  A challenge in multivariate problems with discrete structures is the
inclusion of prior information that may differ in each separate structure. A
particular example of this is seismic amplitude versus angle (AVA) inversion to
elastic parameters, where the discrete structures are geologic layers.
Recently, the use of systems of linear stocastic partial differential equations
(SPDEs) have become a popular tool for specifying priors in latent Gaussian
models. This approach allows for flexible incorporation of nonstationarity and
anisotropy in the prior model. Another advantage is that the prior field is
Markovian and therefore the precision matrix is very sparse, introducing huge
computational and memory benefits. We present a novel approach for
parametrising correlations that differ in the different discrete structures,
and additionally a geodesic blending approach for quantifying fuzziness of
interfaces between the structures. Keywords: Gaussian distribution,
multivariate, stochastic PDEs, discrete structures
