Question 11 of 19: Geostatistics – Advocates and Detractors

Question 3.4: Geostatistics – Advocates and Detractors (5 marks)

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3.4.1 — Deposit-style suitability. Geostatistics (variogram-based kriging) performs best on deposits with a diffuse, gradational grade field sampled on a fairly regular grid — the classic case being disseminated porphyry or epithermal deposits, where grade varies continuously and a stationary variogram model is a reasonable description across a large volume. Advocates would argue geostatistics still applies to lenticular/vein deposits provided the domain is correctly restricted to the vein envelope and a strongly anisotropic variogram is used; detractors counter that narrow, structurally-controlled vein/lens mineralization is often too discontinuous and too poorly/irregularly sampled (underground drilling from drifts, not a regular surface grid) for a stable variogram to be fitted at all, and that simpler polygonal or sectional methods honouring the vein geometry directly can outperform a poorly-conditioned geostatistical model in that setting.

3.4.2–3.4.4 — IDP vs. kriging as a function of drill spacing. At wide drill spacing relative to the selective mining unit (SMU), neither inverse distance power (IDP) nor ordinary kriging can resolve grade variability smaller than the sample spacing itself — both methods necessarily smooth across (and therefore "miss") individual high-grade SMUs that happen to fall between drill holes, so the two methods converge to similarly inaccurate, over-smoothed "mineable" reserve estimates despite kriging's theoretical statistical optimality; the estimation-method choice stops mattering once data density is the binding constraint. At close drill spacing (dense infill or blast-hole data, spacing comparable to or smaller than the SMU), both methods are constrained by nearby, locally-representative data and converge toward each other again in the immediate vicinity of a sample — the two methods differ most in the intermediate data-density regime, where kriging's use of the actual spatial correlation structure (rather than IDP's arbitrary distance-power weighting) gives it a genuine, demonstrable edge in local accuracy.

3.4.3 — Breadth of the geostatistical toolkit. Beyond simple ordinary kriging, geostatistics offers indicator kriging (probability of exceeding a cut-off), co-kriging (using a correlated secondary variable), simple/universal kriging (different stationarity assumptions), and conditional simulation — a substantially richer set of tools than IDP's single distance-weighting scheme, letting a practitioner match the method to the actual statistical behaviour of the data (e.g. skewed grade distributions, trends, multiple correlated variables) rather than applying one fixed rule everywhere.

3.4.5 — Conditional simulation for grade control. During active production/grade-control periods, conditional simulation generates many equally-probable realizations of the grade field, all honouring the actual sample data at sample locations, rather than the single smoothed "best estimate" that kriging alone produces. This gives mine planners a realistic sense of the true local grade variability (not just the mean) at SMU scale — critical for ore/waste dig-line decisions and short-term scheduling — because a kriged block average systematically understates how much any individual SMU inside that block could deviate from the mean, exactly the smoothing effect the earlier sub-parts describe as the source of "missed" high-grade material at wide drill spacing.