Multipoint statistics sim. and SNESIM

Question 1

Why do we use multipoint statistics simulation

Answer 1

Because variograms only capture two point spatial statistics

Question 2

What are the pros and cons of traditional two-point stochastic simulation?

Answer 2

Pros:
-Obeys conditioning data and provides a better assessment of variability (low- and high-grades).
-Restores spatial relationships (reproduces variogram models).
Cons:
* Variogram models do not capture connectivity and curvilinear structures.
* Variogram parameters are not necessarily intuitive (nugget, structures, anisotropic directions, ranges, etc.).

Question 3

Give the takeaways from this graph and to what it is due.

Answer 3

Different geological structures behavior for each simulation but they all have roughly the same variograms. This is the limits of two point geostatistics.

Question 4

Explain how Multiple-Point Geostatistics Simulation works generally

Answer 4

We look at the relationships between multiple points simultaneously, and we find the multiple-point statistics. It contains a substantial amount of information about connectivity and curvilinear geological structures.

Question 5

What is a data template

Answer 5

a search neighbourhood of size 𝑛

Question 6

Define data event

Answer 6

Its centred at 𝐱, and is comprised of a set of values for surrounding data within the template

Question 7

Why is it difficult to calculate reliable MP statistics from experimental data (ex; drill holes)? How can we solve this?

Answer 7

Because it becomes increasingly difficult to find replicates of a given template as 𝑛 increases. We use training images to solve this issue.

Question 8

Where does training images come from and what are their use?

Answer 8

• TIs may come from from historical data (mined-out areas), geological face mapping or 3D geological models.
• TIs serve as a “pattern database” for repeating large- and short-scale features in the deposit.

Question 9

Multipoint gestates also utilizes_____ and _________. Briefly describe those.

Answer 9

-Image analysis: our simulations should be consistent with our understanding of geological conditions.
-Image reconstruction: our simulations should be consistent with input data, and any secondary information (if available/possible).

Question 10

Name all the components used in MP gestates

Answer 10

-Data template
-Data event
-Training images
-Image analysis
-Image reconstruction

Question 11

State the steps of the SNESIM algorithm

Answer 11

1. Scan the training image to construct a pattern database.
2. Assign the original sample data to the closest grid nodes.
3. Define a random path to simulate un-sampled nodes.
4. At each un-sampled location in the random path:
   i. Get the conditional probability of the point 𝐱 belonging to a category 𝑠𝑘, i.e., 𝑃𝑟𝑜𝑏 {𝑆 (𝐱) = 𝑠𝑘|𝑑𝑛 }∀𝑘 = 1, … ,𝐾.
   ii. Randomly select a category from the distribution in the previous step. This will serve as conditioning data to the next point to be simulated.
5. Repeat steps 2-4 for each simulation to be generated.

Question 12

Why use a search tree?

Answer 12

• Construction requires only scanning training image once.
• Minimizes memory demand.
• Allows for fast retrieval of all training probabilities for the template adopted

Question 13

Donne la formule Prob {A_k=1 |D=1} = ??

Answer 13

Question 14

Define all parameters in these

Answer 14

Question 15

What is the probability that the central node (A) belongs to a channel (blue), given the following data event (B)?

Answer 15

From image we can see that the central node (A) is blue 3 times and 1 time yellow for the local data event (B).

Question 16

Explain template selection for extensions

Answer 16

• Large template dimensions often need more RAM and take longer to build the conditional distributions,
• Small templates may only capture local patterns.

Question 17

What does handling non-stationarity in multi-point geostatistical simulation involve?

Answer 17

Handling non-stationarity in multi-point geostatistical simulation involves dealing with spatial datasets where statistical properties, such as mean, variance, and spatial correlation, change over space.

Question 18

How to deal with non-stationarity

Answer 18

• Rotations [Rotation map]
• Ratio gradient [Stretching ratio (affinity) map]

Question 19

Give some background on Yandi Iron deposit

Answer 19

They are producing iron ore from clastic channel iron ore deposits (CID). These deposits formation in a fluvial environment with variable sources and deposition of the material as well as post-depositional alteration resulted in very large high quality but complex iron orebodies.

Question 20

What’s the issue with Yandi deposit?

Answer 20

Ore qualities depend on lithological domains that are modelled using sectional interpretations and grade cut-offs. Defining and modelling boundaries to low-grade over-burden and to internal high-aluminous areas cause problems in the current resource estimation, assessment, and modelling practices.

Question 21

what are the main takeaways from these lithologies in Yandi deposit: WCH, GVU, GVL

Answer 21

• Weathered Channel (WCH) → High SiO2 waste unit with a gradational uncertain boundary to the GVU below [Bad]. In WCH and GVU there are high Al2O3 waste (WAS) [Bad]
• GVU – Goethite-Vitreous Upper → Fall within economic mining parameters [Good]
• GVL – Goethite-Vitreous Lower → Fall within economic mining parameters [Good]

Question 22

Where was the study area for the Yandi Case? What spacing?

Answer 22

• They went to Junction Central deposit of the Yandi CID placed called Hairpin as the study area.
• The study area has been drilled out in various campaigns to nominal spacing of 100m by 50m.

Question 23

How did they introduce the knowledge about un-drilled areas into the simulations? (in Yandi context)

Answer 23

The areas around the drilled deposit were assigned arbitrarily as WAS with 50m by 50m spacing.

Question 24

Why would we add artificial data to our drillhole database? (applicable to Yandi)

Answer 24

To add simulation boundaries so the simulations work properly with the need for expensive drilling for these areas of least interest.

Question 25

Goal of the training image, more precisely in the Yandi context.

Answer 25

The training image contains the relevant geological patterns of the simulation domain.So, in the context of the Yandi CID:
The TI must characterise the shape of the channel and of the internal boundaries within the study area.

Question 26

Why was the geological model of the mined out initial mining area (IMA) chosen? (in Yandi context)

Answer 26

Because:
1. The model is based on relatively dense exploration drilling on a 50m×50m grid.
2. It consists of a straight section of the CID thus having a constant channel axis azimuth.

The TI was generated as a regular geological block model of the IMA prospect.

Question 27

How do we validate that the TI is consistent with the available data within the simulation domain? (Yandi context)

Answer 27

• The variograms and cross-variograms of the geological categories are used.
• Two data sets will be compared with the TI

Question 28

Talk about the results from Yandi case. Top image is two realizations vs wirferame.

Answer 28

• The overall shape of the channel has been well reproduced.
• The incised shape (digging into ground) of the channel was generated on a large scale and the stratigraphic sequence (layering) has been reproduced.
• The proportion of GVL is higher in the simulations than in the wireframe model but proportions were still reproduced.
• Boundaries in the simulations are less smoothed for both the GVL-GVU and the GVL-WAS contacts.
• In some areas, channel material was generated in small pods outside the continuous channel.
• The channel margins, holes and saw-tooth shaped contacts are inconsistent with the depositional environment of the deposit.
• The boundary of GVL and GVU is undulating and shows an increased irregularity in comparison with the wireframe model.
• In the northern part of the channel where the realisations contain GVU, while the wireframe model consists mainly of GVL.
• In the southern end of the channel, the GVU patches in the realisations have an increased extension compared to the wireframe model.
• On average probability for unit GVU (P(GVU)), the locations of the lowermost parts of the GVU are match the wireframe model.
• The outline of the GVU to the surrounding WAS in the realisations is very fuzzy, overall, compared with the wireframe model. This higher disorder occurs on two scales:
  1. On a very fine scale of a few blocks, the outline is strongly undulating.
  
  2. On a larger scale of about 15 – 25 blocks, the undulations are less extreme.
     However, they are still present and not consistent with the TI.
• The shapes of the channel margins are not well reproduced: Instead of an expected rather smooth outline as in wireframe model, the appearance is sharply stepped (left margin of Sim1 and Sim2).
• The top part of the channel is very fringy. All the sections depicted show saw-tooth shaped features at the channel margins, indicating slight problems of the algorithm to reproduce the patterns of the channel margins.

Question 29

Comment on the reproduction of two-point stats

Answer 29

• WAS variograms are well reproduced in the main direction (EW), but the experimental data variograms suggest less continuity of lags up to 350m,
• For WCH, the variogram reproduction is mediocre and suggests more continuity of the simulations compared to the data. The simulations deviate for lags larger than 50m and reach the sill of the TI-variogram only at a lag of about 450m.
• GVU and GVL variograms are well reproduced and correspond to the experimental data variograms.

Question 30

Comment on differences with deterministic wireframes and uncertainty in grade tonnage curves

Answer 30

• The intersection of stochastic realisations and estimated grades allows an assessment of uncertainty due to uncertain geological boundaries.
• Al2O3 shows the differences between simulated geology and conventional wireframing, because Al2O3 is not a well understood variable in the resource model of the deposit.
• The grade uncertainty appears relatively small.
• Massive differences in tonnage curves between HIY and Sim for cut-offs below 6%.
• The resource tonnage indicated by simulations is on average 12 Mt (9%), smaller than the tonnage indicated by the best-guess wireframe model.
• The simulations allow for estimating a tonnage confidence interval.
• This shows that the contribution of the geological uncertainty to the overall grade uncertainty is considerable.

Question 31

Give conclusions from the Yandi case

Answer 31

• The position of boundaries in between drillholes changes from realisation to realisation, thus reflecting the uncertainty about the boundaries’ exact shape.
• On the margins of the channel, the generated patterns are not always geologically meaningful. The visual validation showed inconsistencies of the algorithm, reproducing patterns at the margins of the channel.
• In the cross-sections, the major critical observation is that the erosional contact to the formation is not consistent with observations in the pit nor with geological knowledge originating from modern geomorphologic analogues.
  o Two sources for these issues with pattern reproduction have to be considered : The TI and The algorithm
• It was shown that the TI and the data in the simulation domain are not fully consistent with respect to two-point statistics. The extent to which this influences the quality of reproduced patterns is difficult to assess.
  Using a set of different training images can provide further insight.
• Using grade simulation instead of grade estimation techniques would add realistic grade variability to this model and allow the assessment of total grade tonnage uncertainty.
• Potential areas of application are in areas of little geological understanding or definition of boundaries by drilling.
• At Yandi, internal clayey high-aluminous waste that cannot be defined with the 50-100m spaced resource evaluation drilling and simulation could create value by better defining grade tonnage curve about contaminants.