D2 ยท Publication Volume 18

Search Strategy and Neighbourhood

search ellipsoids, sample counts, octants and discretisation

Learning objectives

By the end of this lesson, the learner should be able to design a search ellipsoid from continuity and data geometry; choose minimum and maximum samples, drillhole limits, sectors and passes; select block discretisation; diagnose weight pathologies and conditional bias; and validate a neighbourhood without optimising a single metric.

The neighbourhood determines which data can influence a target and how the estimator behaves in sparse, clustered and boundary settings. It is part of the estimation model, not a computational afterthought.

Search geometry and coordinate system

Orient the ellipsoid with defensible continuity axes. Relate radii to variogram ranges, data spacing, domain thickness and intended extrapolation. A search may be shorter than a modelled range where pair support is weak or geological boundaries intervene. Locally varying orientation requires a documented field and transition rules.

Test ellipsoid containment visually in plan, section and three dimensions. Rotation order and sign conventions can turn the intended long axis into another direction without an obvious numerical error.

Sample counts, drillholes and sectors

Set minimum and maximum samples, maximum samples per hole, minimum holes and spatial sectors. The objective is a geometrically balanced neighbourhood with adequate information, not simply a large count. Many composites along one hole do not provide the same three-dimensional support as several holes.

Sector or octant rules can reduce clustering and screen effects, but strict rules may leave blocks unestimated or select distant data over nearer coherent data. Map which constraint binds each block.

Multiple passes and extrapolation

Use passes to distinguish well-informed estimation from controlled extrapolation. Each pass should have a purpose, search geometry, data requirements and output flag. Do not allow later passes to overwrite earlier estimates without retaining the pass identifier.

Unestimated blocks may be more honest than estimates based on distant or one-sided data. The decision to estimate is separate from the decision to classify. A wide final pass can support a geological inventory while remaining unclassified.

Block discretisation and support

Block kriging requires average covariance between data and a block. Approximate it with internal discretisation points. Increase points until estimates or average variogram values stabilise within a chosen tolerance. Match discretisation in the drilling direction to composite and block dimensions so the calculation does not imply artificial sub-support information.

The parent block, subcell geometry and estimation support need not be identical. Estimate at the declared support and copy or regularise values only with an explicit rule.

Neighbourhood diagnostics

Review number of samples and holes, average distance, pass, negative weights, sum of absolute weights, weight by hole, kriging variance, slope-of-regression-type diagnostics and estimates at data locations. These measures describe behaviour under the model; none alone selects the correct search or block size.

Compare global and local bias, smoothing, high-grade influence, boundary behaviour and coverage. A neighbourhood that improves one efficiency metric may worsen spatial balance or create unacceptable conditional bias.

A rotated search ellipsoid with sectors, drillhole limits, passes and a discretised target block
A rotated search ellipsoid with sectors, drillhole limits, passes and a discretised target block

Synthetic worked example

Three neighbourhoods are compared. A small search preserves local variability but leaves 21% of target blocks unestimated. A very large search gives full coverage but strong smoothing and endpoint weights. The adopted first pass uses radii of 90, 55 and 18\,\mathrm{m}, at least four holes, a maximum of three composites per hole and eight sectors.

A second pass expands radii by 1.5 with lower hole requirements and remains unclassified unless other evidence supports it. Discretisation tests from 2\times2\times2 to 6\times6\times4 stabilise at 4\times4\times2 because the vertical block dimension is close to the composite support.

Practice and review checklist

  • Verify ellipsoid rotations with known axis vectors and section views.
  • Map the constraint that limits every estimated or unestimated block.
  • Compare sample, hole and sector configurations rather than sample count alone.
  • Test discretisation until block estimates stabilise within a stated tolerance.
  • Evaluate coverage, smoothing, weight behaviour and validation together.

Decision record and integration

The neighbourhood specification should record axes, rotation convention, radii, sample and hole limits, sectors, passes, discretisation, domain boundary rules, diagnostics and rejected alternatives. Store pass and information metrics in the block model.

Classification may use neighbourhood evidence, but the thresholds must be combined with geological continuity, data quality and estimation sensitivity. A search-pass flag is not a confidence category.

Sources