NivaarExam PrepOfficial exam papers ↗

24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2013

Question 2 of 13: The Semivariogram – Axes, Nugget and Range

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A4 Mine Valuation and Mineral Resource Estimation, 2013-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 1.1–1.7); 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, selective mining units); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration and evaluation stages, ore reserve classification).

Question 1.2: The Semivariogram – Axes, Nugget and Range (6 marks)

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.

Lag distance hγ(h)Sill C₀ + CNugget C₀Range a
Fig. 1.2 – Schematic semivariogram: experimental points (blue), fitted spherical model (red curve), with nugget C0, sill C0+C and range a labelled.

Axes. The X axis is lag distance h, the separation between pairs of sample points, in the same length units as the drilling/sampling grid (metres in most Canadian metric mine grids, occasionally feet on legacy imperial grids). The Y axis is the semivariance γ(h), the average of one-half the squared difference in grade between all sample pairs separated by lag h; its units are the SQUARE of the grade variable's units (e.g. (%Cu)² for a copper deposit, (g/t Au)² for gold), which is why practitioners often normalize by the variable's variance (a "relative" or "standardized" variogram) before comparing deposits with different grade units.

Nugget effect, C0. The nugget is the Y-intercept of the fitted model – the semivariance value the curve appears to jump to as h → 0 even though γ(0) is defined to be exactly zero. In simple terms it represents variability that is uncorrelated at any sampling distance actually drilled: assay/analytical error, sample-preparation error, and true geological variability occurring at a scale finer than the closest drill-hole spacing (the "nugget" name comes literally from coarse, erratic gold nuggets that can sit in one half-core sample and not its immediate neighbour). A large nugget relative to the sill means a large fraction of the deposit's variance can never be explained by spatial position alone, and estimation variance stays high no matter how tight the drilling.

Range, a. The range is the lag distance at which the fitted curve first reaches (or asymptotically approaches, for a Gaussian/exponential model) the sill. In simple terms it is the distance beyond which two samples are no longer spatially correlated – the "zone of influence" of a single drill hole. Sample pairs separated by less than the range still carry useful information about each other's grade; pairs separated by more than the range behave as statistically independent observations. The range is what directly sizes an appropriate drill spacing and the search radius used in a kriging or inverse-distance estimation pass.