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.
Given. C11=C22=0.75, C12=C21=0.38, C1,B=0.425, C2,B=0.455.
Substituting into the general 3×3 ordinary-kriging system from Question 4.1: $$\begin{bmatrix}0.75&0.38&1\\0.38&0.75&1\\1&1&0\end{bmatrix}\begin{bmatrix}w_1\\w_2\\\mu\end{bmatrix}=\begin{bmatrix}0.425\\0.455\\1\end{bmatrix}$$ This is the exact system the exam states was inverted/solved to give the weight vector used in Questions 4.2.5–4.2.6. The top-left 2×2 submatrix is symmetric (C12=C21=0.38, since covariance between two points doesn't depend on direction), which is why the two sample-weight equations are themselves symmetric before the constraint row/column is added; the third row (1, 1, 0) and third entry of the right-hand vector (1) are the same for every ordinary-kriging system regardless of the covariance values, since they encode the unbiasedness constraint Σwi=1 rather than any deposit-specific data.
