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.
Ordinary kriging estimates the block grade as a weighted linear combination of the two samples, $$Z_B^*=w_1Z_1+w_2Z_2$$ minimizing estimation variance subject to the unbiasedness constraint w1+w2=1. Introducing a Lagrange multiplier μ to enforce that constraint, the general 3×3 system is: $$\begin{bmatrix}C_{11}&C_{12}&1\\C_{21}&C_{22}&1\\1&1&0\end{bmatrix}\begin{bmatrix}w_1\\w_2\\\mu\end{bmatrix}=\begin{bmatrix}C_{1,B}\\C_{2,B}\\1\end{bmatrix}$$ where Cij is the covariance between samples i and j (from the fitted variogram/covariance model at their separation distance), and Ci,B is the average covariance between sample i and the block B (averaged over the block's discretization points). The system extends directly to n samples by adding one row/column per sample: the top-left n×n submatrix is always the sample–sample covariance matrix, the last row and column are always 1's (except the 0 in the bottom-right corner), and the right-hand vector's last entry is always 1, enforcing Σwi=1 regardless of how many samples inform the block. Solving the system simultaneously yields the weights that minimize estimation variance subject to that unbiasedness constraint, which is exactly what "ordinary" (as opposed to "simple") kriging means — simple kriging omits the constraint row/column entirely and instead assumes a known, constant mean.
