Rare earth drilling targets: Kriging variance at 40% — Drill or Delay?

This guide explains how to interpret a 40% relative kriging variance at rare earth drilling targets.

It shows when to drill now and when infill drilling will not cheaply fix sampling-design failure.

What 40% Kriging Variance Actually Means

Kriging variance is not a measure of grade, but a measure of estimation uncertainty. As noted in Wikipedia's geostatistics overview, geostatistical techniques rely on random-function models to quantify that uncertainty, and for ordinary kriging the variance at an unsampled location is computed strictly from the variogram model and the sample locations alone. This means a 40% relative kriging variance can be calculated before any new assay values are known, since the actual grade numbers do not enter the variance calculation at all.

For the purpose of this section alone, the defining form is σ²_k = sill − Σλᵢγ(hᵢ). The kriging weights λᵢ are chosen to satisfy unbiasedness and minimize variance, so the subtraction represents how much of the total sill variance is accounted for by the spatial correlation captured through the sample pairs. A 40% of sill value is the residual left after that cancellation. The immediate check is not the magnitude of the mineralization, but which input is deficient: the sample geometry, the modeled nugget effect, or the modeled range of correlation.

Because of this, two targets with the same variogram can produce different kriging variances solely from drill spacing. A tighter cluster can pull more correlation into Σλᵢγ(hᵢ), while a block wiSamples located only at the edge of the search neighborhood can leave a much larger residual. The geometry of the search neighborhood is therefore just as much a part of the 40% figure as the variogram itself, and it can be inspected without looking at a single new assay.

To trace that residual, decompose it by testing the neighborhood against the model: first see how much of the correlation is lost to the nugget, then see how many samples fall within the correlated distance. As a direct check for this decomposition, if the search neighborhood reaches fewer than 3 samples within 0.5× the modeled range, the geometry is the likely driver. If the neighborhood is already filled to that extent but the residual remains high, the modeled nugget is the likely driver. This distinction is the only way to know whether the 40% figure points to a lack of samples or to a lack of correlation to capture in the first place.

How to Diagnose the Variance Source

Before committing to any new holes, the uncertainty must be broken down by its source. This section alone provides the nugget-vs-range decomposition workflow with the 0.5× range sample-count check. Begin with Step 1: refit the experimental variogram on existing assays for the TREO variable. Do not inherit a curve from a previous report. Instead, record your own model parameters: the nugget/sill ratio and the range. Treat both as site-specific, as even a small change to lag selection can shift them without adding a single new assay.

Move to Step 2 with a strict neighborhood audit for each drill target. Count thesamples within half the modeled range. If fewer than 3 fall inside it, the estimate is dominated by extrapolation. With such a sparse neighborhood, the geometry itself drives uncertainty up, and infill holes that fill that gap will sharply reduce variance. In that narrow case, the right action is to drill. This checks support, not visual continuity from a single cross-section.

Step 3 covers the opposite failure mode. If the sample count passes the check but uncertainty remains high, the nugget effect dominates. A high nugget-to-sill ratio points to short-scale variability that cannot be resolved by spreading more holes across the same neighborhood. For that exact situation, do not blanket the target with infill. Instead, twin an existing hole with a 5 m downhole split to test assay repeatability at that location before expanding the pattern.

These three steps must be run in order, and only for the domain and TREO variable that were actually estimated. As Wikipedia's geostatistics article notes, spatial uncertainty is quantified with random-function models, but the parameters that drive action must come from your own experimental variogram. Without that discipline, a geometry fix gets mistaken for a repeatability fix, and the wrong drilling decision becomes the most expensive one.

Drill Now vs. Delay: Options Compared

With a variance-source diagnosis in hand, the question shifts from magnitude to response. This section alone compares the three response strategies (infill, twin, defer) agaIn-situ variance-source diagnosis. When the uncertainty is geometry-driven, infill drilling is the only one of the three that attacks the root cause directly: placing new holes inside the modeled range expands the neighborhood of support, so each hole has a realistic chance of reducing kriging variance for the blocks it influences. The value of that hole is tied to location relative to existing samples, not to drilling more holes blindly across the target.

When the diagnosis instead points to a nugget-driven source, the problem is short-range repeatability, not spacing. Adding more holes at the same grid may simply reproduce the same local scatter with no meaningful gain. In that case, a twin-hole sample is the more disciplined first action. By drilling a second hole in close proximity to an existing one for direct comparison, it is possible to learn whether the deposit's short-range chaos is severe enough to make any broad infill program uneconomic before committing to a pattern of new holes.

There is a third path: defer. If the variogram itself is unreliable due to too few pairs per lag bin, drilling to fill a grid only solidifies a search neighborhood built from a weak model. In line with the random-function view of spatial uncertainty described by Wikipedia's Geostatistics, the structure of dependence must be credible before its effect on uncertainty can justify new drilling. Deferring to stabilize that structure prevents spending capital on a response that cannot be targeted correctly.

These three are not interchangeable. Infill attacks geometry, twin sampling attacks short-range repeatability, and defer attacks model reliability. The correct action is determined by which of those has failed, not by treating high uncertainty as an automatic call to drill.

Costs of Being Wrong in Each Direction

At a fixed 40% relative kriging variance, the cost of being wrong is asymmetric: drilling into the wrong uncertainty type spends cash that cannot be recovered, while delaying the right uncertainty type spends calendar time that may not be recoverable. This section frames that cost matrix; it does not redefine kriging variance or prescribe the full response strategy.

If the variance is nugget-dominated, infill holes cannot reduce estimation error below the nugget floor. The money spent on drilling, sampling, and re-estimation is unrecoverable, and the affected blocks remain Inferred because the added data do not change the irreducible component of uncertainty.

If the variance is geometry-driven, the cost of delay is a lost field season. In rare earth exploration, permitting timelines and rig availability can make a one-year delay push a resource update past a funding window. Because no published figure applies universally, the season length must be quantified for the specific project before the delay cost is compared with drilling cost.

The asymmetry is that cash loss from nugget-dominated drilling is bounded by the program budget, whereas schedule loss from geometry-driven delay can be unbounded if it crosses a funding or permitting milestone. The same 40% threshold should therefore be read as a cost trigger, not as an automatic drill order: action is cheaper when uncertainty is spatially reducible, and redesign is cheaper when it is not.

A practical check is to compare the cost of one additional season against the cost of one redundant hole program before committing funds. The 0.5× range sample-count check used to diagnose the variance source also separates the two cost regimes: sparse neighborhoods make delay the larger risk, while denser neighborhoods make redundant drilling the larger risk.

Worked Example: Run the Numbers

Consider an illustrative rare-earth target for ExampleCo, a fictional operator, with an evaluation date of 2026-09-15 used only as an illustration. The modeled variogram range is 200 m, the relative kriging variance is 40%, and two existing holes fall within 100 m of the target block. These inputs are invented for demonstration and are not verified project data.

The arithmetic is therefore 200 m ÷ 2 = 100 m; two holes are inside that radius; 2 is less than 3; and an illustrative split of the 40% variance is 10% nugget plus 30% range. The range share is three times the nugget share, so the example is range-driven rather than nugget-driven.

That split matters because the drill-now case in the thesis is a low nugget with a range-driven shortfall. Here the range term is the larger share, so the uncertainty is consistent with sparse sampling of a continuous horizon rather than with erratic short-scale variability. The two holes do not provide enough local support for the 200 m range, which is why the variance stays at 40%.

Winner for this example: drill now. Break-even trigger: the recommendation changes when the neighborhood reaches three samples within 100 m and the range component stops dominating the 40% variance. Until then, the example treats one added hole as the cheaper information purchase; if the nugget share were the larger term, the same 40% would point away from cheap infill.

No cost figures are supplied in the available sources, so the break-even is expressed as a sample-count and variance-source condition rather than as a dollar threshold.

And Drill-or-Delay Checklist

Run this sequence when a 40% relative kriging variance is reported: refit the variogram and confirm at least 30 pairs per lag bin; count the samples within 0.5× the modeled range; drill infill only when that count is below 3, and recompute the kriging variance after each hole, stopping when it falls below the project's classification threshold.

Worked example: with a nugget/sill ratio of 0.30, a 200 m modeled range, and two existing holes within 100 m of the target block, the sample-count check gives 2 < 3, so the geometry-driven pattern calls for infill at roughly 200 m spacing; recompute the kriging variance after each hole and stop when it drops below the classification threshold.

After each infill hole, recompute the kriging variance using the same search neighborhood and variogram model, and record the pre-drill and post-drill values. If the variance did not fall, treat the result as a nugget problem and revisit the sampling design with a twin hole instead of adding more holes.

Record the pre-drill and post-drill kriging variance and the change between them, using the same search neighborhood and variogram model for every recompute. If the neighbor count is 3 or more within 0.5× the modeled range, do not add holes; revisit the sampling design instead.

Frequently Asked Questions

Can a 40% relative kriging variance be calculated before receiving any new assay results?

Yes, because it is computed strictly from the variogram model and the sample locations alone, with actual grade numbers not entering the variance calculation at all.

Is kriging variance a measure of rare earth grade?

No, kriging variance is not a measure of grade, but a measure of estimation uncertainty.

According to the defining form, what does a 40% of sill value represent?

It is the residual left after subtracting Σλᵢγ(hᵢ) from the sill, representing how much of the total sill variance is not accounted for by the spatial correlation captured through the sample pairs.

If two targets share the same variogram, will they have the same kriging variance?

No, because the variance is computed from the variogram model and the sample locations alone, so different sample locations can produce different results.

When evaluating a 40% relative kriging variance, should the focus be on the magnitude of mineralization?

No, the immediate check is which input is deficient: the sample geometry, the modeled nugget effect, or the modeled range of correlation.

Does a 40% relative kriging variance always mean infill drilling is a cheap fix?

No, the guide shows when infill drilling will not cheaply fix sampling-design failure.

Quick answers

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