When the variable governing the problem under study has spatial variations, the desired properties of the variable change by moving away from a point. In other words, points close to one another are more similar, and points distant from one another behave relatively independently. This spatial correlation has led to the development of a science known as geostatistics, which, of course, is not limited to the earth sciences and covers any discipline in which spatial variability is a concern.
This training course is prepared in two sessions. In the first session, a problem with spatial variables is described. Then the spatial data of the example is presented and imported into the MATLAB environment. In the following, the distance matrix and the lag distance criterion are introduced and their calculations are explained step-by-step. The concept of cloud variogram is then introduced and implemented in the MATLAB environment. In addition, various types of variogram estimators, including spherical, exponential, and linear models, are described and calculated. In the second session, the Kriging method is discussed as one of the most well-known methods in spatial statistics. For this purpose, first the required subject theories, such as weighted average of neighborhood points and Lagrange optimization, are explained, and then the formulation of the Kriging method is explained. The matrix form of the equations is then extracted and implemented as an example in the MATLAB environment. Moreover, the Kriging interpolation error is explored using the variance criterion and is plotted as an error contour alongside the Kriging prediction.
This course is beneficial for all students and researchers who work with spatial statistical models and explains the fundamentals of the required programming techniques and procedures in a straightforward way.