mathematics

Geostatistics & Spatial Analysis

Geostatistics transforms scattered spatial measurements into continuous maps of uncertainty — from mining ore grades to environmental contamination, these methods quantify how spatial correlation decays with distance and use that structure to make optimal predictions at unsampled locations.

geostatisticskrigingvariogramspatial analysisMoran's ILISAblock modelore estimationspatial correlation

Geostatistics emerged from the South African mining industry in the 1950s when Danie Krige noticed that simple averaging systematically overestimated ore grades. Georges Matheron formalized Krige's insights into a rigorous mathematical framework, creating kriging — the best linear unbiased predictor for spatially correlated data. Today geostatistics underpins resource estimation in mining, petroleum reservoir modeling, environmental remediation, precision agriculture, and epidemiological mapping.

These simulations let you explore the core geostatistical workflow: model spatial correlation with variograms, interpolate with kriging, map probabilities with indicator kriging, detect spatial clusters with Moran's I and LISA, and estimate block grades for mine planning. Each technique builds on the fundamental insight that nearby things are more alike than distant things — Tobler's First Law of Geography made mathematically precise.

5 interactive simulations

simulator

Ore Body Block Estimation Simulator

Estimate ore grades in a 2D block model grid using kriging and classify blocks as ore or waste based on economic cutoff

simulator

Indicator Kriging Probability Mapper

Map the probability of exceeding a critical cutoff grade using indicator kriging with binary-transformed spatial data

simulator

Ordinary Kriging Interpolation Simulator

Watch ordinary kriging build optimal interpolated surfaces from scattered sample points using spatial correlation structure

simulator

Moran's I & LISA Spatial Clustering Detector

Detect and visualize spatial clusters and outliers using global Moran's I statistic and Local Indicators of Spatial Association

simulator

Semivariogram Modeling & Range Estimation

Explore how spatial correlation decays with distance by fitting spherical, exponential, and Gaussian variogram models to scattered data