Kriging Neighborhood Analysis: Finding the Right Search Ellipse

The search ellipse is one of those parameters that geologists set once and never revisit. They pick a range from the variogram, add a few samples, and click “Run.” The estimate comes out, the map looks reasonable, and the parameter is never questioned again.

But the search ellipse is the single most influential kriging parameter after the variogram itself. It determines which samples contribute to each block estimate. Too large, and you over-smooth — distant samples dilute the local grade. Too small, and you under-smooth — the estimate is noisy and overly influenced by individual samples.

Kriging Neighborhood Analysis (KNA) is the process of systematically testing search ellipse parameters to find the configuration that gives the most accurate estimates. It’s not optional — it’s a JORC 2012 Table 1 Section 3 requirement. But in my experience, fewer than 20% of Indonesian resource reports document any form of KNA.

This post covers how to do KNA properly, with practical guidance for Indonesian deposits.

What the search ellipse does

When kriging estimates the grade of a block, it uses samples within a defined neighborhood — the search ellipse. The ellipse has:

• Orientation: aligned with the variogram anisotropy (usually the mineralization direction)
• Radii: the maximum distance along each axis (major, semi-major, minor)
• Minimum/maximum samples: how many samples must be found to produce an estimate
• Block discretization: how many points within the block are evaluated

Each of these parameters affects the estimate. Changing any one can shift the global resource by 5-15% and local block grades by 30% or more.

The KNA methodology

KNA is a form of cross-validation. You test different search parameters and measure which gives the most accurate estimates. The process:

Step 1: Define test scenarios

Create 5-10 scenarios with different parameter combinations:

The variogram range is your starting point — samples beyond the range have no correlation with the block, so the search radius should not exceed 1.5-2× the range.

Step 2: Run cross-validation

For each scenario, perform leave-one-out cross-validation:

1. Remove each sample from the dataset
2. Estimate its value using the remaining samples and the search parameters
3. Compare the estimate to the actual value
4. Calculate error metrics

Step 3: Evaluate error metrics

For each scenario, calculate:

Mean error (ME): Average of (estimated − actual). Should be near zero — a non-zero ME indicates bias.

Mean absolute error (MAE): Average of |estimated − actual|. Lower is better.

Root mean squared error (RMSE): Square root of average of (estimated − actual)². Lower is better. More sensitive to large errors than MAE.

Slope of regression: Plot estimated vs. actual. The slope should be close to 1.0. A slope <1.0 means the estimator is over-smoothing (underestimating high grades, overestimating low grades). A slope >1.0 means the estimator is under-smoothing.

Kriging efficiency: 1 − (kriging variance / data variance). Higher is better. Low efficiency means the kriging variance is high relative to the data variance — the estimate is uncertain.

Step 4: Choose the best scenario

The best scenario has:

• ME near zero (unbiased)
• Lowest RMSE (most accurate)
• Slope of regression near 1.0 (correct smoothing)
• Highest kriging efficiency (most precise)

In practice, there are trade-offs. A scenario with slope = 1.05 and RMSE = 0.8 might be better than one with slope = 0.95 and RMSE = 0.75 — the slight over-smoothing is acceptable if the overall accuracy is better.

Common KNA mistakes

Mistake 1: Not doing KNA at all

“We used a search radius of 150m based on the variogram range, with a minimum of 6 and maximum of 15 samples.”

This is the extent of KNA documentation in most Indonesian resource reports I’ve reviewed. No testing, no validation, no comparison. The parameters were chosen by feel.

JORC 2012 Table 1 Section 3 requires: “The nature and appropriateness of the estimation technique(s) and key parameters, including… the search window, the minimum and maximum number of data points used.”

“Appropriate” means tested. If you haven’t tested alternatives, you can’t claim appropriateness.

Mistake 2: Testing only the search radius

The search radius is important, but so are:

• Minimum number of samples: Too few and the estimate is unstable. Too many and you’re using distant, irrelevant samples.
• Maximum number of samples: Too many and the estimate is over-smoothed. Too few and it’s noisy.
• Block discretization: Too few points and the block grade is poorly estimated. Too many and computation time increases with no accuracy gain.

Test all parameters, not just the radius.

Mistake 3: Using global metrics instead of local

Global metrics (calculated across all samples) can hide local problems. A scenario might have good global RMSE but poor performance in high-grade zones or at domain boundaries.

Fix: Evaluate metrics by:

• Grade range (low, medium, high)
• Domain (oxide vs sulfide, vein vs halo)
• Drillhole spacing (well-drilled vs poorly-drilled areas)

Mistake 4: Ignoring the slope of regression

The slope of regression is the most diagnostic metric. It tells you whether your estimator is over-smoothing or under-smoothing:

• Slope = 0.7: Over-smoothing. High-grade blocks are underestimated by 30%. Your resource will be conservative — the mine will outperform the model. This is common with large search radii and high maximum sample counts.
• Slope = 1.3: Under-smoothing. High-grade blocks are overestimated by 30%. Your resource will be optimistic — the mine will underperform the model. This is common with small search radii and low maximum sample counts.
• Slope = 1.0: Correct smoothing. The estimator reproduces the grade distribution.

For most Indonesian deposits, a slope between 0.9 and 1.1 is acceptable. Outside that range, adjust your search parameters.

Practical guidance for Indonesian deposits

Search radius

Start with the variogram range. Test:

• 0.75× range (conservative — local estimates)
• 1.0× range (standard — uses all correlated samples)
• 1.5× range (aggressive — includes weakly correlated samples)

For high-nugget epithermal deposits, use 0.75-1.0× range. The high nugget means distant samples add noise, not information.

Sample count

Test minimums of 4, 6, and 8. Test maximums of 8, 12, and 16.

For deposits with 50-100m drill spacing, 6-12 samples is typical. For tighter spacing (25-50m), 8-16 samples may be appropriate.

Octant search

An octant search ensures samples are distributed in all directions around the block. Without it, all samples might come from one drillhole, biasing the estimate.

Use a minimum of 1 sample per octant, with a maximum of 2-3 per octant. This prevents any single drillhole from dominating the estimate.

Block discretization

Use at least 5×5×5 (125 points per block). For high-nugget deposits, 7×7×7 (343 points) may be needed. Below 3×3×3, the block grade is poorly estimated.

Documenting KNA in your report

Your JORC Table 1 Section 3 should include:

Kriging Neighborhood Analysis was conducted by leave-one-out cross-validation 
using 8 search scenarios. The optimal neighborhood was determined as:
- Search radii: 120m (major), 60m (semi-major), 40m (minor)
- Minimum samples: 6
- Maximum samples: 12
- Octant search: 1 minimum per octant, 3 maximum
- Block discretization: 5 × 5 × 5

This configuration produced a slope of regression of 0.96, kriging efficiency 
of 0.72, and RMSE of 0.58 g/t Au.

This is what “appropriate” looks like. Not a sentence — a paragraph with numbers and a rationale.

The bottom line

KNA is not a nice-to-have. It’s the difference between a defensible estimate and a guess. Your search ellipse parameters determine the accuracy of every block in your model, and the only way to know if they’re correct is to test them.

Run the analysis. Document the results. Show your work. The geologists who do this produce estimates that survive due diligence and, more importantly, match the mine. The ones who don’t spend years explaining why the model overestimated the high-grade tonnage by 40%.