measures the combined effect of F1 & F2.
* F3 factor indicates whether the goals set on the production schedule will be achieved with respect to tonnage, grade, and metal
Formula
F1xF2 = F3 = Run-of-Mine Quantities/Estimated In Situ Quantities
Describe generally estimation and then lists 7 points
Provides a single map representing a smooth view of the underlying mineralization.
1. Globally unbiased
2. May be conditionally biased
3. Does not reproduce histogram shape
4. Does not reproduce variogram
5. Honors local data
6. Locally accurate
7. Assessment of local averages
Describe generally simulation and then lists 7 points
Provides several equally probable alternative versions of the underlying mineralization.
1. Globally unbiased
2. Conditionally unbiased
3. Reproduce histogram shape
4. Reproduce variogram
5. Honors local data
6. Not locally ‘accurate’
7. Assessment of local uncertainty
What is grade control?
Grade control is the operation where truckloads are flagged as ore or waste based on blast hole, drill hole and geologic information. Classification of material basically.
Why does grade control matter?
Classification errors generate expense. If a block of ore is misclassified, a net loss ($) occurs. Such misclassification errors can never result in a net $ gain.
Give the actuall loss formula.
In Maximizing profit classification, what is the opportunity cost formula.
In Maximizing profit classification, what is the correct classification formula.
Explain Sequential Indicator Simulations
Indicator Transform: SIS often employs an indicator transform, turning a continuous variable (like grade) into a binary one (ore/waste) based on a specific cutoff. This binary decision-making is crucial for operational decisions in mining.
