Application of a semivariogram based on a deep neural network to Ordinary Kriging interpolation of elevation data

Abstract

The Ordinary Kriging method is a common spatial interpolation algorithm in geostatistics. Because the semivariogram required for kriging interpolation greatly influences this process, optimal fitting of the semivariogram is of major significance for improving the theoretical accuracy of spatial interpolation. A deep neural network is a machine learning algorithm that can, in principle, be applied to any function, including a semivariogram. Accordingly, a novel spatial interpolation method based on a deep neural network and Ordinary Kriging was proposed in this research, and elevation data were used as a case study. Compared with the semivariogram fitted by the traditional exponential model, spherical model, and Gaussian model, the kriging variance in the proposed method is smaller, which means that the interpolation results are closer to the theoretical results of Ordinary Kriging interpolation. At the same time, this research can simplify processes for a variety of semivariogram analyses.