The ultimate objective of all exploration is to predict, with the greatest accuracy possible, the shape, distribution, and concentration of ore before mining begins.  This involves the creation of a geologic model.  The purpose is to use a three dimensional model to calculate the quantity and quality of the ore deposit.  Modeling looks at the three dimensional perspective or an ore deposit, by combining drill section information with surface information.  The information is examined along both horizontal slices (plan maps) and vertical cross sections (drill sections).  The geologic model is one interpretation of the subsurface.  Different interpretations can lead to drastically different results (Figure F15), so great care must be taken in choosing the best model. 

Part of the purpose of ore deposit modeling is to predict the geology.   This is done by extrapolating outward from known sample data into areas which are not yet drilled.  Modeling involves prediction of the grade (concentration) and tonnage (weight) by using a geometric model.  Volume formulas for the specific geometric shapes can be used to calculate the volume.  For example, a vein deposit could be estimated using a “slab” shape, where:   volume =  length  x  width  x  thickness.

Geologic modeling for mine planning is typically based on a large amount of drill data (close-spaced drill holes).  Drill holes are generally placed along a parallel drill lines, to make the calculation of the volume easier.  A square grid is convenient, but not essential.  The chance for misinterpretation is greatly decreased by more drilling, but this is generally also followed by some type of excavation, usually trenching at the surface or drifting underground, to further decrease the risk or error in estimating the resource. 

Tonnage and grade calculations are done using geostatistical methods, which are most easily done with a computer. However, even the computer programs require input of geologic model before a calculation is made.  After the volume calculation is complete, the volume is converted to weight by multiplying the volume by the “tonnage factor”.  The tonnage factor states the density of the ore and host rock, in terms of cubic feet per ton.   Various methods can be used to calculate the grade of the material, but simple arithmetic averaging of the sample values usually provides a reasonably good approximation.

Figure 15:   A)  Drill intercepts interpreted to represent large, laterally continuous ore bodies.  B)  Same drill intercepts interpreted to represent discontinuous, small scale ore bodies.

Block Models

Block models are the simplest of all models which can be used (Figure F16).  The method is as follows:

                 

  

A                                                                                  B

Figure F16:   A)  Block model based on geologic interpretation of a dipping ore body.  The volume and grade of each block is summed for the total.  B)  Block model based on vertical drill section, with ore blocks A, B, C and D, based on drill intercepts.

Polygon Models

The polygon model is more appropriate for scattered, or bulk mineable deposit.  The polygon model establishes a polygon shape around each drill hole (in plan view), which is within a specified “area of influence”, or maximum distance, from each hole (Figure F17).  The boundaries of each polygon correspond to the mid-point between two adjacent drill holes.  Ore intervals are set to a specified  thickness, and established in advance.  The intervals, sometimes referred to as “benches” are chosen to correspond to bench mining elevations.  The volume of each polygon can then be determined, although this is generally done with sophisticated computer programs. 

The average value for the polygon is calculated for each polygon by deriving the arithmetic mean value for all the values within each polygon’s depth range (thickness).  Then the weighted average grade can be determined in the same manner as used for the block model, by summing the tonnage of all polygons for a specified drill hole, and then dividing this into the sum of the individual resource calculations (grade x tonnage) for each block.

Triangular Models

The triangular method is similar to the polygonal method.  It calculates the volume of a triangular-shaped prism formed between three adjacent drill holes (Figure F18).  Like the polygonal method, bench levels are specified.  Grade determinations for the prisms are determined differently than the polygon model.  In the triangular model, the grade is determined by averaging the value of the three values at the corners of each triangle.