ORE RESERVES Using Modern Geostatistical Analysis To Determine Ore Reserves

NOVEMBER 30, 2016 SHIVAM SHARMA

Laurentian University

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DATA IMPORT Importing data from .txt files to .csv was rather simple. Converting most of the data from imperial to

metric wasn’t much more difficult. With the use of the CONVERT function in Excel, data was easily

converted. The tricky portion of this task was converting the DISTANCE in the ASSAY table into the FROM-

TO format. This problem was quickly solved by using the TO values from the previous drillhole as the new

FROM value for the ensuing drillhole. The final TO value for each drillhole was the total DISTANCE/LENGTH

of the drillhole. Doing so, the ASSAY table was easily converted into the ideal format.

DRILLHOLE WORKSPACE Importing data into GEMS is very simple. But before importing the data, a workspace DRILLHOLE was

created along with subspaces called ‘ASSAY’, ‘LITHOLOGY’, AND ‘SURVEY’. Starting with the HEADER file

as the primary HEADER table file, all of the remaining files (ASSAY, SURVEY, and ROCKS) were subsequently

imported as secondary tables, all linked to the HEADER file via the HOLE-ID key data. As the import

finished, a basic DRILLHOLE DISPLAY was using the profile TRACE:

Figure 1 View of TRACE profile for DRILLHOLES, from XYZ plane towards YZ plane.

CONDUCTING STATISTICS Statistics are an important portion

of any analysis of mineral

reserves. They allow us to better

understand the deposit that we

are dealing with. For example,

creating a grade profile is

important in understanding the

general concentration of minerals

within the orebody. To see a

visual depiction, we can create a

histogram in GEMS. Using a new

workspace COPPER as ‘POINT

AREAS’, we can create a geo-

statistical workspace titled

ANALYSIS 1, combined with a data

source named COPPER POINTS;

the histogram in Figure 2 can be

Figure 2 CU histogram after all zero-values are removed

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achieved. Instead of using ‘NUMBER OF

BINS’ to determine histogram width, it is more

beneficial to use ‘WIDTH OF BINS’ as it results in

a smoother distribution. Using a ‘WIDTH OF

BINS’ of 0.75, roughly 6 bins are created. From

this graph, we can create our COLOR GRADES

profile. The best COLOR profile involved using 5

profile ranges (0.00000 – 0.00010, 0.00010 –

0.25000, 0.25000 – 1.50000, 1.50000 –

3.50000, and 3.5000 – 5.00000). The colors

used can be seen in Figure 3.

Figure 3 Color profile for GRADES

Creating a GRADE COLOR PROFILE isn’t the only benefit of

using Statistics. Knowing some of the other basic statistics

like variation, skewness, kurtosis, and coefficient of variation

can tell us important information about our orebody such as

the probabilities of higher grades versus geological profiles.

Table 1, below, summarizes some of the basic statistics that

are of interest and use.

Another unique feature of GEMS is that it allows us to project

and plot bar charts of the grade distribution along our

drillhole data. It is really handy as it allows us to see the grade

concentration of copper per drillhole. If a drillhole has

segments of copper deposits that are richer than the rest of

the drillhole, we can see it right on the drillhole as opposed

to going to the data editor to find it.

Figure 4 Zooming into the DH-27 (left) and DH-25 (right), the plotted bar charts onto the drillholes

can be seen

CROSS-SECTIONS Defining limits for a work area is essential as it accurately presents the extent and the size of the overall

orebody. GEMS, if no external change is introduced, uses preset settings to create limits that are based

on the open data. However, to visualize a more accurate work area, limits have to be defined. To create

Descriptor Value

Mean 0.780294

Median 0.630000

Variance 0.416798

Standard Deviation 0.645599

Coefficient of Variation 0.827379

Skewness 1.684170

Kurtosis 7.151805

Q1 0.245500

Q3 1.111500

95.0 Percentile 1.876000

97.5 Percentile 2.736000

Table 1 Summary of basic statistics

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more accurate limits, the upper and the lower bounds of

the X-plane, Y-plane, and Z-plane have to be found from

the data. The lower bounds are entered under the ‘Lower-

Left’ tab and the upper bounds are entered under the

‘Upper Right’. As Figure 5 shows, the ‘Lower Left’ and the

‘Upper Right’ included the following limits (X, Y, Z):

(1300613.0000, 95837.0000, 530.0000) and

(1300990.0000, 96417.0000, 636.0000).

Figure 5 Upper and Lower bounds for Work Area

Since the drillholes aren’t taken from the same horizontal

plane (vertical distance from an arbitrary plane); in order

to view the drillholes from every possible angle, inclined

sectional views were used along with vertical sectional

views. Twenty-two vertical sectional views were created at a distance of ∆𝑥 = 25 from one another, using

naming increments of 5.

Figure 6 Screenshots of the DRILLHOLE workspace displaying the vertical cross sections (left) and

the inclined cross sections (right)

To optimize viewing angles of the drillholes, the inclined cross sectional views were also created. Unlike

the vertical cross section, the inclined cross sections were constructed using the ‘Plane Through 3 Data

Points’ function, which allows us to drive a plane through plane multiple drillholes (see Figure 6). Upon

creating the inclined sectional views, the plan views were made. Like vertical sectional views, creating

plan views was easy as parallelization simplified the work. Using intervals of 10 and 15 for the elevation,

9 planar view were created, as seen in Figure 9. Choosing intervals of 10 and 15 made the most sense as

it allowed us to capture all of the orebody without creating too many planes (see Figure 6).

Figure 7 Plan sectional views of the DRILLHOLE workspace

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DETERMINING ZONES OF MINERALIZATION One of the crucial steps in determining the total economic value (viability) of a deposit is its zones of

highest mineralization, as these zones become the economic backbone of the mine. The orebody can be

subdivided into 4 geological zones: QUARTZ, SEDS, LOW, ANDO, and DYKE. To determine which one of

these zones will serve as the ‘backbone’ of the future mining operation, a statistical analysis of the drillhole

samples was conducted. To do so, it was imperative that a point area workspace, ‘CuRockType’, be created

and the following fields included: “Rock_Code” and “Cu%”. After extracting the all of the data point from

‘DRILLHOLES’ to ‘CuRockType’ using the ‘Rock_Code’ filter, point areas titled after the geological zones

(QUARTZ, SEDS…) were created. The results of the ensuing analysis can be seen below in Figure 8 and

some of the relevant statistics regarding each zone can be found in Table 2.

Figure 8 Histograms depicting the Cu grades within each geological zone: Low (Upper Left), Dyke

(Upper Right), Ando (Bottom Left), and Seds (Bottom Right). Drillholes from Quartz yielded no Cu points.

Each histogram has a maximum value of 5.000.

ZONE MEAN MEDIAN VARIANCE MAX SAMPLES COMMENT

ANDO 1.006 0.902 0.583 4.37 169 Highest grade of all deposits; backbone of the mining operations

LOW 0.444 0.241 0.145 1.75 132 Surrounds ‘Ando Zone’; has significant economic value

SEDS 0.007 0.000 0.001 0.19 27 Lowest grade; no economic value QUARTZ 0.000 0.000 0.000 0.00 0 No evidence of copper found DYKE 0.655 0.531 0.162 1.81 52 High grade but sample size is too

small; Worth further exploration

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Table 2 Ando and Low will serve as the zones of highest mineralization for the project. Further

exploration is warranted in the DYKE geological zone.

The statistical analysis of the geological zones answers the question of the zones of interest. The ANDO

and LOW geological zones will be the zones of mineralization. However, the raw data has to be first be

composited prior to modelling.

COMPOSITING Compositing, as a process, serves the purpose of combining random discrete samples into larger, more

meaningful ones. Assay results are combined using the weighted – averaging. The data has to be

composited using the 3 major techniques: ‘Grouping by Similar Values’, ‘Intervals From Another Table’,

and ‘Length Within Intervals From Another Table’. The DRILLHOLES workspace was edited to include the

‘Comp_Lith’, ‘Comp_Grade’, and ‘Comp_Fix’ tables, as the compositing data will reside in these tables.

Upon finishing this task, the composite profiles were created, as seen in Figure 9.

Figure 9 Composite profiles for the ‘Comp_Lith’,

‘Comp_Grade’, and ‘Comp_Fix’ profiles.

Upon completing the profiles, the tables were then

prepared. First, the ‘Comp_Lith’ table was prepared

by using the ‘Grouping Similar Values’ method.

Second, the ‘Comp_Grade’ table was subsequently

prepared using the ‘Intervals From Another Table’

method with the ‘Another Table’ being the

‘Comp_Lith’ table, which was created in the step

above. Finally, the ‘Comp_Fix’ composite was created

using the ‘Length Within Intervals From Another Table’ method. The twist of using this method is that a

composite interval must be chosen as the method requires a length to divide the interval lengths by. This

calculation and result can be seen in Table 3.

Methodology Formula Result

The average of the drillhole lengths will be subdivided into 6 lengths

∑ 𝐷𝑟𝑖𝑙𝑙ℎ𝑜𝑙𝑒 𝐿𝑒𝑛𝑔𝑡ℎ𝑠𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑟𝑖𝑙𝑙ℎ𝑜𝑙𝑒𝑠

6

∑( 34.80816 + 32.3088 + ⋯ + 34.1376)436

Interval Length 5.63

Table 3 Interval length can be calculated by dividing the average drillhole length into 6 equal sections.

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The interval may have been calculated, but it is important to understand what it really means. The interval

length of 5.63 meters means that the smallest interval inside any drillhole will not smaller than 5.63

meters. This can very easily be confirmed as there isn’t a single drillhole interval with a composite length

smaller than 5.63. The smallest composite length, 5.65 meters, can be found in DH-08 at the 3rd COMP-

ID. Composite values for DH-10 can be seen below in Figure 10.

Figure 10 Composite values for DH-10.

Comparing Raw Data With Composited Data

Figure 11 Histogram of Composited Data (Left) and Raw Data (Right), on a FREQUENCY axis to 5.00.

The primary function of compositing is to normalize the data from discrete values into continuous ones.

As a result, the composited data produces a smooth (and more realistic) distribution of the data than the

raw data. Some of the numerical statistics can be seen in Table 4.

Statistic Raw Data Composited Data

Mean 0.780 0.530

Median 0.630 0.291

Variance 0.417 0.434

Max 4.372 4.372

Min 0.111 0.000

Number of Samples 337 109

Table 4 Comparing composited data with the raw data.

Compositing the data yield some interesting results. First, the minimum value of the copper falls from

0.111 to 0.000. This is correct as it is highly unlikely that there isn’t a single point within the orebody

without the presence of copper. Interestingly, the mean value drops from 0.780 to 0.530. This is also

correct as it corrects for ‘lucky’ drilling. This correction downward corrects the problem that it is likely that

the copper deposit was over sampled.

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MODELLING SOLIDS

Creating Polygons Before we can start triangulating the solids, it is imperative to first

create the polygons. Since we are only interested in mining the

ANDO and the LOW geological zones, only these zones will be

modelled into solids. To begin creating the polygons, two new

workspaces were created under the ‘POLYLINES’. These two

workspaces are called ‘MZ1’ (for ANDO) and ‘MZ2’ (for LOW), as

seen in Figure 12.

Once these workspaces were created, the polygons were digitized.

Using the sectional views that were created previously, 3D ring

feature lines were used to digitize the polygons. These rings, along

with the tielines that connect them, can be seen below in Figure 13.

Figure 13 MZ1 (Left, ANDO) and MZ2 (Right, Low)

Figure 12 MZ1 and MZ2 Polyline

Workspaces.

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Creating Solids Finally, the polylines were converted into solids. By first creating a new workspace, ‘SOLIDS’, under the

TRIANGULATIONS header, and then creating the solids, we can now visualize how the orebody likely looks

like.

Figure 14 MZ1 (Left, ANDO, Yellow-Gold color) and MZ2 (Right, LOW, Dark-Red color)

Figure 15 Different view of the mineralized zones. ANDO zone lies within the LOW zone.

As seen within Figure 15, the ANDO geological zone lies within the LOW zone, hence there is a possibility

for overlap. However, it will not create a problem for resource estimation as the two zones are still

separate. Since, the MZ1 was created after MZ2, the data points for MZ2 that overlapped MZ1 were

overwritten. Using the ‘REPORT VOLUME’ function within GEMS, the volumes of the solids were

determined. GEMS reported a volume of 619, 602 for MZ1 (ANDO) and 2, 083, 382 for MZ2 (LOW).

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SETTING UP THE BLOCK MODEL After having created the solids in the previous projects, the solids have to be rendered in a block model.

Considering the data implies a small copper porphyry deposit, the number of blocks needed to render an

appropriate block model is quite low. Using the origin of (1300405, 96605, 650) with no rotation, with the

block size of (15,15,10) (column, row, level size), 51,675 blocks were created using 53 columns, 65 row,

and 15 levels. Considering the deposit is relatively flat and massive in nature, the number of rows needed

to appropriate model the deposit must be high while the number of levels has to be low. The blocks do

not need to particularly small considering the spacing between the drillholes. The model also be wide

enough to accommodate the horizon of the topographical model, as seen in Figure 16.

Figure 16 The rendered block model titled “BlockModel”

ROCK TYPE MODEL Prior to initializing the rock types in the block model, the rock type

profile must first be updated. The information stated in Table 5. One

of the problems faced while updating the rock code profile was the

variable densities for the ‘Sediments’ and the ‘Quartz’. As a means

of preventing unnecessary complications, an average was taken and

used instead. After the Rock Code Profile update, the model can be

initialized. The blocks above the ‘ground’ (as dictated by the

topographic file) were initialized as ‘AIR’ using an integration level

of 4. The remainder of the blocks were initialized in the following

order: Quartz, Low, and Andesite. The ‘Sediments’ and the ‘Dyke’

were not initialized as the waste rock can only be one rock type

without either knowing which level, column, row combinations belongs to which rock type or creating

solids for every rock type. This order was necessary as a means of preventing an errors during grade

estimation. Since the Quartz is the furthest from the deposit, the blocks were initialized as quartz. This

process was repeated for Sediments, then Dyke, and finally for the Low and Andesite rock types to render

the most accurate depiction of the rock model, as seen in Figure 17.

Figure 17 BlockModel as seen using the 50V vertical section after all rock types’ been rendered.

Rock Type Density Tonne/m3

Rock Code

Sediments 2.00 200

Quartz 2.65 100

Andesite 2.70 20

Low 2.80 30

Dyke 2.80 40

Table 5 Summary of

information input into Rock

Codes Profile

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The significance of order in rock type updating cannot be understated, as the process can and will have

an impact on the block grade estimation that will be conducted using the inverse distance method. The

program, GEMS, has to be ‘told’ which block is represented by which rock type. For example, if ANDESITE

is initialized prior to QUARTZ, then model will assume all of the blocks that were not explicitly initialized

as QUARTZ belong to the ANDESITE rock type. This is incredibly problematic as it will dilute the block grade

value during estimation. To prevent this issue, the mineralized zones are initialized last in order of size

(first LOW then ANDESITE). Upon updating the rock types in the block model, the density block properties

were updated using the DENSITY model under ‘BlockModel’.

GRADE MODEL To estimate the block grades using the inverse distance method, a new workspace ‘CUPOINTS’ was

created. Subsequently, the copper points were extracted from the DRILLHOLES workspace to the

CUPOINTS workspace, where a new point area ‘CUAREA’ was made. After the points were extracted, an

‘INTERPOLATION’ profile was created. Within this profile, the search ellipses for each mineralized zone

were created, and can be seen in Figure 18. The rotation of the search anisotropy was left alone as it was

determined that insufficient information existed to make that decision. Having in depth geological

information regarding the deposit such as the dip, dip direction (azimuth), or which axis the deposit could

rotate about would have aided in the determination of the rotation of search anisotropy. However, since

none existed, the option was not exercised.

Figure 18 Dimensions of each search ellipse, CU-MZ1 (LEFT) and CU-MZ2 (RIGHT).

The dimensions chosen for each profile were based on the size of the 2 criterion: horizontal and lateral

extent of each zone (Anisotropy ‘X’ and Anisotropy ‘Y’), and length of drillholes (Anisotropy ‘Z’). Since the

LOW zone has a greater extent, and thus the points are further apart, than the ANDO zone, the size of the

ellipse in the X and Y directions is far greater. However, the length of the drillholes is relatively the same,

and thus the vertical extents of the search ellipses is the same at 10ft. For example, the approximate

rounded length of each drillhole is roughly 30ft, therefore an Anisotropy Z of 10ft is appropriate. Similarly,

the horizontal extent of the LOW zone (x-direction) is roughly the same as ANDO zone, therefore the

values are fairly similar at (180ft vs. 125ft respectively). However, the lateral extents of the zones are quite

different, as LOW extends further than the ANDO zone, and therefore the values are quite different as

well (280ft vs. 150ft respectively).

The grade interpolation was carried out right after

determining the size of the ellipses using the

‘INTERPOLATE AND REPORT’ option under TOOLS

in GEMS. The results are stated in Table 6.

Rock Code Mean Block Grade Sample Mean

20 1.07218 0.53044

30 0.59270 0.53044

Table 6 Mean block grade interpolation

using Inverse Distance Method.

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As means of showing the cross-sectional geology of the deposit, two vertical cross-sections were cut at

96,225Y (NORTHING) and can be seen in Figure 19.

Figure 19 Cross-section 1, LEFT, shows the drillholes, topographical surface, and the blocks plotted

using the ‘LITH’ color profile; Cross-section 2, RIGHT, shows the block model using the ‘GRADE’ profile.

VARIOGRAPHY – DATA PREPARATION Before the variograms could be made to computationally

render the search ellipses, the data first had to be

prepared. First, new drillhole composites had to be

created. By accessing the ‘DRILLHOLES’ workspace and

adding a ‘COMP05’ table, then creating the composite

profile titled ‘BYLENGTH’, and finally calculating the length

required to create equal-length composites, the necessary

data required was created. The results can be seen in

Figure 20, a screenshot of COMP05 table in DRILLHOLES

workspace.

Figure 20 Composite results generated for

COMP05 table, which will be used in variography.

The next step was to create a workspace that would enable the storage of the data in the newly created

COMP05 table in DRILLHOLES workspace. This workspace was titled ‘PAMZ1ANDO’. Using the ‘EXTRACT

POINTS’ function under the ‘WORKSPACES’ tab, COMP05 composite data was imported into a newly

created ‘CUMZ1’ point area under the PAMZ1ANDO

workspace. The CU101 point area was then opened along

with the MZ1 solid (ANDO solid) where the points within the

solid were selected and imported into a newly created point

area titled ‘OreMZ1’. The points inside this workspace are the

same points that were imported from the COMP05 table to

the CU101 point area. Since the data must first be filtered

before it can be examined, a SQL data filter was created.

Titled ‘MZ1ANDO’, this filter was created to filter all of the CU

points in the OreMZ1 point area prior to data processing and

can be seen in Figure 21.

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Figure 21 SQL filter for PAMZ1ANDO workspace.

After creating this filter, the data was tagged using the term ‘MZ1ANDO’. This process was then repeated

for the MZ2. A similar workspace ‘PAMZ2LOW’ was created, along with a point areas ‘CUMZ2’ and

‘OreMZ2’, and a SQL data filter ‘MZ2LOW’ and a tag ‘MZ2LOW’.

The data stored in the point areas stated above was then statistically analyzed and the results can be seen

below in Figure 22. As seen in the graphs, there are no significant outliers within the data set.

Figure 22 Histograms depicting copper points within OreMZ1 (LEFT) and OreMZ2 (RIGHT).

Upon eye-balling both histograms, it is clear that the top cut of the deposit is probably less than Cu-3% by

weight. A new field, CU_CUT, was added to both PAMZ1ANDO and PAMZ2LOW Point Area Workspaces,

and the data was subsequently manipulated to show the top-cut of the deposit. The data was then

reanalyzed using the ‘BASIC STATISTICS’ tool, and can be seen in Figure 23 and Table 7.

Figure 23 Histograms depicting the newly created CU_CUT field in the PAMZ1 & PAMZ2 workspaces

Applying the top grade confirms the hypothesis that the

ANDO rock type contains more higher-grade copper zones

than the LOW rock type. The higher copper zones also

persist far more in the ANDO zone than in the LOW zone as

seen by the differences in the mean and the median of both

areas. The mean-median ratio of MZ1ANDO is

approximately 1, meaning that the data is relatively

normally distributed. This is not true for the MZ2LOW zone

as the mean is more than 2x greater than the median,

implying that the distribution skews positively as 50% of the

zones have a %Cu of less than 0.21%.

Variable CU_CUT

MZ1ANDO MZ2LOW

Mean 0.988803 0.444084

Median 0.962836 0.212413

Variance 0.324510 0.146607

Value, Max 2.717831 1.699597

Value, Min 0.035189 0.000000

Table 7 Univariate statistics for

point areas PAMZ1ANDO and PAMZ2LOW

using top-grade data in CU_CUT.

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OMNI-DIRECTIONAL VARIOGRAM Prior to creating the variograms along the major axis, the sill of the MZ1 deposit must be determined.

Omnidirectional variogram will be used to determine this nugget of information.

First, a new geostatistical workspace titled ‘GEOMZ1ANDO’ was created. Using the PAMZ1ANDO as the

‘SOURCE WORKSPACE’ along with the OreMZ1 as the ‘DATA SOURCE’, CU_CUT as the ‘FIELD’, ‘MZ1ANDO’

as the ‘TAG’, along with the data provided in Figure 24, an omnidirectional variogram was created for the

MZ1ANDO zone. A similar process was conducted for the MZ2LOW workspace, and the results can be

seen below to the results for GEOMZ1ANDO in Figure 25.

Figure 24 Data (LEFT) used to create the omnidirectional viariogram for GEOMZ1ANDO and the

resulting variogram (RIGHT).

Figure 25 Data (LEFT) used to create the omnidirectional viariogram for GEOMZ2LOW and the

resulting variogram (RIGHT).

A data comparison was made to describe some of the key pieces of information that were extracted from

both variograms, and are summarized in Table 8.

GEOMZ1ANDO GEOMZ2LOW Analysis

Lag Distance (ft) 10 10 The lag distance was far greater for the MZ2 solid as the horizontal extent and the variance of the solid is far greater than that of MZ1. MZ1 will probably provide better results than MZ2 when comparing both ranges.

Dip/Dip Direction (deg) 40 40

Spread Angle (deg) 0/0 0/0

Spread Limit (ft) 0/0 0/0

Range (Distance to Sill) (ft) 70 70

Figure 8 Comparing data set and the results for both geostatistical workspaces.

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LINEAR (DOWNHOLE) VARIOGRAM Linear variograms serve a critical purpose in variography as they are often used to determine the nugget

effect for horizontal variogram modelling. To begin this process, the ‘LINEAR SEMI-VARIOGRAM’ function

under ‘TOOLS’ in GEMS was used. Using the geostatistical workspaces created previously, a new analysis

‘VERTICAL’ was conducted using the ‘DRILLHOLES’ as the ‘SOURCE WORKSPACE’ and the COMP05 as the

‘DATA SOURCE’. For this analysis, the composited copper values stored in the COMP05 table were used.

To minimize the effect of directional anisotropy, a dip from -90 to 90 was chosen, along with an azimuth

ranging from 0 to 360 degrees. Scanning the COMP05 table revealed that the average composite length

was somewhere between 4.0 and 5.0 feet with 4.5ft composing the majority. Therefore, 4.5 feet was

chose as the lag distance with 30 total classes, as seen in Figure 27. A spherical model was used.

Figure 26 Data set-up and graph for Linear Variogram for MZ1ANDO. The nugget effect was zero.

A similar process was conducted for GEOMZ2LOW workspace. Using the ‘DRILLHOLES’ and the COMP05

as the sources, a dip from -90 to 90 degrees, an azimuth of 0 to 360 degrees, along with a lag of 4.5ft, the

graph depicted in Figure 27 was created. Like the variogram for ANDO, the nugget effect is 0 for LOW.

Figure 27 Set-up and graph for Linear Variogram for MZ2LOW. The nugget effect was zero.

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Table 9 summarizes the key pieces of information extracted from both variograms. An important point to

note: variance in number of classes between both rock zones is irrelevant so long as the product of the

classes and the lag distance is greater than 60ft, the distance where the distribution ends as seen above.

MZ1ANDO MZ2LOW Analysis

Lag Distance (ft) 4.5 4.5 Using a spherical model for both variograms, it is apparent that, at least vertically, the variance in the data is somewhat similar in the vertical distance. Also, nugget value of 0 means that at r = 0, the data doesn’t vary.

Number of Classes 30 15

Nugget Effect [Gamma(h)] 0.000000 0.000000

Sill [Gamma(h)] 0.813026 0.798837

Range (ft) 35.411 31.166

Table 9 Summary of linear variograms for both MZ1ANDO and MZ2LOW.

DIRECTIONAL HORIZONTAL VARIOGRAPHY

Determining Dip and Dip Direction (Azimuth) Finding exact values for dip or dip direction is a futile and an unnecessary effort. These values can be

approximated using the MEASURE tool within GEMS that determines the dip and the azimuth of a line

connecting 2 points. Simply analyzing the geometry can be helpful in determining in which direction the

orebody dips. Multiple measurements from different points is necessary as the data set will be averaged

to determine what the approximate both dip and azimuth of the orebody, as tabulated in Table 10.

MZ1ANDO MZ2LOW Example of MEASUREMENT

REPORT using the MEASURE tool (1st measurement for MZ2LOW)

MEASUREMENT Dip Azimuth Dip Azimuth 1 -22 150 -12 151 2 -24 113 -24 23 3 -27 61 -10 140 4 -15 58 -16 73 AVERAGE (APPROX) -15 – -25 90 – 120 -10 – -20 80 – 100

Table 10 Approximated dips and dip directions for both rock zones, MZ1ANDO and MZ2LOW.

Having calculated the approximate dip and azimuths for each solid, horizontal 3D variograms can be

created now. Using the geostatistical workspaces, GEOMZ1ANDO and GEOMZ2LOW, the variograms can

be set up using the data tabulated in Table 11.

GEOMZ1ANDO GEOMZ2LOW

LAG DISTANCE (FT) 20 40 NUMBER OF CLASSES 15 15 DIP DIRECTION 120 85 DIP -22 -10 SPREAD ANGLE 50 75 SPREAD LIMIT 300 600

Table 11 Setting up the horizontal variograms.

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An important question arises from analyzing the data: what variables are necessary in determining the lag

distance, spread angle, and the spread limit? The answer to this question is multi-faceted. Since the

horizontal extents of the LOW rock zone is far greater than ANDO’s, the spread limit and the lag distances

have to compensate and thus have to be greater as well. Larger lags allows for the creation of smoother

variograms. Spread angle is determined through the histogram analysis above. Considering the data for

MZ1ANDO is fairly normally distributed, a spread angle around 45 degrees is ideal therefore an angle of

50 degrees chosen for GEOMZ1ANDO is appropriate. However, since the grade distribution for

GEOMZ2LOW is positively skewed, the spread angle has to compensate for this occurrence. Therefore, a

spread angle of 70 degrees was chosen in an effort to capture all the points for further analysis.

Figure 28 Best graphs for each solid, MZ1 (LEFT) and MZ2(RIGHT), at the darkest variogram map.

It is important to determine the best lags for each variogram. The simplest way of determining this fact is

through manipulating the lag slider and watching the changes in the variogram map. The ideal variogram

map has a low range with a color distribution composed primarily of dark colors (signifying the lowest

variance). It is important to watch the changes in the variograph during lag manipulation. The graph that

looks ‘best’ at the chosen lags will be used for modelling. These graphs can be seen above in Figure 28,

and the best lags can be seen below in Figure 29.

MZ1ANDO

30ft 35ft 37ft

MZ2LOW

41ft 37ft 34ft

Figure 29 Best variograms for each zone and their corresponding lag distances (above each map).

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Determining the ideal graph for modelling requires quite a bit of analysis. The easiest way of doing so is

by generating a graph depicting the variographs for all values, as seen in Figure 30. Determining the graph

is relatively easy for MZ1ANDO as the data behaves relatively well. There isn’t any significant changes in

variance at shorter distances (no spikes; smooth transition). Therefore, the best graph will be 21.5559

287.892 (as seen in Figure 28) as it has the longest range and it represents one of the longest distances.

Figure 30 ‘ALL ORIENTATIONS’ variographs for both MZ1ANDO and MZ2LOW.

However, this isn’t quite as simple for MZ2LOW. At the distance of 25ft, there is a significant increase in

variance that lasts until the distance of 80ft where it curtails downward, bottoming out at 120ft where it

increases back to the sill again. Using the ‘ALL ORIENTATIONS’ graph, the choice can be narrowed down

to two particular graphs: -7.05302 130.439 and

7.05302 219.561. Since the difference in range between the former and the latter is negligible, with

the latter representing a greater distance and a lower maximum variance, 7.05302 219.561 will be

chosen. Best noted, the choice is far from ideal as the data distribution in the orebody is quite poor.

Figure 31 ‘TILL WINDOWS’ for both zones (ANDO, LEFT; LOW, RIGHT); all viable option are circled.

After modelling the selected graphs (cumulative graphs will be shown further below), the direction of

maximum continuity was selected (see Table 12). These directions will play a crucial role in determining

the direction of maximum continuity along the semi-major axes of the ore bodies. The secondary

variogram maps were selected from the

‘VARIOGRAM MAP’ option in the toolbar.

Using the same procedure as used for

MZ1ANDO MZ2LOW

Max Continuity Direction 168.0981 134.8460

Table 12 Direction of maximum continuities for

variographs along MAJOR AXIS.

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selecting the variographs for the major axes above, the following graphs in Figure 32 were selected. The

only criterion change was that the graph had to be in close proximity to the ‘RED LINE’ on the variogram

map (direction perpendicular to the direction of maximum continuity determined for major axis).

Figure 32 Semi-Major axis variograms for MZ1ANDO (LEFT) and MZ2LOW (RIGHT) zones.

The results for each model for the semi-major axis is tabulated below in Table 13.

After modelling along the semi-major

axes, the variograms were extracted

where an uniform model was created to

model both of the variograms (Major and

Semi-Major) along with a variogram

modelling the minor axis. It was ensured

that the variogram for the Semi-Major axis

was to the left of the variogram for the

major axis. The results can be seen below

in Figure 33, in the form of an ‘ALL ORIENTATIONS’ graph as well as the graphs for each axis for MZ2LOW.

Figure 33 Major, Semi-Major, and Minor variographs for MZ2LOW (TOP); ALL ORIENTATIONS

graphs for MZ1ANDO (LEFT) and MZ2LOW (RIGHT).

Nugget Structure Sill Range

MZ1ANDO 0.000000 1 0.739473 55.181

2 0.261747 239.469

MZ2LOW 0.000000 1 0.823450 53.271

2 0.175181 217.855

Table 13 Summary of spherical models used for

Semi-Major variograms for both solids.

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Finally, to conclude this portion of the project, the search ellipses were generated using the variogram

model. However, visualization of the ellipsoids was necessary prior to plotting. Using the VISUALIZER

function in GEMS, each ellipsoid was previewed and subsequently plotted, as seen in Figure 34.

Figure 34 Variogram-computed search ellipsoids for MZ1ANDO (TOP) and MZ2LOW (BOTTOM).

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BLOCK MODEL SET-UP To begin the analysis to determine total amount of ore serves, an additional two block models need to be

made. The first model will be for the true Inverse-

Distance model, and the other will be used for Ordinary

Kriging. These workspaces are shown in Figure 34.

Figure 35 All 3 block models that will be used to

determine the total ore reserves.

The sizes and origin for both of these block models is

the same as the dimensions defined for ‘BlockModel’. Using (1300405, 95605, 650) as the origin, with no

rotation, with the block size of (15,15,10) (column, row, level size), 51,675 blocks were created using 53

columns, 65 row, and 15 levels for both block models. After both workspaces were created, the next step

was to initialize both model according to the geology. The entire model was, first, initialized to QUARTZ

(WASTE rock), then the TOPO solid was imported after which the area above the surface was initialized to

AIR. Upon finishing this task, the solids were imported and updated according to ROCK TYPE and initialized

based on their rock codes. The results can be seen in Figure 36.

Figure 36 Surface above the TOPO initialized to AIR (LEFT); Cross-section of the fully-initialized

BLOCKINVERSE block model (UPPER RIGHT); MZ2 Solid (LOW) updated according to Rock Type and Code

(LOWER LEFT).

After fully initializing the block model according to the ROCK TYPE, the density attribute profile was then

updated according to the ROCK DENSITIES. Turning on the DENSITY attribute transforms the block sizes

according to the density of the rocks. The same steps were then repeated for the BLOCKKRIGING block

model.

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INTERPOLATION The next step in determining the total mineral resources have to do with resource interpolation. GEMS

uses statistical estimation to determine (or ‘INTERPOLATE’) the average block grade for each block in the

model in accordance with the search ellipses created (using CU-MZ1, CU-MZ2 for BlockModel,

CU_MZ1AN, CU_MZ2LOW for BLOCKINVERSE) and the built-in Ordinary Kriging Formula (KRIGING). In

order to interpolate, however, interpolation profiles must be created. Therefore, 3 profiles were created,

one for each model, as seen in Table 14: CU-ID, KRIGING, PAMZ-ID.

CU-ID KRIGING PAMZ-ID

Method Inverse Distance (True) Ordinary Kriging Inverse Distance (True)

ID Power 2 N/A 2

Search Ellipses

CU-MZ1, CU-MZ2 CU_MZ1AN, CU_MZ2LO

CU_MZ1AN, CU_MZ2LO

Table 14 Summary of steps taken in creating each INTERPOLATION profile.

Once the interpolation profiles were created, the interpolations were carried out on each block model.

Table 15 reports the results generated from the INTERPOLATE AND REPORT function.

BLOCK MODEL Rock Type: 20 (ANDO) Rock Type: 30 (LOW)

Mean Block Grade

Variance Median Mean Block Grade

Variance Median

BlockModel 1.07319 0.43432 0.29140 0.59656 0.43432 0.29140

BLOCKINVERSE 1.10762 0.32451 0.92579 0.45632 0.14661 0.21241

BLOCKKRIGING 1.11450 0.32451 0.92579 0.46156 0.14661 0.21241

Table 15 Summary of INTERPOLATION REPORTS for each Block Model.

To display the results generated from INTERPOLATION calculations, a new grade profile was created. Using

CU_CUT point areas for both MZ1 and MZ2, basic statistics were generated to determine the grade ranges

with the most number of samples. Using these ranges, a new COLOR profile was created and used in the

CU attribute profile. This range, CUST_GRD, was adjusted to the cut-off grade of the ore body of 0.67, and

the result can be in Figure 36.

Figure 36 CUST_GRD color profile was created to display the grade ranges with most samples.

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SURFACE ELEVATION GRIDS (SEG) Now that the blocks have been assigned grades and a color profile exists to display them, the PITS can be

imported into each respective block model and SEGs (Surface Elevation Grids) can be made. First, the PIT-

BM1 was imported into the BlockModel and an SEG was created, as seen in Figure 37. The background

elevation of 565 feet was chosen by averaging

the highest and the lowest points of each pit

Figure 37 Vertical cross-sections were

used to determine the average elevation of

each pit, which was calculated to be roughly

565 feet (LEFT); The imported PIT-BM1 was

converted into a SEG to display the

topography of the surface to the bottom of

the pit and how the ore “sits” within the pit

(RIGHT).

The same process was then subsequently

repeated for all of the other pits. Since the size of each pit roughly the same, the same background value

of 565 feet was used. The SEGs generated for the pits in each block model can be seen below in Figure 38.

Figure 38 SEGS for PIT-BM1 SEG (LEFT), PIT-INV (MIDDLE), PIT- KRIG (RIGHT).

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RESOURCE ESTIMATION GEMS calculates the reserves based on levels. It averages the grade of each block on a level and provides

the totals for reserve estimation based on levels. When the block models were created, there were 15

levels created, as seen in Figure 39. Since the block model pits the ore body relatively well, all of the levels

will be used with each block on every level representing a 10m block. For a small porphyry deposit, the

size of this block is far too large (a more realistic block size would 3m x 3m x 3m). However, this fact poses

a far more significant problem in terms of mine optimization, as opposed to mine reserve estimation.

Figure 39 All 15 levels for

the PLAN VIEWS (LEFT) and the

GRADE GROUP profile (RIGHT)

will be used in creating the

VOLUMETRIC PROFILE.

Using the newly created levels

(PLAN VIEWS), the VOLUMETRIC

PROFILE can be created to report

the reserves. However, before

the profile can be created, both

the ROCK GROUP and GRADE GROUP profiles have to be created. The ROCK GROUP profile was created

to help the software identify and separate the ore from the waste. The GRADE PROFILE, as seen in Figure

39 above, helps the identify ore reserves that meet a certain cut-off. For this deposit, a break-even cut-

off grade of 0.67 was chosen. The REPORT FORMAL profile was also created and was adjusted to allow to

report all values in imperial units (feet, tons, etc.) Using this information, the VOLUMETRIC PROFILE was

created. Some of the key selections that were made in the reporting process are highlighted below:

- Rock Codes – all rock codes will be extracted from the Block Model

- Excavation Surfaces – reserves can only exist between the TOPO and the PIT

- All 15 planes (level) were chosen to be used for all block models

- Gaussian needle pattern was used with a 3x3 needles per cell integration level

- Reporting-Group Profile: ALL

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Using this profile, reserves were generated for each model and the results are tabulated in Table 16.

BlockModel BLOCKINVERSE BLOCKKRIGING

ANDO (20)

Ore Tonnage (t x 1000)

1,518.489 1,522.964 1,522.964

Cu Product 1,596,211.6 1,690,537.2 1,698,540.6

Cu Grade 1.05 1.11 1.12

LOW (30)

Ore Tonnage (t x 1000)

2,515.138 2,504.523 2,515.338

Cu Product 1,563,996.3 766,633.3 777,172.8

Cu Grade 0.62 0.31 0.31

Total

Total Tonnage (t x 1000)

4,033.627 4,027,487 4,038.302

Cu Product 3,160,207.9 2,457,170.6 2,475,713.5

Overall Cu Grade 0.78 0.61 0.61

Variance 0.212 0.237 0.244

Table 16 Resource Estimation for each block model.

Table 16, above, is the net summary of this entire project. By determining the totality of the reserves

within the given ground and the drillhole samples provided, it was determined that the approximate total

reserves amount to between roughly 2.5MT of Copper at an approximate grade of 0.61%-Cu. The numbers

vary across the board depending on the model used. The block model ‘BlockModel’ estimates the reserves

to be far higher than the more accurate models, BLOCKINVERSE and BLOCKKRIGING, at greater than

3.0MT with a pit-grade of 0.78%-Cu. This variance is a result of the type of estimation method used. The

search ellipses used for BLOCKINVERSE and BLOCKKRIGING were based upon the variograms built upon

the drill hole compositing data, and hence the results from both of these models are likely to be more

representative of actual tonnage of copper in the soil.