24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 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-May. 3 hours duration; closed book, with one handwritten 8.5×11 in. reference sheet (both sides) permitted; only an approved Sharp or Casio calculator allowed. Question 1 is compulsory (40 marks, parts 1.1–1.9); 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); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, cut-off grade theory, incremental analysis); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, cash flow/risk, smelter contract terms, NSV/NSR); SME Mining Engineering Handbook, 3rd ed. (ore deposit models, mineral exploration/evaluation stages, equipment utilization); O'Hara, T.A., “Quick Guides to the Evaluation of Orebodies,” CIM Bulletin, Feb. 1980 (parametric capital-cost estimating); CIM Definition Standards for Mineral Resources and Mineral Reserves / National Instrument 43-101 (resource/reserve classification and reporting).
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.
In the source sketch, sample b sits closest to the block, c at an intermediate distance, and a the farthest of the three — used qualitatively below since exact coordinates and the variogram parameters are not given numerically.
4.3.1 Sum of sample weights. For ORDINARY kriging the Lagrange-multiplier-constrained system explicitly enforces $$\sum_j w_j = 1$$ exactly, unconditionally, regardless of sample configuration — this is what lets OK remain unbiased WITHOUT assuming a known stationary mean (unlike simple kriging in Question 4.2).
4.3.2 Effect of block size. As the estimated block grows larger, it is being averaged against MORE of the internal point-to-point variogram structure (the average γ between the block and each sample, and among points within the block itself, both increase toward the sill), which SMOOTHS the estimate (block estimates carry less extreme high/low grades than point estimates — the well-known volume-variance / support effect) and REDUCES the kriging variance relative to a point estimate at the same location, because averaging over a larger volume cancels more of the short-scale (nugget-dominated) noise.
4.3.3 Negative weights. A sample can receive a negative OK weight when it is nearly “shielded” by a closer sample lying almost on the same line to the block (the SCREEN EFFECT) — the system detects that the closer sample already carries almost all of the shielded sample's information, and assigns the more distant, redundant sample a small negative weight to correct for double-counting through the closer one, especially when the variogram model has a small or zero nugget. A negative weight is not necessarily wrong mathematically, but a large negative weight risks producing a grade estimate outside the range of the input data (a physically implausible negative or extreme grade) and inflates sensitivity to any single sample's error; the practical remedies are to re-examine and, if needed, add a small nugget effect to the model (dampens the screen effect), restrict the search to fewer, better-distributed samples, or clip/reset an unreasonably large negative weight to zero and renormalize the remaining weights to sum to 1.
