Decomposition of multivariate spatial data into latent factors

Abstract

Listen

Translate article

Simulating spatial Gaussian realizations is one of the core components of geostatistics and numerous other fields involving uncertainty, risk, and reliability. The use of decorrelation methods and truncated Gaussian algorithms further promotes the use of Gaussian realizations. In multivariate cases, geological variables may represent different scales and exhibit different spatial structures and anisotropy that complicates decorrelation methods. For cases where spatial dependencies cannot be removed using techniques such as the projection pursuit multivariate transform coupled with maximum autocorrelation factors, cokriging is advocated and requires a model of coregionalization. However, blind source separation represents the original multivariate problem as a linear combination of latent source variables, each one having a spatial structure from the linear model of coregionalization (LMC). The latent source variables or factors are independent and follow a standard normal distribution facilitating the use of Gaussian simulation algorithms. Moreover, different algorithms may be utilized for each variable given that some are more efficient at generating realizations for different spatial covariance functions. Recovering the original variables afterwards is straightforward. The theory for this decomposition is presented. A small numerical example is used to explain the theory and the proposed approach is illustrated through a case study with geochemical sample data.