Moving-Window Kriging Sharpens the Radioactive Maps That Guide Gold Hunters

Every year, aircraft criss-cross vast stretches of terrain, measuring the faint gamma rays that potassium, uranium, and thorium in the top few centimeters of the Earth’s crust emit as they decay. These airborne gamma-ray spectrometry surveys have become indispensable for geological mapping, mineral exploration, and environmental monitoring, but the raw measurements are only half the story. To turn a ribbon of flight-line data into a continuous map, geophysicists must interpolate between the lines, and the choice of interpolation method can either reveal or bury the geological detail that explorers are hunting for. A new study from São Paulo State University in Brazil now offers a locally adaptive alternative that promises to sharpen those maps where it matters most: at geological contacts.

The research, published in Discover Geoscience by Dionisio Uendro Carlos, César Augusto Moreira, and Guilherme Libardi Maestrelo, introduces a moving-window ordinary kriging (MW-OK) algorithm designed specifically for airborne and ground radiometric data. Conventional interpolators such as inverse distance weighting and minimum curvature are fast and widely used, but they share a fundamental weakness: they do not explicitly account for the local spatial structure of the data. In practice, that means they can oversmooth short-wavelength variability, blurring exactly the sharp radiometric gradients that mark boundaries between rock units or zones of hydrothermal alteration.

Kriging, by contrast, is a geostatistical method built on a statistical model of how a property varies in space. Because radioactive decay is inherently a stochastic process, the authors argue, an interpolator that respects this randomness is desirable. Yet standard kriging typically relies on a single global variogram, the mathematical function describing spatial correlation, assumed to hold across the entire survey area. Radiometric variables rarely obey that assumption at regional scale. Lithological boundaries, weathering domains, and survey-related effects all conspire to make the spatial structure change from place to place, so a global model can over-smooth local features or produce biased estimates where the structure shifts.

MW-OK sidesteps this problem by abandoning the global model altogether. For every prediction node on the output grid, the algorithm defines a circular window of investigation, in this case with a radius of 750 meters, roughly 1.5 times the 500-meter flight-line spacing, so that each window intersects two adjacent flight lines. Within that window, the method assumes second-order stationarity holds only approximately and locally. An empirical semivariogram is computed from all unique pairs of samples in the neighborhood, binned into eight lag classes, with any bin containing fewer than three valid pairs rejected. An exponential model is then fitted to each local semivariogram by bounded non-linear least squares, yielding a nugget effect, partial sill, and range parameter tailored to that specific patch of ground.

The computational scale is striking. The study area, a 40 by 40 kilometer subset of the Sul-Riograndense Shield Aerogeophysical Project flown by the Geological Survey of Brazil in 2010, contains 50,374 measurement points. Because the algorithm estimates a local variogram for each measurement point, it effectively generates 50,374 variograms. Neighbor retrieval is accelerated with a k-dimensional tree using ball queries, and safeguards keep the local kriging systems well conditioned: a minimum of eight neighbors, a maximum of thirty, removal of duplicate coordinates to prevent singular matrices, and a tiny ridge term added to the kriging matrix diagonal for numerical robustness. If a non-linear variogram fit fails, the workflow falls back on physically sensible defaults derived from the local data variance and median nearest-neighbor spacing.

The fitted local variograms themselves carry geological information. For potassium, the nugget effect was essentially zero at the scale of the data support, meaning microscale variability and measurement noise are minor compared with the spatially structured component, and correlation decayed over a practical range of about 1.3 kilometers. Equivalent uranium showed an even longer continuity, around 1.7 kilometers, consistent with smoother spatial behavior, while equivalent thorium displayed a larger partial sill, indicating higher structured variance, with a moderate range near 1.5 kilometers. These parameters confirm that, within each window, the radiometric variability is predominantly spatially structured rather than random noise.

When the researchers applied MW-OK to the survey data, the resulting potassium, uranium, and thorium maps reproduced the broad patterns that geologists expect. Potassium enrichment above 4 percent traced the São Sepé Granite in the north, elevated values of roughly 4 percent marked the Ramada Granite in the southwest, and low concentrations coincided with the metatuff-dominated Bossoroca Complex and the sandstones of the Maricá Group. Thorium highs of about 21 parts per million again outlined the São Sepé Granite, with additional anomalies over the Cerro da Cria Granite and nearby rhyolites. But the kriged surfaces went further than the conventional minimum-curvature grids: they better represented local gradient variations near lithological contacts and revealed internal heterogeneity within the felsic bodies that the smoother deterministic algorithm muted. Notably, three east-west linear artifacts aligned with the survey tie lines, visible in the minimum-curvature uranium map, were suppressed in the kriged surface.

A key advantage of kriging is that it also delivers an estimate of its own uncertainty. The kriging variance maps for all three radioelements bore the clear imprint of the acquisition geometry: uncertainty was minimized along and near the north-south flight lines and increased in the gaps between them, telling interpreters exactly where the estimates are most reliable. To quantify how closely MW-OK matched the industry-standard approach, the team performed pixel-wise comparisons with the minimum-curvature grids. The agreement was remarkably strong, with coefficients of determination of 0.9938 for potassium, 0.9727 for equivalent uranium, and 0.9946 for equivalent thorium, and residual histograms tightly centered near zero. Ordinary least-squares fits revealed a subtle but systematic amplitude scaling, with slopes slightly below unity, suggesting MW-OK modestly attenuates the highest values while remaining close to the identity overall. The authors are careful to frame this as evidence of methodological consistency rather than broad superiority: the two methods agree at the domain scale, and their differences emerge primarily at local scales.

Beyond the three radioelement grids, the workflow generates the interpretive products that exploration geologists actually use. It computes standard radiometric ratios (K/eTh, K/eU, eU/eTh) and the F-parameter, a widely used proxy for hydrothermal alteration that relates potassium abundance to the uranium-to-thorium ratio. It also produces ternary radioelement maps in three complementary forms: the classical K-eU-eTh display, normalized ternaries, and compositional-data transformations using additive, centered, and isometric log-ratios that respect the closure constraint and reduce spurious correlation when treating the three elements as parts of a composition. In the study area, a historically significant gold district in southern Brazil where mineralization is hydrothermal and structurally controlled in quartz veins hosted by schists and granites, these products delineated the main lithological contacts and showed spatial correspondence with known gold-mineralized zones and areas of gold enrichment identified by stream-sediment prospecting.

Perhaps most importantly for the wider community, the entire workflow is open source and exports standard deliverables, including GXF grids, GeoTIFF rasters, KMZ overlays, and PNG figures, with proper spatial metadata, making it directly interoperable with both open-source tools such as Python, QGIS, and Google Earth and commercial platforms like Oasis Montaj, Intrepid Geophysics, and ArcGIS. The authors acknowledge the method’s limitations: effective spatial resolution remains constrained by flight-line spacing and sampling interval, computational cost grows with finer grids and larger neighborhoods, and sparsely sampled sectors can yield under-populated windows with unstable variograms, which the workflow mitigates through minimum-neighbor thresholds and k-nearest-neighbor fallbacks. Looking ahead, they plan to incorporate co-regionalized cokriging constrained by lithology and structure, and deep-kriging approaches, within the same moving circular-window framework. For now, MW-OK stands as a robust, locally adaptive alternative that offers incremental rather than transformative gains over deterministic gridding, but gains that could make the difference between a blurred contact and a clearly resolved exploration target.

Subject of Research: A locally adaptive geostatistical interpolation method for processing airborne and ground gamma-ray spectrometric data

Article Title: A moving-window ordinary kriging approach for airborne and ground gamma-ray spectrometric data processing

Article References: Carlos, D. U., Moreira, C. A., & Maestrelo, G. L. (2026). A moving-window ordinary kriging approach for airborne and ground gamma-ray spectrometric data processing. Discover Geoscience, 4(1), Article 289. https://doi.org/10.1007/s44288-026-00674-4

Image Credits: AI Generated

DOI: 10.1007/s44288-026-00674-4

Keywords: gamma-ray spectrometry, kriging, geostatistics, radiometric mapping, mineral exploration, semivariogram, interpolation, gold prospecting, geological mapping, Brazil, open-source software, compositional data