Print3.2.2: The Concept of an Area or Volume of Influence
Procedurally, we do this by calculating an area and volume of influence for each hole. The weighted average for the grade, or whatever characteristic is of interest, is obtained by multiplying the value of that characteristic by the volume of influence; and then summing the products and dividing the sum by the sum of the weighted volumes.
Mathematically, this is expressed as:
where = the % grade for the nth hole, and = volume of influence for the nth hole.
Let’s continue with the example by adding the thickness at each hole and inserting columns for the calculated values.The area of influence is the area surrounding each hole, and if the holes are spaced at 400’ intervals, then the area represented by each hole is 1.6x 105ft2.
| Hole # | Area of Influence, ft2 z 103 | Thickness, ft | Volume of Influence, ft3 x 106 | Grade, % | Weighted Grade, %-ft3 x 106 |
|---|---|---|---|---|---|
| 1 | 1600 | 40 | 64 | 2 | 128 |
| 2 | 1600 | 45 | 72 | 3 | 216 |
| 3 | 1600 | 70 | 112 | 4 | 448 |
| 4 | 1600 | 54 | 86.4 | 3 | 259.2 |
| 5 | 1600 | 58 | 92.8 | 4 | 371.2 |
| 6 | 1600 | 70 | 112 | 5 | 560 |
| 7 | 1600 | 42 | 67.2 | 2 | 134.4 |
| 8 | 1600 | 56 | 89.6 | 3 | 268.8 |
| 9 | 1600 | 65 | 104 | 4 | 416 |
| Sum | 14400 | 800 | 2801.6 |
The average grade of the orebody is the weighted grade, 2801 x 106 %-ft3 divided by the volume of influence, 800 x 106 ft3, which equals 3.5%.
Note that the average grade is NOT the arithmetic average of 3.33%. A tenth of a percent error in the grade is quite meaningful. It is important to calculate weighted rather than arithmetic averages in all cases.
In the foregoing example, we had a convenient simplification: the area of influence was the same for each of the holes. In practice, this would rarely be true because the property boundaries are generally irregular and the holes are most likely not spaced evenly. In these common situations, we need a way to determine the influence that a given hole should have in our estimation of the reserve.
Defining an Area or Volume of Influence for a Drill Hole
Consider the following property.
The new challenge here is to determine the area of influence for each hole. Once we have done that, we can continue by using the same procedure that we followed for the previous example.
Each hole is likely to have a different value for the characteristics of interest, and for this discussion let’s say that we are looking at grade. How far from the hole should we assume that the grade of that hole applies? Halfway to an adjacent hole? What if the grade in the adjacent hole is significantly different? Should that alter where we draw the area of influence? Perhaps, we should use a scheme that says the value at the hole decreases inversely as we go further from the hole? In fact, many deterministic and statistical methods have been developed over the years, and some provide better results than others for certain types of ore bodies. Let's take a look at a few methods for determining an area of influence for each drill hole.