24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2018
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, 2018-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 1.1–1.8); 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, anisotropy); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV/IRR and cut-off grade methodology); Gentry & O'Neil, Mine Investment Analysis (smelter/refining contract terms, net smelter return, taxation and risk); Guilbert & Park, The Geology of Ore Deposits, and Evans, Ore Geology and Industrial Minerals (VMS/SEDEX and porphyry deposit models); 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.
Directional (anisotropic) variograms map how spatial continuity CHANGES with orientation — computing γ(h) separately along a fan of azimuth/dip directions and comparing their ranges/sills reveals the deposit's dominant trend (e.g. a longer range along strike than across strike identifies the strike direction as the direction of maximum continuity, directly informing both drill-grid design and the search ellipse orientation used in kriging).
3.3.1 Tolerance (included angle) is the angular half-window (e.g. ±22.5°) around the nominal search direction within which a pair of points is still accepted as belonging to that directional variogram — without it, almost no pairs would lie EXACTLY on the nominal azimuth and every directional lag class would be empty.
3.3.2 Band width is a PERPENDICULAR distance limit that caps how far off-axis (laterally) an accepted pair may lie, independent of the angular tolerance — it prevents the angular tolerance cone from admitting distant, laterally-offset pairs at long lag distances that the angular criterion alone would still accept.
3.3.3 Anisotropy is the directional dependence of the variogram's range and/or sill, reflecting the deposit's own geological fabric (bedding, structural trend, alteration elongation); GEOMETRIC anisotropy (same sill, different range by direction) is corrected by an affine transform of coordinates, while ZONAL anisotropy (different sill by direction) requires a more general nested model.
3.3.4 Azimuth 90°/dip 0° and azimuth 270°/dip 0° describe exactly OPPOSITE ends of the same horizontal line (a purely horizontal vector reversed is still the same line, just traversed the other way). Since the semi-variogram is computed from |z(x)−z(x+h)|, it is symmetric under h → −h by construction (γ(h)=γ(−h) always) — so these two directions sample the IDENTICAL set of point pairs and must give the identical variogram, which is simply the general symmetry property, not a special geological result.
3.3.5 At a non-zero dip, reversing azimuth by 180° while KEEPING the same sign of dip does NOT reverse the 3-D vector — the true negation of "azimuth 90°, dip +45° (down)" is "azimuth 270°, dip −45° (up)", not "azimuth 270°, dip +45° (also down)". "Azimuth 90/dip 45" and "azimuth 270/dip 45" are therefore two genuinely DIFFERENT inclined directions (both plunging downward, but toward opposite horizontal quadrants), not a symmetry pair, so they can show different ranges/sills whenever the deposit's grade continuity has its own preferred PLUNGE direction (e.g. a shoot or fold hinge plunging preferentially one way) — the dip-0° case is the special (and only) case where azimuth-reversal alone reproduces the true vector negation.
