  In geosciences, the use of classical Euclidean methods is unsuitable for
treating and analyzing some types of data, as this may not belong to a vector
space. This is the case for correlation matrices, belonging to a subfamily of
symmetric positive definite matrices, which in turn form a cone shape
Riemannian manifold. We propose two novel applications for dealing with the
problem of accounting with the non-linear behavior usually presented on
multivariate geological data by exploiting the manifold features of
correlations matrices. First, we employ an extension for the linear model of
coregionalization (LMC) that alters the linear mixture, which is assumed fixed
on the domain, and making it locally varying according to the local strength in
the dependency of the coregionalized variables. The main challenge, once this
relaxation on the LMC is assumed, is to solve appropriately the interpolation
of the different known correlation matrices throughout the domain, in a
reliable and coherent fashion. The present work adopts the non-euclidean
framework to achieve our objective by locally averaging and interpolating the
correlations between the variables, retaining the intrinsic geometry of
correlation matrices. A second application deals with the problem of clustering
of multivariate data.
