Transformations of spatial correlation lengths in random fields

Abstract

The paper describes the theoretical relationship between spatial correlation lengths in lognormal and hyperbolic tangent (“tanh”) random fields, and the underlying Gaussian random fields from which they are derived following transformation. The inevitable change in the spatial correlation length following transformation has been noted in several studies, but has not, to the authors’ knowledge, been rigorously investigated before. The paper presents derivations that show the dependencies for normal/log-normal and normal/tanh transformations together with three different correlation functions. The one-dimensional derivations are extrapolated to two- and three-dimensional models, with particular emphasis on vertical and horizontal correlation lengths. The paper concludes with an example probabilistic bearing capacity analysis using the Random Finite Element Method (RFEM). For the example considered, the untransformed solutions were slightly unconservative, but the differences were generally quite modest.