TASC3D: A program to test the admissibility in 3D of non-linear models of coregionalization

Most multivariate applications of geostatistics conveniently rely on the linear model of coregionalization (LMC). However, it is common that the secondary data represent a variable defined over a larger support than the primary variable. In these cases, the LMC cannot provide a good fit for the secondary variable variogram and the cross-variogram, leading to a loss of precision in cokriging and even more so in simulation. In the multivariate case, covariance models fitted on the direct and cross-variograms need to be checked for admissibility as a non-LMC (N-LMC). This non-trivial task is done by program TASC3D (for testing admissibility of symmetrical covariances in 3D). The admissibility verification is done based on the radial spectral densities of most common covariance functions. Two new spectral densities are derived for the penta and cubic models and expressions for anisotropic covariances are presented. The program enables checking the admissibility of 3D N-LMC coregionalization models or, alternatively, identification of the domain of admissibility for up to two free parameters. It can accommodate any number of variables, with any number of components for each structure, each component being isotropic or anisotropic. A series of examples are presented illustrating the program capacities. A simulated reference field is compared to conditional realizations from the LMC and the N-LMC. The precision of N-LMC shows improvements of 5.2% and 13.7% respectively for the primary and the secondary variables. By simplifying the modeling task, program TASC3D favors the use in applications of tailored N-LMC models.