24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A4 Mine Valuation and Mineral Resource Estimation, 2013-May. 3 hours duration; one handwritten 8.5×11 in reference sheet permitted (not an open-book exam); only approved Sharp or Casio calculators allowed. Question 1 is compulsory (40 marks, parts 1.1–1.7); candidates then select FOUR of the six optional Questions 2–7 (15 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, volume–variance relations); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV and cut-off grade methodology, mineable reserves, selective mining units); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration and evaluation stages, ore reserve classification).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Polygonal (nearest-neighbour / area-of-influence) method. Each sample is assigned a zone of influence (a polygon, or a fixed-radius circle/rectangle in 3-D a prism) built from perpendicular bisectors to its neighbours, and every block or tonne inside that polygon is assigned the sample's grade directly, unweighted by distance. Merits: extremely simple, transparent, requires no variogram, and is defensible as a first-pass, conservative reserve for a very early-stage deposit with sparse, irregular drilling. Weaknesses: it produces abrupt grade discontinuities at polygon boundaries, ignores the grades of nearby samples entirely (no smoothing), is highly sensitive to a single erratic high or low assay, and gives no measure of estimation error – it is now considered obsolete for anything beyond a scoping estimate.
Inverse power (distance) weighting, IDW. Block grade is a weighted average of all samples within a search neighbourhood, weight wi proportional to 1/dip (commonly p = 2 or 3). Merits: smoother and more realistic than polygonal, easy to compute, requires no variogram modelling, and the power p gives a tunable knob between "polygonal-like" (high p) and "over-smoothed" (low p) behaviour. Weaknesses: the weighting exponent is chosen subjectively rather than derived from the deposit's own measured spatial continuity, it takes no account of sample clustering (a tight cluster of samples can dominate the weighted average even though they carry largely redundant information), and – like polygonal – it produces no estimation-error/confidence measure.
Ordinary Kriging, OK. A generalized-least-squares linear estimator whose weights are derived directly from the fitted variogram, subject to the constraint that weights sum to one (making it locally unbiased without requiring the mean to be known). Merits: statistically optimal (minimum estimation variance) for a given variogram model, automatically de-clusters redundant close samples (they receive less combined weight than an isolated sample of equal value), and delivers a kriging variance that can be mapped and used for confidence classification (Measured/Indicated/Inferred). Weaknesses: requires a defensible variogram (needs enough data to model, and is sensitive to modelling choices), is computationally heavier, and conditional bias/smoothing (regression to the mean) can still distort local grade–tonnage curves used for selective mining, especially with a wide search neighbourhood.
