Variograms and regression methods of their creation

摘要

The role of interpolation methods in creation of the Digital elevation models (DEM) is an actual problem from theoretical and application aspect. Geo-statistical interpolation methods respect autocorrelation of input data, which is expressed by variogram function. The aim of this paper is to describe creation of variogram model functions and estimation of their parameters and also implementation of variogram to software Surfer for using Kriging interpolation method. The main contribution is creation of variogram function by parametric and nonparametric regression methods and their comparison. Kriging geo-statistical interpolation method, some types of variogram models and their properties are presented. The Least square method is used in estimation of regression functions by parametric regression method. The statistically analyzed results of four noted model functions were presented and used for implementation variogram model to software Surfer. Comparison of variograms created by parametric and nonparametric method demonstrated that nonparametric method respects input data more than model created by parametric regression, however in prediction of data the parametric regression methods are preferable.