24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2017
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, 2017-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 1.1–1.6); candidates then select THREE of the five optional Questions 2–6 (20 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, transportation logistics); SME Mining Engineering Handbook, 3rd ed. (cost-estimating relationships, mineral exploration/evaluation stages, ore reserve classification); Evans, An Introduction to Ore Geology and Guilbert & Park, The Geology of Ore Deposits (ore deposit models); 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) Included angle (angular tolerance). When computing an experimental (directional) variogram, sample pairs are grouped by their separation direction, but real drilling rarely produces pairs at an EXACT bearing. The included angle is the half-width of the angular window (e.g. ±22.5° about the target direction) within which a pair is still accepted into that directional bin – wider tolerance gathers more pairs (more stable statistics) at the cost of blurring genuinely different directional structure together.
(b) Band width. A perpendicular distance limit applied alongside the angular tolerance: even within the accepted angle, pairs are excluded once their perpendicular offset from the target directional line exceeds the band width. This prevents the angular tolerance cone from sweeping in pairs that are, in absolute terms, far off the intended search line at long lag distances (where an angular tolerance alone would otherwise admit an ever-widening physical corridor).
(c) Anisotropy. The condition where the variogram's range (and/or sill) genuinely differs by direction – e.g. continuity extends much farther along a mineralized structural trend (strike/plunge) than across it. Geometric anisotropy (same sill, different range by direction, correctable by an anisotropy ellipse/affine stretch) and zonal anisotropy (different sill by direction, requiring a nested structure with a direction-dependent range that goes to infinity in the low-variance direction) are the two standard forms modelled in practice.
