Midterm

Question 1

What are the important formulas for simple kriging?

Answer 1

Question 2

Name the steps and substeps of SGS

Answer 2

1. Normalize Data (Normal Score)
2. Model Variogram, Covariance, Correlogram
3. Define a random visit path for each nodes
4. 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
5. Back transform

Question 3

What is a random variable? What are the types of RV?

Answer 3

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 ….)

Question 4

Draw a cumulative distribution function.

Answer 4

Question 5

What is a random function (RF)

Answer 5

is a set of random variables defined over an area (domain) of interest

Question 6

Comment on the search ellipsoid

Answer 6

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

Question 7

What affects Variation of sample weights and estimation variance

Answer 7

1. Nugget effect
2. Range
3. Anisotropy
4. Block size
5. Position of samples around block

Question 8

What is a random number generator?

Answer 8

Responsible for creating a sequence of random numbers which follow the characteristics of a specified distribution (most common distribution is the uniform distribution)

Question 9

What makes a random number?

Answer 9

1. Generated by chance
2. Independent from previous values
3. Associated probability of occurring

Question 10

What makes a good random number generator?

Answer 10

1. long period
2. ability to reproduce sequences
3. speed and simplicity
4. agreeance of statistical properties of uniform distribution

Question 11

Give the Linear Congruential Generator formula and variables

Answer 11

Question 12

Give the coeffient of variation formula.

Answer 12

Question 13

Why do we use the coeffient of variation formula?

Answer 13

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.

Question 14

Why variance increases overtime in this forecast.

Answer 14

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

Question 15

What is Sequential Gaussian Simulation with Screen-Effect Approximation?
Advantage?

Answer 15

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

Question 16

What is a selective mining unit?

Answer 16

The selected block size basically.

Question 17

Comment on the SMU size and the grade tonnage curve.

Answer 17

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.

Question 18

Give the main LU Method formulas.

Answer 18

Question 19

Give the full covariance matrix

Answer 19

Question 20

Give the formulas to compute the values of the L matrix.

Answer 20

Question 21

Give the steps of GSGS.

Answer 21

1. Define a path visiting each of the k groups
2. Define a path visiting each of the v nodes inside each of the k group
3. Find a neighbourhood for nodes inside visited group
4. Compute conditional mean and variance for nodes inside visited group
5. Generate simulated values of the current group nodes
6. Add simulated values into the data set
7. Loop until all groups are simulated

Question 22

Explain loss of accuracy in GSGS.

Answer 22

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.

Question 23

Give the O notation for runtime and all intergrated variables for GSGS, SGS and LU.

Answer 23

N is number of points
vmax is the neighborhood size
v is the group size

Question 24

What does the dispersion variance do?

Answer 24

The dispersion variance evaluates the difference in variability within the values of the small block compared to the entire large block.

Question 25

Give the F1 factor intent, formula and interprétations.

Answer 25

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

Question 26

What are the factors for F1 to be different from 1.

Answer 26

1. Data problems
2. Poor estimation method
3. Over smoothing of estimated block grades
4. Change of support corrections

Question 27

Give the F2 factor intent, formula and interprétations.

Answer 27

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

Question 28

What are the factors for F2 to be different from 1.

Answer 28

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

Question 29

Give the F3 factor intent, formula and interprétations.

Answer 29

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

Question 30

Describe generally estimation and then lists 7 points

Answer 30

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

Question 31

Describe generally simulation and then lists 7 points

Answer 31

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

Question 32

What is grade control?

Answer 32

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.

Question 33

Why does grade control matter?

Answer 33

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.

Question 34

Give the actuall loss formula.

Answer 34

Question 35

In Maximizing profit classification, what is the opportunity cost formula.

Answer 35

Question 36

In Maximizing profit classification, what is the correct classification formula.

Answer 36

Question 37

Explain Sequential Indicator Simulations

Answer 37

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.