Reducing the number of orthogonal factors in linear coregionalization modeling

The simulation of vector random fields whose spatial correlation structure is represented by a linear coregionalization model can be performed by decomposing the vector components into spatially orthogonal factors and by simulating each factor separately. However, when the number of basic nested structures is large, so is the number of factors, making simulation computationally demanding.This paper proposes a methodology to construct linear coregionalization models with as many nested structures as desired, together with as few orthogonal factors as possible. The construction rests on the decomposition of the model coregionalization matrices into pairwise commuting matrices, followed by a factorization by principal component analysis. The proposed approach is illustrated through a case study in mineral resources evaluation and compared to the traditional fitting procedure, obtaining an equally good fit of the direct and cross variograms but with significantly less factors.

► Coregionalized variables can be decomposed into spatially orthogonal factors.
► The number of factors increases as the coregionalization model has more structures.
► It is proposed to fit linear coregionalization models that provide fewer factors.
► The proposal relies on the use of pairwise commuting coregionalization matrices.
► Algorithms and computer programs are presented and illustrated through a case study.