Geological Model Simulation

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Faulted Geological Model Simulation of the Resolution PorphyryCopper Deposit

G Verly 1, K Brisebois 2, W Hart 3 and J Hammitt 4

ABSTRACTA significant portion of the risk in a mining operation is tied to thegeologic model that is being used to constrain the resource and reserveestimates. Yet little has been published on geological model simulation inthe mining industry, perhaps because the original geologic setting has oftenbeen disturbed by metasomatism and tectonism, making it often difficult tointerpret and simulate. One general method to realistically simulate thegeology consists of first establishing a priority ranking of the geologicalfeatures and then simulating them one at a time. This can be done bystarting with the interpreted outlines or shapes and incorporating theuncertainties as specified by the geologist during the simulation process.Two steps that could be part of this methodology are considered in thispaper: simulation of fault surfaces, and simulation of layered rock typeswithin the simulated faulted blocks. The algorithm consists of a series of sequential Gaussian simulations that are merged together after variousrescaling to account for non-stationary uncertainties. A detailed descriptionof the procedure is given. Examples of results obtained on a porphyry-stylecopper deposit are provided.

INTRODUCTION

A significant portion of the risk in a mining operation or study istied to the geological model that is being used to provide domainsfor mineral resource and reserve estimation and/or conditionalsimulation. Simulating the geology is a common procedure in thepetroleum industry but is rather the exception in the miningindustry. Perhaps one reason is that the original geological settingof a mineral deposit has often been disturbed by metasomatismand tectonism, making realistic simulations of the geologydifficult to produce. Some of the methods that can be used tosimulate different aspects of the geology are boolean modelling(de Fouquet et al , 1989), indicator simulation (Alabert, 1987),plurigaussian simulation (Armstrong et al , 2003), probability fieldwith local means (Srivastava, 2005) and potential field (Chiles et al , 2007).

The case considered in this paper is the Resolutionporphyry-style Cu-Mo deposit, located in Arizona, USA. Thedeposit is deep and sparsely drilled. The geological interpretationis complex and contains faults, metamorphosed rocks of sedimentary origin, intrusions, breccias and alteration assembl-ages. One general method to realistically simulate such complexgeology consists of establishing a priority ranking for each of thegeological features and simulating them one at a time, startingwith the interpreted outlines or shapes and incorporating the

uncertainties as specified by the geologist (Verly, Bridebois andHart, 2008). Details on how to simulate a fault block modeltogether with faulted rock types are presented in this paper alongwith some results.

GEOLOGY

Deposit geologyThe Resolution Cu-Mo deposit is late-Cretaceous to early-Tertiary in age and is hosted within a buried, fault-boundedsequence of Paleozoic and Precambrian sedimentary strata,Precambrian diabase sills and Cretaceous-aged layeredvolcaniclastic and siliciclastic rocks. Host strata are faulted andhave been intruded by porphyry bodies of late Cretaceous age.Mineralised breccia bodies have also been identified, with somebeing spatially related to faults and porphyry intrusions (Hammittand Ballantyne, 2007). The mineralised rocks are buriedunconformably beneath a 1000 m to 1500 m thick sequence of

barren sediments and volcanic rocks of Tertiary age. Figure 1shows a plan view and two vertical sections of a portion of the2007 geological interpretation.

Fault interpretation and uncertainty assessment

Figure 2 illustrates a common method used by geologists for theidentification of simple block bounding faults where folding isassumed to be minimal, using a distinctive lithologic markerintersected in multiple drill holes (eg a formation contact).

Stage 1

Distinctive lithologic marker intercepts in each drill hole arevisually identified in section view (red symbols) and groupedbased on their apparent relative degree of colinearity (orcoplanarity).

Stage 2

A 2D marker horizon is interpreted and constructed, defined by asmooth line (red dashes) connecting all controlling data points forthe marker within each geometric grouping. Zones of abrupt andsignificant changes in position (eg elevation) between differentsegments are suspected locations for fault displacement. Faultplanes are then interpreted and constructed within these suspectzones based on numerous geological principles including: observed apparent sense of displacement of the marker

horizon; actual fault intercepts in one or more drill holes (true snap

points); typical fault geometries observed nearby on surface or in

underground workings; and fault geometries predicted by well-established structural and

tectonic field studies within a similar geologic terrane, orpredicted by laboratory experiments on rock.

Stage 3

The spatial uncertainties of faults are assessed purely by distancefrom controlling data points. Multiple fault snap points that arespatially aligned may greatly reduce the uncertainty of a givenfault interpretation. Simple surfaces are then constructed thatdefine the limits of all permissible fault positions (blue dashed

lines).

Advances in Orebody Modelling and Strategic Mine Planning I Spectrum Series Volume 179 299

1. AMEC, Suite 400, 111 Dunsmuir Street, Vancouver BC V6B 5W3,Canada. Email: [email protected]

2. AMEC, 780 Vista Boulevard, Sparks NV 89434, USA.Email: [email protected]

3. Resolution Copper Mining, LLC 102 Magma Heights, Superior AZ85273, USA. Email: [email protected]

4. MAusIMM, Geologist, Kennecott Exploration Company, Rio Tinto,224 North 2200 West, Salt Lake City UT 84116, USA.

Email: [email protected]

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G VERLY et al

N = 1 0 0 6

E=206

E=206

N=1006

High Cu Shell

FIG 1 - Plan view and vertical sections through the geological interpretation. The black dots on the plan view indicate the drill hole intercepts.

FIG 2 - Diagram illustrating the methodology for the interpretation of simple faults (Stage 2, solid blue lines) in section and plan view, usingonly lithologic markers intersected in irregularly-spaced or widely-spaced drill holes (Stages 1 and 2). Stage 3 illustrates the potential

degree of spatial uncertainty (orange polygons) inherent in the resulting fault model where all possible fault positions and orientations haveequal probability (dashed blue lines).


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Faulted layered rock type interpretation anduncertainty assessmentAs described in the previous section on fault interpretation, theboundaries for the Faulted Rock Types (layered rocks) areinterpreted and constructed on sections or in three dimensions byfirst identifying the controlling drill hole data points for eachmajor stratigraphic horizon, and then constructing smooth lines,polygons, or surfaces that pass through these controlling pointsand enclose lithologically distinct domains. As with the faults,every attempt is made to honor established geological principles of stratigraphy. The resultant interpreted domains for the FaultedRock Types are then modelled as triangulations. Based on existinginformation from both drilling and surface mapping, analysis of the geological interpretation is performed far from drill holeintercepts the limit of variation for the vertical position of domain boundaries was assessed to be 30 m. For thickness, thelimit of variation was assessed as 20 per cent of the interpretedthickness.

FAULT MODEL SIMULATION

Seven faults defining eleven fault blocks have to be simulated. Thegeneral procedure consists in simulating one fault at a time as

a 2D surface and flagging a 3D grid accordingly. The seven3D grids corresponding to the seven faults are then mergedtogether using the proper priorities. Each 2D surface simulation isconstrained within a variable and asymmetrical uncertainty band-width assessed by the geologist. The simulation methodology isfurther described below and is illustrated in Figures 3 and 4.

Presimulation work

The available information for one fault consists of the faultsurface, the uncertainty information and three snap points for onefault. The fault surface is modelled as a triangulation. Theuncertainty information is provided as a series of locations on thefault surface with two maximum possible envelopes, one on eachside of the fault. The spacing between the locations is about 500 m 500 m. In a first step, the fault triangulation surface is sampledon a dense grid using a draping technique. The approximate plane

of the fault is identified, and the normal offsets of the fault surface

to the plane are calculated. These kinds of manipulations arereadily available in several resource modelling packages. Note thatthe offset terminology is used for the distance from the interpretedfault surface to the fault plane. It is not the displacement of thefault as in normal geological parlance.

The fault plane is rotated to the horizontal. The coordinates of the fault information (surface offsets from the plane, uncertaintyand snap points) are similarly rotated. The reason for the rotation

is that most 2D simulation algorithms do not handle 2D planes of any orientation. Furthermore, the post-simulation grid manip-ulations are simplified in the rotated space. After rotation, thefault surface offsets are vertical distances from the horizontalplane. Because the angle of the fault surface with the fault planeat any location is always small, the maximum possible offsets atthe recorded uncertainty locations are assumed to be verticalafter rotation. The fault surface is clipped by the other faults.Different realisations will result in different clipping. To avoidgaps between the simulated fault blocks, the simulated 2D gridneeds to be extended sufficiently beyond the extent of the rotatedinterpreted fault surface. The rotated fault surface offsets and thevertical uncertainties are estimated on a dense 2D grid (Step 1d,Figure 3). For the offsets, the estimation method does not mattermuch as the draped information is very dense. Thisinformation, however, was available only on the clipped faultsurface and was estimated within the rotated outline of thesurface. The estimated values had to be extended to the limit of the 2D horizontal grid. For the uncertainty, the available pointsare much farther apart and ordinary kriging was used with aspherical model with no nugget and very long ranges. Inversedistance could have been used as well. No extensions werenecessary because the information was available for unclippedsurfaces. Figure 5 shows the estimated uncertainties on one sideof one fault.

Simulation

The rotated fault simulation is achieved in three steps:

1. conditional simulation of standard normal scores,2. rescaling the simulated normal scores to account for the

non-stationary and asymmetric uncertainty bandwidth, and

3. adding the offsets to the rescaled normal scores.

The conditional simulation is sequential Gaussian. A unit-sillGaussian variogram model with no nugget effect and a 1000 misotropic range has been used to ensure a very smooth surface. The1000 m range was chosen after some experimentation. At thisstage, 100 realisations of standardised fault surface deviations areavailable. Theoretically, the 100 simulated values at a givenlocation are standard normally distributed except within the zoneof influence of a snap point. The simulated values of onerealisation should also be standard normally distributed if thesurface extent is very large with respect to the variogram range.Figure 6 shows the validation statistics for one fault surface. Thetop left histogram (a) shows that the mean simulated value is veryclose to zero as expected, whereas the standard deviation of agiven realisation is on average 0.66, which is lower than 1. This isdue to three snapping points that significantly reduce the possiblefluctuations and also due to the extent of the simulation being notvery large with respect to the 1000 m variogram range. Thebottom left graph (c) indicates that the variogram is reproduced bythe simulation even though significant fluctuations are observedfrom one realisation to the next (d). Alfaro (2008) notes that wildvariogram fluctuations between realisations are to be expectedbecause the Gaussian variogram is not microergodic. Theprobability plots (b) of the realisations are not straight linesbecause the variances are less than one.

A local rescaling of the simulated normal scores is needed toaccount for the non-stationary uncertainty. If the uncertainty was


FAULTED GEOLOGICAL MODEL SIMULATION OF THE RESOLUTION PORPHYRY COPPER DEPOSIT

For each of the 7 faults

Step 1: Pre-simulation processing1a) Get original fault information:

- Fault surface (triangulation)Drape the fault surface (dense grid)

- Uncertainty information (series of points with 2 max. distances frominterpretation)

- Snap points1b) Get fault plane + offsets:

- Work out approximate fault plane- Work out fault surface offsets from fault plane (draped grid)

1c) Rotate the fault information:- Work out rotation to bring the fault plane to horizontal- Rotate the offset information- Rotate the uncertainty information- Rotate the snap points

1d) Grid the rotated fault information:- 2D horizontal grids- Grid the offsets and the uncertainties

Step 2: 2D simulation2a) 2D stationary simulation, conditional to snap points2b) Rescale the simulation to account for variable uncertainty2c)Add the offsets 100 rotated fault surfaces

Step 3: 3D simulation3a) Rotate the 3D grid to be simulated3b) Flag the rotated grid nodes

- Flag as above/below the simulated surfaces100 fault simulations coded as 0/1 3D grids

Merge the simulated 3D gridsMerge grids with proper priorities100 simulated fault grids, 7 faults/ 11 fault blocks per realisation

FIG 3 - Faulted model simulation process.


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symmetrical on each side of the fault, the rescaling factor at agiven location would be a third of the maximum distanceestimated for the uncertainty at that location meaning that thestandard deviation of the rescaled simulated normal scores is athird of the maximum distance. This ensures that approximately99.75 per cent of the simulated fluctuations are within thespecified maximum ( 3 standard deviations). Simulatedfluctuations outside that interval are reset to the maximumdistance. The uncertainty at a given location, however, isasymmetrical, and two rescaling factors are used, depending onthe sign of the simulated normal scores. The distribution of therescaled simulated normal scores consists of the halves of twonormal distributions with same zero mean but different standarddeviations. The two standard deviations are one third of themaximum possible distances at that location. Figure 7 shows anexample of such a distribution with 10 m and 15 m standarddeviations, corresponding to maximum fluctuations of -30 m and+45 m, respectively. Note that the mean of the resultingdistribution is not zero anymore.

One hundred realisations of fluctuations around the faultinterpretation are available at this stage. Figure 8 shows onesection with the trace of one rotated fault interpretation (red lineat deviation = 0), the maximum possible deviations (blue lines on

top and bottom) and 20 realisations of the simulated fluctuations

(grey lines). Note that the offsets from the horizontal have not yetbeen added, which is why the interpreted fault trace lies atdeviation = 0. The final simulation step is adding the fault offsetsonto the rescaled fault fluctuations, resulting in 100 rotatedsimulated fault surfaces on a dense 2D grid.

Post-simulation work

Two sets of coordinates of the simulated 3D grid nodes areavailable:

1. original unrotated, and

2. rotated as per the fault rotation.

The second set of coordinates is used to flag the rotated grid asabove or below the simulated rotated fault, which is equivalent toflagging the original grid as one or the other side of the un- rotatedfault. The previous steps presimulation work, simulation, 3Dgrid flagging are repeated for each fault. When this iscompleted, seven simulated 0/1 fault indicator grids are available,with 100 realisations each. The final simulated fault block modelis obtained by merging the seven individual fault simulated modelstogether with the proper priorities. Figure 9 shows eight realis-ations of the simulated fault model at mid-elevation in the model.

Results and discussion

Table 1 shows the statistics for the simulated fault block models.

To preserve confidentiality of the original data, each of theinterpreted fault block volumes has been reset to 100. The tableshows that the interpreted (modelled) fault block volumes are notalways reproduced. Differences from -14 per cent to +10 per centare observed. These differences are due to the asymmetric faultuncertainties. Some simulated fault blocks have a greater chanceto become smaller than interpreted and vice versa. The table alsoshows there can be very large differences between two realisationsfor a given fault block. For example the average simulated volumefor Fault Block No 1 is 89, with minimum and maximum valuesof 20 and 135. The coefficient of variation (CV) is 28.3 per cent.Assuming a normal distribution, there is a 95 per cent probabilitythat the simulated Fault Block No 1 volumes are within 56.6 percent of the average.

The approach used to simulate the faults is considered

reasonable. Indeed, the results are statistically consistent with the


G VERLY et al

Uncertainty (m)

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FIG 5 - Gridded uncertainty on one side of the fault after rotation.

FaultPlane

Horizontal

1) Rotatea) Fault

2) Create dense 2D grid

3) Simulate fault in 2Da) simulate deviationsb) rescale deviations to account

for the uncertaintyc) add fault offsets

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gridswithproper priorities

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FIG 4 - Faulted model simulation main steps.


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input data, the simulated faults are conditioned to the availablesnap points and the fault location uncertainties as assessed by thegeologist have been reproduced. The simulated fault surfaces arevisually reasonable and have more chance to be close to theinterpretation than far away. On average, the interpreted faultblock volumes are generally well reproduced by the simulation.Where there are discrepancies, they can be explained by theasymmetrical input uncertainties. Although not necessary for theResolution deposit, different aspects of the simulation could bemodified and/or improved. With the current simulation



0m +30m +45m+15m-10m-20m-30m

67%

95%

100%

FIG 7 - Example of asymmetrical fault fluctuation distributions.Two normal distributions with zero means but different standard

deviations are, in effect, glued together. In this example, thestandard deviations are ten and 15 m. Simulated values outside

the 3 standard deviation interval are reset to three standard

deviations.

A)

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FIG 6 - Simulated normal score statistics. (A) Mean of realisation histograms; (B) realisation cumulative probability curves (grey) plus meanof the curves (red thick line); (C) variogram model (green) plus mean of realisation variograms (red dashes); (D) same as in (C) plus ten

realisation variograms along two directions (grey full and dashed lines).

Faultblock

Simulation volume Modelvolume

Model tosimulation

% ChgMin Max Average CV

1 20 135 89 28.3% 100 -10.8%

2 57 147 108 16.8% 100 7.8%

3 33 114 86 22.2% 100 -13.9%

4 79 133 101 11.0% 100 1.4%

5 42 201 109 28.1% 100 8.6%

6 52 156 104 22.2% 100 3.6%

7 80 124 99 9.6% 100 -0.7%

8 63 171 103 20.6% 100 3.2%9 51 135 96 19.6% 100 -4.1%

10 501 176 110 29.9% 100 10.1%

11 83 120 99 8.2% 100 -0.6%

TABLE 1

Simulated and interpreted fault block volume statistics. The interpreted (model) fault block volumes have been reset to 100.


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methodology, the total number of faults before and after

simulation is static, as per the geological interpretation. The twosemi-normal distribution rule used to rescale the fault fluctuationscould be changed to generate wider or narrower fluctuations with-in the specified uncertainty bandwidths. The range of the Gaussianvariogram could be revisited. The simulation methodology couldbe changed to generate surfaces that are more planar.

FAULTED ROCKTYPE SIMULATIONIn the simulation described below, faulted rock types representrock types that are interpreted to have been offset by faulting.These rock types consist of stacks of subhorizontal layers within abackground made of two rock types separated by an unconformity.The faulted rock types are intruded by dykes and breccias that donot appear to be offset by faulting. The general procedure forsimulating faulted rock types consists in processing one faultblock at a time. The preintrusive/prebreccia rock types are

reconstructed. The 3D interpretation of each layer is converted to a

2D interpretation of elevations and thicknesses. 2D simulations of the elevations and thicknesses are performed, conditional to drillhole intercepts and accounting for the uncertainties specified bythe geologist. The 2D simulation results are converted back to 3D.The faulted blocks are stitched back together at the very end. Thissimulation methodology is further described below and isillustrated in Figure 10.

Presimulation work

The available information consists of a 3D gridded geologicalmodel, uncertainty information and drill hole sample locations.The uncertainty information is the same for all layers a 95 percent confidence interval (two sigma) of 30 m from theinterpreted elevation and of 20 per cent from the interpretedthickness. Note the deviations for thickness are in terms of arelative percentage of the interpreted (modelled) thickness.


G VERLY et al

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FIG 8 - Simulated fluctuations from one fault interpretation.

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FIG 9 - Eight realisations of the fault block model at mid elevation in the model. The red lines represent the original fault interpretations.The grey lines represent the simulated fault traces.


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As previously mentioned, the faulted rock types are processedwithin one fault block at a time. In a first step, thepreintrusive/prebreccia faulted rock types are reconstructed(Step 1b, Figure 10 and Figure 11). This can be done by eitherusing the preintrusive wireframe model, or by eroding away theintrusives/breccias from the grid model. The reconstructed rock types are then extended to the maximum possible fault block limits. Again, this could be done using the original wireframemodel or numerically approximated on the grid model. Themaximum extent of the simulated fault block is obtained byscanning the realisations of the previously simulated fault model.Each reconstructed and extended stack of layers is processed inturn. The 3D interpretation of each layer is converted to a 2Dgrid of elevations and thicknesses. The few drill hole intercepts one to five per fault block are converted to 2D snap points.

Simulation

A series of 2D simulations are performed for each stack: same simulation of elevation fluctuations for all layers (will

tend to prevent crossovers), and one simulation of thickness fluctuations per layer.

Standard normal scores are simulated first, followed by somerescaling to account for the uncertainty. The simulations areconditional sequential Gaussian using a unit-sill Gaussianvariogram model with no nugget effect and a 500 m isotropicrange to ensure smooth surfaces. The checks at this stage consistin verifying that the averages of the simulated normal scores areclose to zero. The variances of the simulated normal scores arenot expected to equal one because of the conditioning and therelatively small extent of the fault blocks compared to thevariogram range.

Rescaling the simulated normal scores is needed to account forthe uncertainty. The assumption is that the simulated fluctuationsfar from snap points are normally distributed with 95 per cent of the values within the specified uncertainty. In other words, thespecified uncertainty is equivalent to two standard deviations of the normal distribution. The uncertainty for the elevation is 30 m the simulated normal scores are multiplied by 15, and reset to 45m if they exceed these values. The uncertainty for the thickness is

20 per cent of the interpreted thickness the normal scores aremultiplied by ten per cent and then reset to 30 per cent if theyexceed these values. The final simulation step incorporates theinterpretation and simulation together. The simulated elevation at alocation is the interpreted elevation plus the rescaled simulateddeviation at that location. The simulated thickness is theinterpreted thickness plus the product of interpreted thickness andthe rescaled relative simulated deviation. Elevation corrections aremade to avoid gaps and overlaps between the simulated layerswithin a same stack.

One hundred realisations of elevations and thicknesses areavailable at this stage for each layer. Figure 12 shows one sectionwith the trace of one layer interpreted elevation and thickness(red lines), the maximum possible deviations (blue lines) and 20realisations of the elevation and thickness (grey lines). Threesnap points were available for the elevation but only two for thethickness because of an incomplete hole intercept. The jaggedaspect of the thickness profiles is due to the exaggeratedresolution of the vertical grid.

Post-simulation work One hundred realisations of one stack of layers within a faultblock are available at this stage as a series of 2D grids of layerelevations and thicknesses. For each realisation, the layers top

and bottom elevations are calculated and used to flag one 3Dgrid. The simulation procedure is repeated for the other stackswithin the fault block. The 3D grids are then merged together.The procedure is repeated for the other fault blocks resulting in11 individual simulated models. The final simulated faulted rock type block model is obtained by merging the eleven modelstogether. For a given realisation and a given location, thesimulated fault block is first identified. The simulated rock typeis then picked from the rock type model that corresponds to thefault block. Figure 13 shows eight realisations of a verticalsection through the faulted rock type model at about midnorthing in the model.

Results and discussionTable 2 shows the statistics of the simulated faulted rock typemodel. To preserve confidentiality, each of the interpreted rock



For each fault blockStep 1 - Pre-simulation processing 3D

1a) Get the maximum simulated fault block footprint1b) Get 3D Indicator Grid:

- Generate an indicator grid of the rock types- Reconstruct pre-intrusive rock types- Extend rock types from interpreted to maximum simulated fault block limit

Repeat Steps 2, 3, and 4 for each stack of layers in the fault block

Step 2 - Pre-simulation processing 2D2a) Create 2D grids of the elevation and thickness of each layer 2b) Create 2D conditioning sample dataset from drill-hole intercepts

Step 3: Simulation 2D3a) 2D stationary simulations of deviations, conditional to snap points.3b) Rescale simulated deviations3c) Incorporate rescaled deviations to interpretations.

- Adjust elevations for gaps or overlaps

Step 4: Simulation 3D4a) Flag 3D grid from 2D simulations

Step 5: Post-simulation processing 3D5a) Recombine the 3D grids corresponding to the stacks into one 3D grid.

Nine sets of 100 realizations (one set per fault block)

Stitch the faulted block rock types back together For a given realization, pick the simulated rock type according to its location andsimulated fault block number at that location

100 simulated faulted rock type grids

FIG 10 - Faulted rock type simulation process.


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FIG 12 - Simulated elevation and thickness for one layer.

FIG 11 - Faulted rock types presimulation steps. (A) Original interpretation; (B) maximum simulated fault block footprint identifiedon left and right; (C) preintrusive/breccia reconstruction; (D) extension to fault block maximum simulated footprint; and

(E) 2D grid of elevations and thicknesses of the mid-layer (pzls).


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type volumes has been reset to 100. The table shows that onaverage the interpreted (modelled) rock type volumes arerelatively well reproduced by the simulation. Differences from-1.5 per cent to +1.2 per cent are observed, which is consideredacceptable, especially since part of these differences is related tothe simulated fault blocks with their asymmetric uncertainties of boundary positions. The table also shows the kind of differencesthat can be observed between two realisations. For example theaverage simulated volume for pzls (Paleozoic limestone) is 99with minimum/maximum counts of 89 and 110 respectively. Thecoefficient of variation (CV) is 4.7 per cent. Assuming a normaldistribution, there is a 95 per cent probability that the simulatedpzls volumes are within +/- 9.5 per cent of the average. Thesedifferences are significantly less than those observed for the faultblock volumes (Table 1). This is partly due to the fact that thesame rock type is found in most faulted blocks. The variability of the rock types within any given faulted block is more significant.

The approach used to simulate the faulted rock types isconsidered reasonable. Indeed, the fault blocks are simulated. Theorder relations between the simulated rock types are reproduced.The simulated results are statistically consistent with the inputdata. The simulated rock types are conditioned to the drill hole

intercepts. The fluctuations in elevation and thickness reflect theuncertainty assessed by the geological staff. Still, several aspectsof the simulation could be improved. The method assumes thatthere are enough holes to get the interpretation of rock sequence100 per cent right at each node. This is optimistic and some

additional uncertainty should probably be injected in the model. Asensitivity study of the results to the range of the variogram wouldbe useful, as local variations could be important as the mine getstarted.

CONCLUSIONSA general method to realistically simulate the geology issuggested in this paper. The method consists of first establishing apriority in the geological features and of simulating them one at atime. The simulation starts with the interpreted outlines or shapesand incorporates the uncertainties as specified by the geologist.Two steps that could be part of such methodology were furtherdeveloped:

1. simulation of a faulted block model, and

2. simulation of layered rock types within the faulted blocks.

The method is relatively simple because the geological featuresare simple once they are treated one-at-a-time. For example, thefaults are surfaces and the faulted rock types are layers. Bothfeatures were simulated by simple 2D sequential Gaussiansimulations with various rescaling to account for the uncertaintiesspecified by the geologist. Last, the method is flexible in the sense

that it can cope with complex geological models, variableuncertainties and a scarcity of data. The method is made powerfulby its incorporation of geological interpretation and uncertaintyassessments, although these can be subjective.

ACKNOWLEDGEMENTS

The authors wish to thank Resolution Copper Mining, LLC andAMEC for permission to publish this paper. They also thank HarryParker and Geoff Ballantyne for their useful comments andsuggestions.

REFERENCESAlabert, F, 1987. Stochastic imaging of spatial distributions using hard

and soft information, Masters thesis, Department of Applied EarthSciences, Stanford University, p 198.

Alfaro, M, 2008. Microergodicity and geostatistical simulation, inProceedings Eighth International Geostatistics Congress:Geostatistics Santiago 08 (eds: J M Ortiz X and Emery), 1:409-417(FCFM U: Chile).



11 21 31 41

51 61 71 81

CuShell

FIG 13 - Simulated faulted rock type sections for eight realisations, in the northern part of the simulated area.

Rocktype

Simulation volume Modelvolume

Model tosimulation

% ChgMin Max Average CV

kvs 98 102 100 0.8% 100 -0.1%

kqs 90 113 101 4.6% 100 1.2%

pzls 89 110 99 4.7% 100 -0.7%

mesc 89 114 101 4.8% 100 1.1%

qzite 91 104 99 2.5% 100 -1.5%

diab 97 103 100 1.4% 100 0.2%

TABLE 2Simulated and modelled faulted rock type volume statistics.

The model rock type volumes have been reset to 100.


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