Armstrong M., et al. Plurigaussian simulations in geosciences

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shows the spatial distribution of the oxidi zed and non oxidized facies from east

to west.

A3Dview of the simulatedshale (Fig. 8.22) illustrates the relative stationarity of

this facies in the ﬁeld as visible in the vertical proportion matrix while Fig. 8.23

shows a 3D view of the simulated oxidized facies.

Fig. 8.19 Vertical proportion matrix (VPM)

140 8 Case Studies and Practical Examples

Fig. 8.20 Experimental and ﬁtted vertical variograms for the oxidizing lithotypes

Fig. 8.21 Vertical cross-section on one of the simulations showing the seven lithotypes

Fig. 8.22 3D block model of the simulated shale facies

Mining Applications of the Plurigaussian Approach 141

Second Issue

As a result of t he deposition process, the high grade uranium is located at the

interface bet ween oxidiz ed fac ies and not oxidized ones. The idea i s to deﬁne

three domains: the non oxidized area (initial state), the oxidized area (swept by

oxidizing ﬂuids) and area where uranium grade is high. The procedure for

transforming the geological facies and thegradesintoindicatorsisthefollowing:

the high grade indicator is obtained using a threshold on the uranium grade and in

the rest, the initial state and the oxidized one, is distinguished depending on the

oxidation factor.

Globally the high grade ore is more or less constant along the vertical axis

(see VPC Fig. 8.24). In the 3D space it is mainly located in the North West

part along a West south- North east axis (see the 3D view of the high grade

proportion upper than 30% (Fig. 8.25). This is the result of the deposition

process.

The lithotype rule was also deﬁned based on the deposition process: the ﬁrst

underlying Gaussian is affect ed to the distinction between oxidized and non

oxidized facies while the second one depends on the grade information. This choice

is conﬁrmed by the behaviour of the experimental variograms. In fact, on the

normalized variograms (same variances for the three types equal to 1) the shapes

of oxidized and non oxidized variograms are similar to each other but are differ-

ent from the one for the high grade ore. The ﬁt of the high grade variogram

gives directly the model for the second Gaussian. The ﬁts of the other types is

a combination of this model and the model for the ﬁrst Gaussian. (Fig. 8.26) The

conditional simulations were then performed with all the previous parameters.

A typical simulation is shown in Fig. 8.27.

Fig. 8.23 3D block model of simulated oxidized facies

142 8 Case Studies and Practical Examples

Fig. 8.25 Proportion of high grades above 30%

0.0 0.5 1.0

–50

–40

–30

–50

–40

–30

Fig. 8.24 Global vertical proportion curves for the three types

Mining Applications of the Plurigaussian Approach 143

Simulation of a Porphyry Copper Deposit: Non-sedimentary

Environment

Thiscase-studyhasbeen includedtoshowthatplurigaussiansimulationscan alsobe

used in non sedimentary geological environments. In these cases, there is no longer

any reason to use vertical proportions, as the geology is not guided by the vertical

sedimentation.

The MM copper deposit is a porphyry copper deposit near the Chuquicamata

mine. In this type of deposit, the mineralization is constrained by rising ﬂuids

through a network of faults and joints and by the interactions of these ﬂuids with the

Fig. 8.27 A simulation with only oxidised and high grade facies shown

Lithotypes

Init type

High grade

Oxydation

__ _

-----

......

Fig. 8.26 Experimental variograms (dotted lines) and ﬁtted models (solid lines)

144 8 Case Studies and Practical Examples

pre-existing minerals. In this orebody, this network is controlled by a major sub

vertical North-South fault, called the MM fault. As the auxiliary faults and joints

principally follow this fault, the copper mineralization, which controls the working

rock types used for this study has a general North South vertical orientation. Four

rock types have been deﬁned, corresponding to different stages of copper enrich-

ment: breccias (higher grade ore), C5 stockwork (also high grade ore), the low

grade ore C1, and the waste rock. Breccias and C5 are generally in direct contact

with the faults of joints network. The copper concentration of the ﬂuids decreased

as they went further from this network. Their interaction with the pre-existing rocks

created the low grade rock type C1.

Further out, there was not enough copper left in the ﬂuids to lead to mineraliza-

tion and the resulting rock type is waste. Figure 8.28 shows the distribution of the

rock types in an east-west vertical section.

Astherocktype dependsmostlyonthe distancefromthefault, it seemsnatural to

use the fault plane which is oriented in a North-South vertical direction, as the

reference level. The ﬂattening consists in shifting the East-West coordinates to

transform the fault into a perfect North-South vertical plane. Consequently, the

BRECHAS

C5 -STOCKWORK 0.5 % CuT

C1 -ENVOLVENTE 0.1 % CuT

PISO As 2002

L E Y E N D A

CODELCO CHILE - DIVISION NORTE

PROYECTO MM

SECCION 25600

FALLA OESTE

TECHO ROCA

PIT PROYECTADO

PISO As

MODELO 2000

Techo de

Sulfuros

Techo de

Mixtos

Zona de mixtos

Zona de Oxidos

Fig. 8.28 Schematic distribution of the rocktypes. in a vertical east-west vertical section. Repro-

duced from Riquelme et al. (2008) with permission

Mining Applications of the Plurigaussian Approach 145

proportions will be plotted along an East-West direction, perpendicular to the MM

fault in the working grid (Fig. 8.29).

The rock type distribution varies perpendicular to the fault. As was mentioned,

the copper rich rock types, breccias and C5 stockwork are closer to the fault, while

the C1 and waste are more distant, but the rock types also vary in the other

directions. For example, the breccias are wider towards the top. So we decided to

use proportions which vary in all directions, hence to use a proportion matrix.

This matrix has been built from 16 local East-West proportion curves, by kriging

with a linear variogram.

With only four rock types, the rock-type rule is quite simple (Fig.8.30). The ﬁrst

gaussian separates C1 from the breccias þ C5 group on one side, waste on the other

side, while the second separates Breccia and C5.

Once the rock-type rule has been chosen, the variograms can be ﬁtted and the

orebody can be simulated. Th e goal of this simulation was to propose a block model

Fig. 8.29 Horizontal

projection view of the MM

fault, the breccias (blue) and

the drillholes (pink).

Reproduced from Riquelme

et al. (2008) with permission

Breccia

Waste

Fig. 8.30 Rock-type rule. The ﬁrst gaussian separates C1 (green) from the richer rock types

(breccias+theC5group)ononeside,andfromthewaste (grey) on the other side, while the second

separates breccia (blue) and C5 (red). Reproduced from Riquelme et al. (2008) with permission

146 8 Case Studies and Practical Examples

without manual smoothing done by the geologis t. the new model compared favour-

ably with the block model previously designed by the mine geologist.

Figure 8.31 compares the block model provided by the geologists (top) with two

simulations. The waste rock has not been represented in the geologists model

whereas it is grey in the simulations. An extended version of this case study can

be found in Riquelme et al. (2008).

26250

8900

8800

8700

9000

9100

9200

9300

8900

8800

8700

9000

9100

9200

9300

24500 24750 25000 25250 25500 25750 26000 26250

24500 24750 25000 25250 25500 25750 26000

Fig. 8.31 Comparison between two simulations (center and below) and the block model given by

the geologist (above). The waste rock (grey on the simulations) has not been represented on the

geologist’s block model. Reproduced from Riquelme et al. (2008) with permission

Mining Applications of the Plurigaussian Approach 147

Chapter 9

Freeware

Introduction

In order to demonstrate the power and the ﬂexibility of the truncated plurigaussian

method, three free programs can be downloaded from the following Web site:

http://pluridemo.geosc iences.mines-paristech.fr

PluriDemoSimu makes itpossible to visualise simple plurigaussian simulations

and to see how changes in the input parameters affect the resulting images.

PluriDemoVario illustrates the relationship between the indicator variogr am

and those of the underlying gaussian random functions (RFs for short) that are

truncated to give the indicators.

PluriDemoSet allows the user to build a random set (two facies only) using the

PluriGaussian Truncated method in a non-stationary framework.

For each program the web site also provides a set of graded exercises showing

how to run the program and how the key parameters affect the simulat ed images or

the indicator variogr ams, as the case may be.

Installation

The package is available for the following platforms:

Windows (XP, Vista, Windows 7) 32/64 bits

Linux x86 32/64 bits. Tests have been madeunder Ubuntu 9, Fedora 8, Redhat 4,

Redhat 5.

Installation Instructions for Windows Users

1. Download the archive ﬁle named pluridemo_winnt.zip and save it into a tempo-

rary directory.

M. Armstrong et al., Plurigaussian Simulations in Geosciences,

DOI 10.1007/978-3-642-19607-2_9,

Springer-Verlag Berlin Heidelberg 2011

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