Space transformation methods in the representation of geophysical random fields

Various aspects of multidimensional random fields are studied by means of space transformations. The latter are elegant and comprehensive Radon operations which can solve complex multidimensional problems by transforming them to a suitable unidimensional setting, where analysis is considerably simpler. It is shown that spatial correlation functions in Rⁿ are uniquely determined by means of their space transformations in R¹. Necessary and sufficient conditions are established in order that a spatial random field (in Rⁿ) be represented as the linear combination of pairwise uncorrelated random processes (in R¹). Space transformations provide analytically tractable criteria for testing the permissibility of correlation functions and constitute an attractive instrument for spatial and spatiotemporal random field simulation and for studying stochastic partial differential equations. Several examples and a case study are discussed