Anisotropic Spatial Structure Kriging Interpolation Method Based on Statistical Characteristic Parameters of Random Media

The spatial structure of subsurface media usually exhibits anisotropic characteristics due to geological factors such as depositional environment, tectonic movement, and overlying pressure, and the spatial structure characteristics are different at different spatial points. The traditional Kriging interpolation method based on global spatial range is difficult to accurately describe the anisotropic spatial structure characteristics of each spatial point in the subsurface medium, and the obtained Kriging interpolation results have larger errors. In this article, we estimate the statistical characteristic parameters of random media from seismic data, which correspond to the anisotropic spatial structure characteristics of each spatial point of the subsurface medium, so as to accurately describe the anisotropic spatial structure characteristics of each spatial point of the subsurface medium. Then the spatial correlation length of each spatial point of the underground medium in different directions is calculated from the statistical characteristic parameters of the random media, and then the anisotropic spatial covariance function is calculated; furthermore, the anisotropic Kriging weight coefficients are obtained, and finally, the final anisotropic spatial structure Kriging interpolation results are obtained. Compared with the traditional Kriging interpolation method, the Kriging interpolation results obtained by the method in this article are more reliable, and better match the actual anisotropic spatial structure characteristics of the subsurface medium, with smaller errors and less uncertainty. Model tests and field data applications demonstrate the effect of this method and verify its feasibility and practicality.