Impact of anisotropic spatial data on Kriging interpolation

YiNing HAN, XiaoBin CHEN

Prog Geophy ›› 2026, Vol. 41 ›› Issue (3) : 1060-1071.

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Prog Geophy ›› 2026, Vol. 41 ›› Issue (3) : 1060-1071. DOI: 10.6038/pg2026JJ0155

Impact of anisotropic spatial data on Kriging interpolation

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Abstract

Gravity, magnetic potential fields, surface heat flow, and GPS velocity fields are common types of geophysical spatial data that often require interpolation for regional-scale analysis. These spatial data often exhibit different variation patterns in different directions, known as spatial anisotropy. However, most interpolation methods do not sufficiently consider the influence of spatial anisotropy on interpolation results, which can lead to suboptimal results. Although Kriging interpolation, which is fundamentally based on variogram modeling, is capable of capturing directional variation in spatial data, in practical applications, directional influences are often neglected, and interpolation weights are typically determined solely based on distance. Consequently, the effects of spatial anisotropy in variograms on interpolation results remain insufficiently insight. To address this issue, a series of comparative experiments were conducted using four datasets: three synthetic datasets—all incorporating observational noise and representing, respectively, isotropic, simple anisotropic, and complex anisotropic spatial structures—and one real-world measured dataset. These experiments were designed to assess the interpolation accuracy of Kriging under both isotropic and anisotropic variogram models across a variety of spatial distribution scenarios. Quantitative analysis revealed that when spatial anisotropy is weak, the interpolation results from isotropic and anisotropic variogram models are comparable. In contrast, under conditions of pronounced spatial anisotropy, the choice of variogram model significantly affects interpolation performance, with anisotropic variograms providing notably higher accuracy. These results suggest that incorporating variogram anisotropy into Kriging interpolation is not only necessary but also crucial, as it enables a more accurate characterization of directional spatial variability and leads to more reliable interpolation outcomes.

Key words

Spatial data distribution / Anisotropy / Variogram / Kriging interpolation

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YiNing HAN , XiaoBin CHEN. Impact of anisotropic spatial data on Kriging interpolation[J]. Progress in Geophysics. 2026, 41(3): 1060-1071 https://doi.org/10.6038/pg2026JJ0155

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