From Values to Probabilities
Indicator kriging transforms the interpolation problem from estimating continuous values to estimating probabilities. Instead of asking 'what is the grade at this location?', it asks 'what is the probability that the grade exceeds a critical threshold?' This shift is powerful because many real decisions are binary — is this block ore or waste? Is this soil contaminated or clean? Is this aquifer polluted or safe? Indicator kriging answers these questions directly, without assuming the data follows any particular distribution.
The Indicator Transform
The method begins by converting each sample value into a binary indicator: 1 if the value exceeds the cutoff, 0 if it does not. This simple transform eliminates the influence of extreme high values (outliers) that plague ordinary kriging of skewed distributions like gold grades. An indicator variogram is then fitted to these 0/1 data, capturing how the spatial pattern of above/below-cutoff zones varies with distance. The indicator variogram is typically shorter-ranged than the value variogram because it captures boundary geometry rather than gradual trends.
Probability Mapping
Ordinary kriging of the indicator variable produces estimated probabilities between 0 and 1 at every unsampled location. In this simulation, the probability surface is displayed as a heat map — red indicates high probability of exceeding the cutoff (P > 0.7), blue indicates low probability (P < 0.3), and yellow/green indicates the uncertain boundary zone near P = 0.5. The uncertainty index quantifies how confidently the domain can be classified: values near 0.5 everywhere indicate poor resolution, while values near 0 or 1 indicate clear classification.
Multiple Indicator Kriging
The full power of indicator kriging emerges when applied at multiple cutoffs simultaneously. By estimating P(Z > z_c) at several thresholds, the complete conditional cumulative distribution function (ccdf) is recovered at each location. This ccdf provides not just the most likely value but the full range of uncertainty — the probability of any value occurring. This is the basis for probabilistic resource classification, risk-based environmental remediation, and conditional simulation in geostatistics.