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The Application of Multiple-Point Geostatistics inthe Modeling of Dike; a case study of Sungun

Porphyry Copper, Iran

Hassan REZAEE1, Omid ASGHARI2, Mohammad KONESHLOO3 1 University of Tehran, Iran,

[email protected] 2 University of Tehran, Iran,

[email protected] 3 Shahrood University of Technology, Iran,

[email protected]

Peer-reviewed IAMG 2011 publication

doi:10.5242/iamg.2011.0302

Abstract

The aim of this study is to assess the application of the new-born technique of Multiple-Pointgeostatistical method to simulate complicated structures in a mining context. The post-mineralization intrusions in porphyry systems may cause such structures hence the dike systemof an Iranian Porphyry Copper deposit has been tried for this study. The TI was extracted fromthe upper benches of the mine’s block model and using the local dike proportion and other con-trolling parameters in SNESIM an E-type grid was produced that reproduced the dike-like struc-tures on the whole mining domain.

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Hassan REZAEE, Omid ASGHARI, Mohammad KONESHLOO, Julián M. ORTIZ

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1 Introduction

Geostatistical techniques have opened a new era in the field of earth phenomenon characteriza-tion. It had a profound role in oil and gas reservoir and mineral deposit simulation and modeling.Variogram has been known as a strong tool to identify spatial variations of phenomenon understudy. It takes into account two points at a while only and in the case of non-linear continuity itsuffers from a main inefficiency. Due to this reason it cannot distinguish vastly different patternsof heterogeneity (Journel, 2005). Consequently the variogram is also an incomplete measure ofuncertainty in complex and non-linear structure; in a reservoir modelling context, curvilineargeometries, such as sinuous channels in a fluvial reservoir or incised valleys over topography,cannot be modeled using only traditional two point statistics such as a variogram (Strebelle,2002).

In every mineral modeling research the post mineralization processes put several problems onexpert’s way of modeling. As the physical and chemical properties of ore, extracted from differ-ent zones differ from one another, so their behavior will be different in processing mill. Having

the 3D model of present facies in a mineral deposit has a beneficial role in production planning.Since, dikes are of one of the most prevalent phenomena in mining projects and their structure iscomplicated enough to not be modeled by traditional variogram-based methods in this study ithas been tried to acquire a taste for the application of MP statistics in dike modeling.

2 Multiple-Point Geostatistics

To go beyond the variogram, a more powerful tool is needed by which not only the variogramscapabilities are considered but also it fails are met. Training Image has been introduced as a re-

placement for variogram. Journel (2005) defined the training image as a conceptional model ofthe random process. It is also a quantitative model. The training image can be produced using

different methods but it completely depends on the data source we have available in modelling phases. Tuanfeng, (2008) refers to the various ways through which TI can be come along e.g.,Object-based algorithms, Process-based models (Boisvert et al, 2008), Sequence stratigraphy etc.Multiple-Point (MP) geostatistics has emerged (Guardiano and Srivastava, 1992, Journel, 2001,Strebelle, 2002) as a new powerful field for obtaining realistic geostatistical models that one ofits great capabilities is to integrate consistently a large variety of different sources of informa-tion, each of which has been taken on different scales. The process of an MPS simulation cansimply be defined as follows:

At the first step and to go beyond the traditional variogram, the variogram should be replacedwith a more powerful tool; which in multiple point geostatistics has been known as Training Im-age (TI) (Journel, 2001). In MPS we use TI as a tool to identify the dominant variation patterns.Albeit there has not been a long time from the advent of MPS; there are several ways of TI pro-duction. The production of TI is the most important stage of the simulation process that all theoutputs are dependent on it. By simulating TI, MPS simulation process can be begun which isconsisted of three main stages (Caers, 2001):

Pattern extraction

Pattern identification

Pattern reproduction

At first, one should extract the existing pattern in phenomenon under study from simulation

space, containing the nodes on which the target value is unknown,. Figure 1 gives an example ofsuch MP pattern simulation in very simple words. Finding such pattern in the simulation grid, the

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The Application of Multiple-Point Geostatistics in Dike Modeling

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available TI will be searched for the same pattern, this will be followed by computing the probability of each facies and then it will be the turn for the next node in the random process. De‐pending on the variable whether categorical (such as facies), or continuous variable (forexample, grade, or any other Geophysical property of the deposit) relevant algorithm

should be used to simulate the phenomena. There is one renowned algorithm known asSNESIM which is provided in SGeMS software, for categorical variables simulation.

Figure 1: Illustration of sequential multiple-point simulation (After Tuanfeng, 2008)

Since Strebelle (2000) introduced snesim in his PhD thesis, within a short period of time, manyother MP simulation algorithms have been developed from, some already in a state of beta test-ing such as Arpat and Caers, 2001 and Zhang et al, 2004. After that several researches have beendone to make a use of MP in the geosciences. (Dovera, 2006, Feyen, 2005, Levy, 2008).

One of the outstanding factors of MP is the ability to integrate data from different sources andtaken on different scales. Hard data like drill hole data and soft one such geophysical data (in this

study it is local proportion data) can easily be considered in simulation process. In this study we plan to use the local proportion data as an auxiliary variable to constrain the realization the pro-cedure of doing so will be described:

2.1 Soft data integration

Soft (secondary) data may be available to constrain the simulated realizations. They are

mainly are acquired by remote sensing techniques such as seismic data but different sort of

soft data can be used. They may be acquired on the realization grid on a very corse resolu‐tion but their effect can be easily tasted (Remy, 2009). The first step is to derive soft data

conditional probability from the soft data . Then at each unknown node a sequen‐

tial simulation will be done then the will be combined with the sofat data probabil‐

ity to get the posterior probability . Finally, a facies indicator value is

drawn using this final probability , which is conditioned to both hard and soft

data. Journel (2002) proposed a ‘‘permanence of ratios’’ algorithm to combaine such prob‐

abilities.

The basic assumption of this algorithm is that the relative contribution of data event is

the same before and after knowing :

Eq. 1

where, the distances to the event occuring are defined as

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Also, Journel proposed the introduce a power τ into Eq. 1 to have the ability to control the

relative role of secondary data:

Setting increases the impact of soft data, coversly, Setting does the vice versa.

3 Study area

The Sungun porphyry copper deposit is located in northwestern Iran (Azarbaijan province) and isassociated with diorite-granodiorite to quartz monzonite of Miocene age which intruded Eocenevolcano-sedimentary and Cretaceous carbonate rocks. Field observations and petrographic stu-dies demonstrate that emplacement of the Sungun stock took place in several intrusive pulses,

each with associated hydrothermal activity (Hezarkhani, 1998). (See Figure 2)

Figure 2. Below: Geological map of Iran showing Sahand-Bazman belt (modified from: Stocklin,

1976; Shahabpour, 2007); Above: Geological map of Sungun deposit area showing various types of

intrusive rocks of dominantly Miosene age and the outline of Cu-Mo porphyry type mineralization.(Modified from Mehrparton, 1993 and Hezarkhani, 2006).

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3. 1 Dike system

The Hypogene zone often contains considerable thickness of un-mineralized porphyry. The dikes(DK1a orange one in Figure 2, DK1b the green dike in Figure 3) strike NNW-SSE, dip steeply tothe west and have thickness from a few centimeters to several tens of meters (Figure 3). They

appear to have acted as a barrier to hydrothermal and Supergenes processes and consequentlysometimes mark the boundary between Leached and Supergene material. They also frequentlyact as a focus for high-grade copper-molybdenum mineralization in the adjacent monzonite por-

phyry host rock (Hezarkhani, 1998). DK1 is the most prevalent type of dike that exists in thestudy area which mainly is composed of Quartz Diorite to Quartz Monzonite. Based on isotopestudies or other evidences like chronological, alteration and mineralogical one, three main typesof dike can be derived from DK1 known as DK1-a, Dk1-b and Dk1-c, each of which has its ownfeatures. Some of distinguishing features are as follow:

a. DK1-a

This the most prevalent type of dike DK1 and also all dikes in the area. Samples belonged to

DK1-a have been exposed to weak and medium to high degree of phyllic alteration. Based onmacroscopic factors three subgroups of DK1-a can be derived from: a. Mineralized dikes thathave some formed pyrites, b. Non-mineralized dikes and c. Mineralized dikes containing Subhe-dral and Euhedral Orthoclase.

b. DK1-b&c

On the other hand, samples from DK1-b have been intruded in before DK1-a and has very weak phyllic and propylitic alterations. They don’t bear any mineralization and the amount of pyrite isvery low. Besides, DK1-c samples are in very weak propylitic alteration and sometimes theyentombed in the DK1-b dikes.

Therefore in an industrial point of view these dikes can cause severe problems as their physicaland chemical features are strongly different rather than host rock. There should be an exhaustivemodel including these variations.

Figure 3: Dike series, and the selected area for this study

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4 Result and Discussion

The most important factor of every MP research is to produce the TI that represents for thewhole area under study. One of the methods through which TI can be produced is to use the geo-logical data that have been gathered during the past exploartion or current mining activities

phases. In this study the sam way was adopted to get TI. The TI was extracted from the blockmodel (Figure 4) from operating mine as the first 200 meters of the mentioned block model wasconsidered to do so. What is shown in Figure 4 is the block model from which the later TI wasextracted. This is the area in which the model has the most validity that can garantee the resultsof being used in mine.

Figure 4: Block model used to extract TI (colors indicates to elevation to well illustrate the block

model used in this study)

Primarily, as there huge number of nodes can be found in this model that are irrelevant to what

we are looking for therefore we cookie-cut it to a smaller volume but more useful in the compu-tational efficiency point of view. For example, the area that contained one very thick dike wasremoved from the TI as it does not need any simulation and based on simple geological rules itcan be extended to the deeper elevations. The existence of such thick dike in the domain understudy can cause several problems as it disturbs the stationarity conditions as because the averagethickness of dike depends on location. (See Figure 5)

Figure 5: The smaller TI that is considered for simulation, some surplus surrounding and the sou-

thern thick dike are removed from the final TI

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Since, the dense geological surveying has been done on this first 200 meters area of mine, moreconfidence can be established upon this layer. As it was mentioned before there are several kindsof dike, each of which has their own features, but in this study which can be cosidered as the firststudy on such phenomenon, only a state of being dike or not case is considered. Therefore, re-gional variable has been considered as an indicator state between dike and non-dike cases:

Following the way, the final TI that was considered for simulation purposes is shown in

Figure 6‐right.

Figure 6: Left: TI including codes for each of the dikes; Right: The final TI that was inputted to

SNESIM algorithm

Although, the surplus parts of the TI was removed to make it as representative as possible butthere may arise another problem too that is: the dike occurence probability differs from part to

part and is the factor through which the next simulation process can be affected with. As it isshown in Figure 7 there two distinct parts with different dike proportions can be found so oneshould account for a secondary variable that represents the local dike proportion. This variationcan be extended to depth so it demands another variable to account it.

Figure 7: Different dike proportions in the study area

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Several methods can come up with to calculate such local proportions like Nearest Neighbor(NN) and proceed the way by using a Moving Average on the NN results. But for this study ashuge number of nodes are going to be simulated, this method suffers from the lack of computa-tional efficiency. Since full Indicator Kriging (IK) bears this onus too it was considered to do so,as after a variography stage IK method was applied on the whole area (covering the whole oper-ating mine) and as the IK results are to some how un-stable the process was followed by apply-ing a Moving Average on the IK estimates (Probabilities) to make it smoother and coarser to beused. Figure 8 refers to the output of applying Moving Average on IK results.

Figure 8: Moving Average on the IK estimates

As can be seen, the higher value (Red color) for dike existence coincides with the local propor-tion that we expected. The same grid was produced for the Sungun Porphyry (Non-Dike do-main). On the next stage, the SNESIM of SGeMS open source software was applied on the gridusing the following input parameters:

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Figure 9: The input parameters for SNESIM algorithm in SGeMS

The conditioning data used for this study were drill hole data including the code for each sample point that represented each of the dike or non-dike states. There were summing to 41520 data points that cover the whole area under study. Servosystem correction factor is important if TI proportions are different from the conditioning data proportions. It should be used moderately toimpose the desired proportions, but allowing some fluctuations. The Servosystem correction of0.7 is due to the big difference between TI and Drill hole proportions as the 0.17 and 0.30 are thevalues for dike proportion for TI and conditioning data respectively.

Eventually, the simulation algorithm was applied on the grid that was produced before (Contain-ing 930,000 nodes). One of the realizations is illustrated in Figure 10 and as can be seen dike-like structures have been produced in the area that shows the ability of this method to model thiskind of phenomena. The conspicious effect of local proportion is appeared in Figure 9 where the

parts with lower probability of dike occurence is simulated in this figure.

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Figure 10: One of the SNESIM realizations, red nodes refers to the Dike occurrence

Moreover, the effect of conditioning data can be better understand when one comes with an E-type grid. To get a representative simulation, 100 realizations were produced and the next step of

project was to calculate the E-type 3D grid. Finally, the E-type map was produced using themean value of 100 values for each node and is illustrated in Figure 10. Again the capability ofSNESIM is appeared in the form of dike-like structures in the simulated area. As can be seen inFigure 10 there are some parts that the dike structure has not been simulated that are mainly onthe corners and the bottom. The lack of conditioning data may cause such problems.

Figure 11: E-type map of the 100 realizations of the study area

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5 Conclusion and future works

In geosciences studies there are many circumstances in which the modeling of phenomena raisesseveral conflicting issues. Among different geostatistical techniques Multiple-Point method hasshown its great capability to solve such problems. In this study one of them was investigated and

the final E-type grid point was an evidence of this ability. The art of Multiple-Point geostatisticsappears when one comes with a comparison between the other tools that are being used in indus-trial projects such as the geological priory geological data. Since MPS has the ability to simulatethe dike model for the deeper areas of mine under exploitation. It extremely decreases the errorof dike modeling in deeper parts of mine as it was done in this study.

Using the geological data containing useful information on dike structures the TI was producedthat is much simpler than carrying out variography step to come with an estimate for each blockin the study area. The simplest state of Multiple-Point technique was used here and it is sug-gested to apply SNESIM with more input data. For example, coding the TI by different kinds ofdike in the same area can bring useful information up on dike models as the chronology of these

dikes differs. A segmentation procedure can be adopted too as it was seen that dike proportionvaries with coordinate. Furthermore, the affinity and rotation factors can play an important rolein making the realizations as fit as possible to reality.

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