Geostatistics

The term refers to specific geostatistics stochastic methods for characterization and estimation of spatially correlated georeferenced data, for example surface temperatures at various points of a lake. The aim is to use the point by way of measured data as a basis for spatial interpolation, ie of a finite number of measurements to derive an infinite number of estimates that are as close as possible to the real present values.

The estimated value of a physical quantity (such as the surface temperature) of a Schätzort is stronger due to the spatial correlation of the measured values ​​as a function of such adjacent remote measuring places. For the estimation of these adjacent measured values ​​are therefore to be considered stronger. We distinguish two methods, the non-statistical and statistical interpolation, the latter based on a geostatistical model.

In order to ascertain up to what maximum distance (range) and to what extent depend readings from neighboring or more distant readings, so-called experimental semi- variograms are modeled: For all distances ( as the x- values), the two measurement locations of the data set to each other have, the differences of the respective measurement values ​​are plotted ( as the y- values): the growing dissimilarity with increasing distance is reflected in the increase in the y- values ​​with increasing x values ​​up to a certain limit resist. This dependency is a model function, for example a quadratic function expressed.

The function that has been obtained from the analysis of the measured values ​​is the basis for the subsequent interpolation of a distribution of estimated values ​​in the space in a process referred to as the kriging. The measurement values ​​are obtained depending on the proximity to the searched estimate value depending on the modeled semivariogram different weighting factors with which they enter into the calculation of the estimated value ( counter-example: arithmetic mean as an estimator: obtain all readings without distinction the same weight ).

Is a prerequisite for the interpolation, that in the study area, the measured value distribution is homogeneous ( criterion of stationarity / homogeneity ). Example of inhomogeneity: the aluminum content of rocks of the study area, in which there are offset by a malfunction of two completely different rock units adjacent to and contiguous with no transition zone.

For example, the surface temperature of a lake, the result would be a distribution of the kriging estimate values ​​in the plane of, for example, as isothermal map or surface relief ( " flying carpet " ) can be visualized with the elevational axis as the temperature axis.