24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2014
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, 2014-Dec. 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); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration/evaluation stages, ore reserve classification); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).
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.
(a) Support. The size, shape and orientation of the physical volume a sample or block represents (e.g. a drill core's diameter×length vs. a 10 m production block). Variance decreases as support increases (the volume–variance relationship), so a variogram fitted on point/core support must be corrected before it can be used to krige block-scale grades — ignoring support mismatch systematically over- or under-states block variance.
(b) Co-variogram. The spatial covariance function C(h) = Cov[Z(x), Z(x+h)], related to the variogram by γ(h) = C(0) − C(h) for a stationary (second-order) random function. It is used directly in the kriging system (as in Question 4) because kriging equations are most naturally written in terms of covariance rather than variogram values.
(c) Correlogram. The standardized covariance, ρ(h) = C(h)/C(0), bounded between −1 and 1 like an ordinary correlation coefficient. It is used to compare spatial continuity across variables of different units or magnitudes (e.g. comparing the spatial structure of Cu grade to Au grade on a common, dimensionless scale).
(d) Trend. A large-scale, systematic (non-random) drift in the mean grade across the deposit (e.g. grade increasing with depth toward a feeder zone), which violates the stationarity assumption ordinary kriging requires. When a trend is present it must be modelled and removed (or handled via universal kriging/kriging with a trend model) before the residual variogram can be validly fitted and used for estimation.
(e) Variogram map. A 2-D (or 3-D) map of experimental variogram values computed over a grid of lag vectors in every direction, used to visually diagnose anisotropy — directions of shorter range (faster rise to sill) appear as "tighter" contours, directions of longer range as "stretched" contours — guiding the choice of principal anisotropy axes before fitting directional variogram models.
