Geostatistics with the Matern semivariogram model: A library of computer programs for inference, kriging and simulation

In many modern applications of geostatistics in the earth sciences, the empirical information is abundant and with complete spatial coverage (e.g. satellite sensor images). In these cases, a critical characteristic of spatial variability is the continuity of the random field that better models the natural phenomenon of interest. Such continuity describes the smoothness of the process at very short distances and is related to the behaviour of the semivariogram near the origin. For this reason, a semivariogram model that is flexible enough to describe the spatial continuity is very convenient for applications. A model that provides such flexibility is the Matern model that controls continuity with a shape parameter. The shape parameter must be larger than zero; a value larger than 1 implies a random field that is m-times mean square differentiable if the shape parameter is larger than m. A package of computer programs is provided for performing the different steps of a geostatistical study using the Matern model and the performance and implementation are illustrated by an example.