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Characterization using block simulation Project extensive documentation 11, September, 2013 CERENA

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Page 1: SICentroidSimulation_extensive_documentation

Characterization using block simulation

Project extensive documentation

11, September, 2013

CERENA

Page 2: SICentroidSimulation_extensive_documentation

INDEX

• Chapter I – What is a block?

• Chapter II – Creating blocks

• Chapter III – Interpreting reality with blocks

• Chapter IV – Kriging with blocks

• Chapter V – Uncertainty characterization with blocks

• Chapter VI – Case Studies

p.3-18

p.19-29

p.30-36

p.37-42

p.43-48

p.49-63

Page 3: SICentroidSimulation_extensive_documentation

Chapter I – What is a block?

• What is a block?

• What is a block value?

• What is a block centroid?

• What is a block error?

• What is a block file?

• Things to know about blocks?

• Types of block data

• Methods for calculating block value

• Methods for calculating block error

• Blocks bottom line

p.4-5

p.6-7

p.8

p.9

p.10

p.11-13

p.14

p.15-16

p.17

p.18

Page 4: SICentroidSimulation_extensive_documentation

What is a block?

1

2

Let’s start with an image with

several pixels, each with it’s own

value.

You can imagine that each of the

pixels is actually a point with a

precise value and location in space.

Grid

Reference image

Point data

Legend

Page 5: SICentroidSimulation_extensive_documentation

What is a block?

3 We create some divisions (for now it’s not important

the division method), some sets of points with less

resolution than the original image.

4 Now our point located space is divided

in different areas. Each of those areas is

something of a primordial block.

Legend

Point data

Divisions

Page 6: SICentroidSimulation_extensive_documentation

What is a block value?

5 From the divisions we must analyze each of

the sets to determine its properties.

6 • Most common value is

• The probability value is “8/9 ; 1/9 “

These are two different methods for calculating a block

value for indicator variables. If variable is continuous than

it could be mean, for example.

Legend

Point data

Divisions

Page 7: SICentroidSimulation_extensive_documentation

What is a block value?

7 Now all the block divisions have a value (for illustration

purposes let’s use the most common value).

Legend

Point data

Divisions

Point whose value

has changed in

the local block If most common

value is used…

8 Some of the points have changed value and so we

have lost some detail when changing an image into

blocks. For this reason (and others…) there is an error

for each block. We’ll talk more about that later.

Page 8: SICentroidSimulation_extensive_documentation

What is a block centroid?

9 Each block has a centroid, a location in X,Y,(Z) which

can be used for search engines or variogram

(correlogram) calculation depending on the type of

implementation of sequential indicator block simulation.

10 We can actually start managing and using blocks

by its centroid location. In fact if we do so it would

similar to having a point-set of centroids with each

point having a specific value (and error).

Legend

Point data

Divisions

Block centroid

* If by any chance you thought the centroid symbol looks like a nipple you

should know that you’re a particularly libidinous person. Just saying…

Page 9: SICentroidSimulation_extensive_documentation

What is a block error?

11 Now we have blocks, each with a number of points,

a centroid, and a value. We can also introduce an

error

0 0

0

0

0 0

0

0.5

0.25 0.11

12

Error, like value, is an user choice. Methods to

calculate error are:

• Using the probability value as error (image above).

• Using the size of the block (bigger the block bigger

the error).

• Using a map to attach errors like a map of distance

to the hard-data (the farther from hard-data the

bigger the error).

The last two methods need a user inserted range for

the error so that the upper error limit would be

equivalent to the bigger block, for example.

Legend

Point data

Divisions

Block centroid

Error

quantification

Page 10: SICentroidSimulation_extensive_documentation

What is a block file?

BLOCK_FILE 99 block #0 0.94;0.00;0.00;0.05 0.3 55.0 0.0 55.0 1.0 55.0 2.0 … …

Probability for each bin Error

Points in block

Number of blocks in file

13

This is how a block file would look like. You have

general information like name of the block set and

number of blocks in file. In this example the value

of the block is the probability for each bin. After

indicating which block the information refers to

(all blocks are on the same file) it gives the

coordinates of the points inside that specific block.

If chosen method for value would be the most

likely value it would appear something like this:

• 1;0;0;0

You must have guessed that this particular

example has 4 indicator bins. If the value was

continuous (no indicator bins) a single value

would appear. The error always goes from 0 to

1 being 1 the maximum uncertainty possible

and 0 completely certain. A less uncertain block

will have less weight in the kriging procedure.

14

* No pretty things in this slide. Here’s Velázquez Rokeby

Venus to get you by.

Page 11: SICentroidSimulation_extensive_documentation

Things to know about blocks?

A

A block doesn’t need to be as dense of

points as the image used to create it. In

fact You don’t even need an image to

create blocks

B

The block doesn’t need to have

a regular shape. In fact it is quite

flexible although implementing

an algorithm to deal with flexible

block shapes is computationally

intensive and may not be worth

the trouble.

Page 12: SICentroidSimulation_extensive_documentation

Things to know about blocks?

C

Block management doesn’t need to be all

about centroids (it’s just faster). We could

use all points inside a block for search and

correlogram calculation.

D A block doesn’t need to be a small set of

points. It could be solid and a search be

done by portions.

Page 13: SICentroidSimulation_extensive_documentation

Things to know about blocks?

E

Blocks don’t need to cover the entirety of

the study area. In fact you may want to

deliberately create high uncertainty areas

with no block information.

F

Even when optimized or minimized for a specific

purpose block simulation is still significantly more

computationally heavier than the common simulation

or co-simulation procedures. Block simulation is about

flexibility.

Co

mp

uta

tion

al t

ime

Page 14: SICentroidSimulation_extensive_documentation

Types of block data

Lithology 1 (example: high porosity lithology)

Lithology 2 (example: low porosity lithology)

High porosity Low porosity

Indicator variable (discrete) Continuous variable

Nothing prevents a block being both indicator and continuous although it may not

be clear how to use this variable duality for characterization purposes.

Page 15: SICentroidSimulation_extensive_documentation

Methods for calculating block value

Indicator variable (discrete)

An indicator variable is a probability variable or, more truthfully, the

probability of occurrence of a given discrete value. For this reason in the

top left block we have:

• Most common value is

• The probability value is “8/9 ; 1/9 “

Which means either:

• 1;0 (probability 1 (100 %) of having the lithology 1 and 0

(0%) of having lithology 2. Thus 1 ; 0 (1;0).

Or:

• 0.89;0.11 (probability 0.89 (89%) of having the lithology 1 and 0.11

(11%) of having lithology 2. Thus 0.89 ; 0.11 (0.89;0.11).

If we would have three lithologies (or any other discrete variable) we would

have three probability fields (“1;0;0” or “0;1;0”, etc.). The methods above are

the most obvious and you don’t need to calculate all blocks in your set with

the same method (both for value and error).

Page 16: SICentroidSimulation_extensive_documentation

Methods for calculating block value

A continues variable works in its own order of magnitude. Porosity for instance

(percentage of empties or voids in a volume, being 100 % completely void).

Since there is no way of counting balls of porosity (without transforming the

variable into an indicator one) the best way to produce a value for a block is to

use the most common (and uncommon if you would like) statistical indicators

such as:

• Mean

• Median

• “n” Percentile

• Maximum

• Minimum

• Etc.

Continuous variable

Page 17: SICentroidSimulation_extensive_documentation

Methods for calculating block error

0 0

0

0

0 0

0

0.5

0.25 0.11

Above is an example of a block error calculated

by the probability of not being the value of that

same block.

Should I decide my maximum

error is 0.5 and minimum is 0.2

than:

𝐸𝑟𝑟𝑜𝑟 =𝑠𝑖𝑧𝑒 − minimum size ∗ (𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑒𝑟𝑟𝑜𝑟 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑒𝑟𝑟𝑜𝑟)

(𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑠𝑖𝑧𝑒 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑠𝑖𝑧𝑒)+ 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑒𝑟𝑟𝑜𝑟

3*3 = 9 2*2 = 4 2*2 = 4

2*2 = 4

2*2 = 4

1*2 = 2

1*2 = 2

1*2 = 2 1*2 = 2

2*

1 =

2

“Size matters” method

0.5

0.29 0.29

0.29

0.29 0.22 0.22 0.22

0.22

0.22 ### Error

Hard-data or

scenario marker

Block centroid

“Error mapping” method

0.5

0.3

0.3 0.3

0.35

0.35

0.35

0.3

0.25

0.2

“Disagreeing” method

Page 18: SICentroidSimulation_extensive_documentation

Blocks bottom line

Block - set

A block-set is set of blocks. A block is an

entity composed of points* located in space

(and delimiting the size, shape and body of

the block). A block has:

• Value (discrete or continuous)

• Error

• Centroid

* For all implementations made so far (at least to our knowledge).

Value can be indicator (discrete) of continuous.

Depending on the type it can be calculated by

procedure such as:

• Most common element (indicator)

• Probability for each phase (indicator)

• Mean (continuous)

• Minimum (continuous)

• Maximum (continuous)

• Median (continuous)

• Percentile (continuous)

• Etc.

Error is measured from 0 (no error) to 1 (full error). This

presentations has proposed some methods to inquiry

error such as:

• “Disagreeing” method (indicator)

• “Size matters” method (both)

• “Error mapping” method (both)

Centroid is a point, in a central location of a block (mean

locations for X,Y,Z, for example), which facilitates

management of the set for search purposes, variogram

calculation, etc. It is a facultative “property” of a block and

its main advantage is to increase performance in a heavy

algorithm.

Page 19: SICentroidSimulation_extensive_documentation

Chapter II – Creating blocks

• A simple net

• A less simple net

• Building a quadtree based procedure

• Void Selection Quadtree

• Marker tolerance

• Centroid management

• Meshing operations

p.20

p.21

p.22-24

p.25-26

p.27

p.28

p.28-29

Page 20: SICentroidSimulation_extensive_documentation

A simple net

1 This is our grid (a bit bigger than

the one on Chapter I).

2 We’ve used a constant step of 2 to create

both horizontal and vertical divisions.

Grid

Divisions

Legend

Page 21: SICentroidSimulation_extensive_documentation

A less simple net

3 Remember that it’s blocks we’re making but

this method gives the same shape on every

single one of them, thus there are no areas

more dense and with less uncertainty.

4 The ideal should be to have more blocks

in areas where we are more certain of

what exists there. But for that to happen

we need some kind of algorithm to do it.

Grid

Divisions

Legend

Block value

Page 22: SICentroidSimulation_extensive_documentation

Building a quadtree based procedure

6 Let’s make our level one division. Cutting

the study area in halves. We got 4 areas,

3 of those are empty therefore saved as a

block area. Let’s go on to the next level.

5 Let’s set out a user rule that says wherever a

point marker (scenario marker ) exists

there should be a more dense net (smaller

blocks). Where none exists a less dense net. This kind of division is called quadtree since it always

splits the areas in four (quad) bits. ?

Grid

Divisions

Legend

Scenario

marker

Page 23: SICentroidSimulation_extensive_documentation

Building a quadtree based procedure

8 Going on to level 3 (let’s stop leveling here)

and we got three more void areas and one

filled. The final result for this particular test is…

7 Level two we continue to split the areas

where scenario markers ( ) remain. There

are 3 new empty areas (voids) and 1 still has

a marker.

Grid

Divisions

Legend

Scenario

marker

Page 24: SICentroidSimulation_extensive_documentation

Building a quadtree based procedure

9 The result is that smaller blocks and denser areas

appear near the marker . Since this grid doesn’t

have a lot of blocks problems such as the division of

odd numbers arise, however in bigger grids (more

nodes) this problem becomes non-existent.

10 You can imagine that the more marker the more

dense areas will exist. You can use markers to

actually build blocks set that are adequate to your

case study. Since it was based on the

quadtree concept and

creates blocks wherever voids

are found we’ve called this

procedure “Void Selection

Quadtree”*.

?

* What can I say. We’re scientists not poets. Although that career

did cross my mind…

Grid

Divisions

Legend

Scenario

marker

Page 25: SICentroidSimulation_extensive_documentation

Void Selection Quadtree

Let’s review. We start with an empty, undivided area

which we start splitting, level by level, in four smaller

areas. But we only split if there’s a marker inside the

area. The user choses the number of levels it wants

to use. This is “Void Selection Quadtree”.

12 So now we must take into account that his hole net

created must be made to generate blocks. Following

the procedures explained on chapter one we would

get something like the example above.

Grid

Divisions

Legend

Scenario

marker

11

Page 26: SICentroidSimulation_extensive_documentation

Void Selection Quadtree

Even if the user is not happy with the final result or he

somehow finds that some areas should have more

detail (and notice we’re making a parallel between

detail and certainty) we can build a new model with a

new marker that will not change the previous blocks.

The procedure has little to none chaotic behavior.

14 We’ve introduced a new marker and got an update.

Better resolution in the area shown above. Working

with this methodology is simple although not without

some more secondary procedures that should be

explained.

Grid

Divisions

Legend

Scenario

marker

13 Update

marker

Update

area

Page 27: SICentroidSimulation_extensive_documentation

Marker tolerance

Sometimes the phenomena shown in the top left net

happens. A point is too close from the division limit and in

the end in only has detail in one of the sides. To solve this

we can use a location tolerance so that when a split area

does not have a marker but it’s within the tolerance of one

it should continue to be split. Notice how better the result

was when using an adequate tolerance (user chosen).

16 There must be some careful planning with marker

tolerance. Too much and the net will loose its

purpose.

15

Grid

Divisions

Legend

Scenario

marker

Marker

tolerance

Page 28: SICentroidSimulation_extensive_documentation

Meshing operations

The idea of Void Selection Quadtree proposed in this presentation was made specifically to be

adequate to the majority of case studies we’ve been having. However is far from the only

solution available. Meshing operations are common in many sciences (3d modeling for

instance) and you should have some other ideas of what you can use. Just keep in mind that

the objective is to have a net which will be used to create blocks.

This is a triangulation and the objective is to make triangles

between all the markers. There are quite some methods available

to do this (Delaunay) but more importantly notice that the denser

the marker the smaller the triangles will be.

There’s a bit of a problem thought. A triangle is not a good

shape to retrieve blocks from a reference image in a regular grid

(where all nodes have the same size, quite common in

geostatistics). Instead we could use something a bit more stable

like quadrangulation.

A

Page 29: SICentroidSimulation_extensive_documentation

Meshing operations

This is a quadrangulation. Instead of making triangles it makes 4

angled shapes which are not necessarily squares (although if

your had some really well chosen markers you could get perfect

squares).

To get perfectly adequate rectangular shapes (dealing only with

90 degrees angles) you must use some method like the one

proposed previously (VSQ).

B

Page 30: SICentroidSimulation_extensive_documentation

Chapter III – Interpreting reality with

blocks

• The thing about reality…

• The assumption…

• Building blocks

• Analyzing the blocks

• Updating our blocks

• Error mapping blocks

p.31

p.32

p.33

p.34

p.35

p.36

Page 31: SICentroidSimulation_extensive_documentation

The thing about reality…

Reality as in what literally exists is not a working concept

since if you knew that, this presentation wouldn’t be in

the first place. What we do work with is our belief (by

experience perhaps) of what is reality. Therefore an

interpretation. Thing of something as the image above.

A well trained eye could leap into something more

recognizable. The interpreter did expect that prior

image was a stratigraphic profile, even if a low

resolution one. It notices however that some

geologic phenomena is in place.

1

2

Grid

Low-res image

Legend

Page 32: SICentroidSimulation_extensive_documentation

The assumption…

That geologic phenomena may actually change the

current view of things since the folds seem too strong

for lithologies present in place. There must be faults…

And faults this strong may originate discontinuities.

Discontinuities lead to traps. Its quite the big leap but

by interpretation alone a strong, probable scenario

was created. Of course there’s quite an amount of

uncertainty here.

3

4

Interpretation

Fault

Legend

Page 33: SICentroidSimulation_extensive_documentation

Building blocks

So we do have a model. A reference image. But it is at

most an educated guess. Does it bode well with the

retrieved variogram model from hard-data? Can we

characterize our model by using this assumption?

Let’s provide a block scenario where we use our well

data as markers and leave the fault areas with higher

uncertainty.

5

6

Interpretation

Fault

Legend

Scenario

marker

Divisions

Variogram

directions

Page 34: SICentroidSimulation_extensive_documentation

Analyzing the blocks

Not the best mode ever generated but the main

purpose is there. We’ve given no marker tolerance since

we got smaller blocks on the center (between two

wells) than in the exterior areas where information lacks.

We can now do simulation with this block set but it

would be cautious to see if all the structures we know to

be the most likely scenario are represented. The truth is

we hardly could perceive something like a fault there.

We have, at most, the generalist behavior for our study

case represented in those blocks.

7

8

Block scenario

Fault

Legend

Scenario

marker

Divisions

Page 35: SICentroidSimulation_extensive_documentation

Updating our blocks

Using hard-data as markers hasn’t given us the probable

scenario we were expecting. For this reason a few

updates markers (that are not hard-data) were used.

The new update still hasn’t gave us the level of detail

that could be considerate most adequate. Still in the

middle fault the most important breaks are represented.

So let’s go on.

9

Block scenario

Fault

Legend

Scenario

marker

Divisions

Update

marker

10

Page 36: SICentroidSimulation_extensive_documentation

Error mapping blocks

So we’ve increased our detail near faults but still want

uncertainty when away from the hard-data. That’s

why we are mapping some error to the blocks.

Now we have a block scenario whose error is a

function of distance to the hard-data. We could now

proceed to characterization. 10

11

Block scenario

Fault

Legend

Scenario

marker

Error colored

centroid

Page 37: SICentroidSimulation_extensive_documentation

Chapter IV – Kriging with blocks

• Let’s review kriging

• Block kriging

• Using error

• Sequential block simulation

• Block kriging facts

p.38

p.39

p.40

p.41

p.42

Page 38: SICentroidSimulation_extensive_documentation

Let’s review kriging

We want to solve this algebraic system in order to retrieve the W’s

(weights). These weights are than multiplied with the values from the

samples 1,2 and 3 and summed together to retrieve the kriged value of

the node*.

Simulation grid

Hard-data

Node to be kriged

1

2

3

k

Simple kriging

example. With

ordinary kriging it

would have an extra

row and column.

Point

Point Node to be

kriged

1

2

3

1 2 3 k

11

22

33

12 13

23 21

31 32

1k

2k

3k

W

W

W

1

2

3

* I’m not being strictly literal. In fact since this is simple kriging the kriged value would be the result of this operation plus the

user input mean. If this would be ordinary kriging (see comment above system) there would be no need for this.

W 1 1 2

W 2 3

W 3 + + k

Page 39: SICentroidSimulation_extensive_documentation

Block kriging

So the procedure would be the same. Solve the system (see previous slide

for detailing simple or ordinary kriging) and use the weights to multiply by

the hard-data and block values retrieving the kriged value.

Simulation grid

Hard-data Block centroid

Node to be kriged

Po

int

Blo

ck

Point Block Node to be

simulated

W

W

W

1

2

3

W

W

W

4

5

6

1

2

3

1 2 3

11

22

33

12 13

23 21

31 32

4

5

6

4 5 6

41

52

63

42 43

53 51

61 62

14

25

36

15 16

26 24

34 35

44

55

66

45 46

56 54

64 65

1k

2k

3k

4k

5k

6k

W 1 1 2

W 2 3

W 3 + + k W

4 4 W

5 5 W

6 6 + + +

1

2

3

k 4

5

6

Page 40: SICentroidSimulation_extensive_documentation

Using error

So the specific error for each block is subtracted

to the correlogram values of blocks. In theory the

system is ready to be solved however since this

operation cannot guarantee that the maximum

values are on the system diagonal all values are

normalized so that the diagonal is strictly

composed of correlogram of value 1*.

* Please consider that this illustration is not taking into account the type of kriging the user might want to use.

We’ve been using ordinary kriging which would add a new line to the system shown in the schematic.

Po

int

Blo

ck

Point Block Node to be

simulated

Error

W

W

W

1

2

3

W

W

W

4

5

6

Point to

point

Point to

block

block to

point

Po

int to

no

de

Block to

node

1 -

1 -

1 -

block to

block

W

W

W

1

2

3

W

W

W

4

5

6

Page 41: SICentroidSimulation_extensive_documentation

Sequential block simulation

Block simulation works pretty much like the common sequential

simulation procedure. That is: already simulated nodes count as point

for kriging system. In our implementations we give no distinction

between hard-data and node-data. So search is done in two phases,

first for points and nodes, second to blocks. So there is always points

and blocks in the kriging system.

Simulation grid

Hard-data

Block centroid

Simulated node

Node to be

simulated now

1

2

3

k 4

5

6

Point Block Node to be

simulated

W

W

W

1

2

3

W

W

W

4

5

6

1

2

3

1 2 3

11

22

33

12 13

23 21

31 32

4

5

6

4 5 6

41

52

63

42 43

53 51

61 62

14

25

36

15 16

26 24

34 35

44

55

66

45 46

56 54

64 65

1k

2k

3k

4k

5k

6k

Po

int

Blo

ck

Page 42: SICentroidSimulation_extensive_documentation

Block kriging facts

A Blocks enter like points in the kriging matrix and are used, like points, to calculate the kriging mean.

B Error is a block property and so is only used in blocks (as far as block kriging goes).

C The simulation procedures are done pretty much as they used to. Simply we have a new kind of

secondary information.

Page 43: SICentroidSimulation_extensive_documentation

Chapter V – Uncertainty

characterization with blocks

• What is uncertainty?

• Kinds of uncertainty

• Using blocks for uncertainty

p.44-46

p.47

p.48

Page 44: SICentroidSimulation_extensive_documentation

What is uncertainty?

Uncertainty is a measure of some kind of variable we are not to sure about. Which

means that, depending on the quantity of uncertainty, the same procedure may have

more or less possible outcomes.

Distance done

Fu

el s

pe

nt

We are doing some distance with some vehicle. We would

like a model of how much the trip will cost. The thing is,

depending on numerous parameters, the fuel

consumption may be more or less (represented by ).

Measuring uncertainty we got this . From here we

could even improve our model to give probabilities based

on the other missing parameters.

The problem is that some case studies have so many

variables of fundamental importance that an analytical

solution to uncertainty is impractical. This is the reason that

gave origin to sequential simulation in geostatistics.

A single node depends on all its neighbors (and perhaps

other factors). And the node to be calculated after this one

depends on the value of the first. When our study case has

thousands to several million nodes (quite common) what

are you going to do?

Page 45: SICentroidSimulation_extensive_documentation

What is uncertainty?

Simulation 1

Simulation 2

Simulation 3

Hard-data ( ), variogram ( ),

and the kriging mean image ( ). We’ve made several simulations with all the statistical and spatial information we

could find an than we’ve calculated the mean of simulations (the more

simulations, the closest to the kriging mean), and variance, among others

(minimum, maximum, percentile, etc.).

Page 46: SICentroidSimulation_extensive_documentation

What is uncertainty?

Simulation 1 Simulation 2

Simulation 3

With our parameterization we can see the areas where our

uncertainty (by means of variance) is higher.

Low

variance

High

variance

Page 47: SICentroidSimulation_extensive_documentation

Kinds of uncertainty

Although the slides above gave some kind of conceptual

idea of what uncertainty is it can still be focused on some

aspects that may be more relevant to your case study.

For instance while studying permeability you may find that

the range equivalent to lower permeability are not relevant

to your study, thus your intended uncertainty being the

higher variance in high permeability areas.

Some studies are focused only on the higher or lower

probability margins (P10, P90, sometimes called) since these

are, commonly, the frontier areas of the bodies (when thing

change rapidly).

Univariate

distribution

Bodies frontier

Anisotropy

characterization Examples of possible

uncertainty fields in spatial

sciences.

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Using blocks for uncertainty

Since blocks are a secondary information support with high

flexibility It is possible to insert heuristic knowledge

(experience) in the model.

In fact by using block characterization, block appearance

(some areas may not have blocks), and block error it’s possible

to provide a localized feature in uncertainty.

Primary data and

parameterization

Block scenario

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Chapter V – Case Studies

• Uncertainty over a deterministic model

• The noisy channel

• Software development

p.50-54

p.55-59

p.60-63

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Uncertainty over a deterministic model

We’ve got both sampling

data (borehole among

others) and lithological

deterministic model of a mine

in Portugal. The thing is the

model does not have any

kind of uncertainty study.

Authors: Júlia Carvalho, Pedro Correia, Amílcar Soares

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Uncertainty over a deterministic model

We’ve used our Void Selection

Quadtree procedure to build the

block net using as markers strictly the

hard-data (since we are trying to

perceive the level of uncertainty

when you get farther from the real

data).

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Uncertainty over a deterministic model

We’ve simulated and got

the most likely image.

Actually it’s pretty close to

the original.

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Uncertainty over a deterministic model

The main model is there

but where are the high

uncertainty areas? We’ve

searched areas where the

value, by comparison with

the reference image, was

mostly disagreeing (80 %

wrongs).

The white dots are the most problematical areas. Notice that they are located in small

bodies, frontier areas, changing anisotropy areas, etc.

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Uncertainty over a deterministic model

Many tests where made as well other information retrieved such as

contingency tables. This was the first case where sequential

indicator block simulation was used. The results were promising.

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The noisy channel

This an attempt to retrieve and characterize a channel from a noisy image of acoustic

impedance. The hard-data was scarse and most of the project was conducted using the

acoustic impedance model.

ACOUSTIC IMPEDANCE CLUSTER ANALYSIS LOCAL MORAN’S I

Attributes were used to

add some contrast to the

model. The channel is the

set of clusters that go from

low left to top right.

Authors: Ângela Pereira, Ana Inês, Pedro Correia, Amílcar Soares

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The noisy channel

A result from an attribute was

chosen and a main shape of the

channel interpreted (mouse picking

shape) thus transforming a

continuous variable to indicator one

(in the first tests was the no-channel

class, and the channel class).

INTERPRETED SHAPE INDICATOR REFERENCE

IMAGE

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The noisy channel

A block set was built with markers

(not hard-data) which stand in the

areas where the interpreter was

most certain of the existence of the

channel.

BUILT BLOCK NET NEW BLOCK SET

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The noisy channel

The simulations were

made a most likely image

retrieved, a probability

map calculated, and finally

a P10, P90 uncertainty

analysis.

• REFERENCE IMAGE

• BLOCK SET AND HARD-DATA

• MOST LIKELY IMAGE

• PROBABILITY MAP

P10, P90 EVALUATION

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The noisy channel

This project lead to the further development of sequential indicator simulation and other

support tools. In fact a software was developed for this purpose. The project is not over and

tests are still being made in both synthetic and real data.

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Software development

A software was designed and developed for the block characterization

project. It as most of the procedures explained in this presentation (and

others) and it was made to provide a platform for sequential indicator

block simulation.

Object manager (where you

chose most of the stuff).

Object viewer (updated

automatically by object

selection on object

manager).

First buttons on the toolbar. You use them to

import your data (there are four types of data

recognized by ShapeWORKS).

Context menus in the object

manager (called by right click button

on the object). You use them to call

for all sort of operations menus

(some specific to each object type).

1

2

3

4 version 1

version 1

Developer: CERENA

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Software development

Phasic interpretation allows a manual creation of an indicator image by

mouse clicking on screen. 1

By clicking the “Interpret” button on the new frame you’ll get a smaller one (which can be maximized)

where you click the vertices of the shape you want to make. To close a shape just click the first vertices (it will

appear as a red dot instead of white). You can do more than one shape on the same phase (selected in the “Phasic interpretation” frame). To finish mouse click interpretation just press the “X” . When you finish

interpretation of all your phases just press the “Mark as object” button. Notice the preview panel will always show the interpretation of all phases with different

colors.

2

Example of phasic interpretation. 3

Interpretation tool

example

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Software development

A web is a new kind of object (used to create blocks). This procedure is

used to create a web from the point markers.

1

From this frame the for the blocks is created. If you chose as “Web style” constant than the point markers won’t be

used. But both VSQ (void quadtree selection) use the markers as can be shown on this preview. Notice the

smaller blocks are closer to the markers.

2

Web creation tool

example

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Software development

Some procedures where never included in the software although that was the

intention (the development phase was getting to long). This is the case for both

the mesh and point variogram. The buttons exist but they were never

implemented.

Also some other things were pointed out by the alpha users such as:

1) Visualizing blocks from its centroids is not easy.

2) “Use all VSQ” method not using all blocks available.

3) In the error mapping frame the first image is not being updated when the

object is changed.

4) While exporting some headers may not be correct.

NOTICE that this documentation was written in the 10th of September, 2013. It is

unlikely that this developer will add new functionalities to the software unless its

utterly necessary for the research project for which it was built to. The software is,

therefore, considered adequate to its purpose and its continuous development

halted.

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