potential type- the paper aims at the development of the fourth order tensor-valued Taylor–Kármán structured covariance/correlation matrices. The characteristic functions of these tensor-valued covariance/correlation matrices, namely the lateral and longitudinal components, will be derived for n-dimensional spaces, here specified for \(n=3\) dimensions in the paper. A special part is devoted to the Hankel transformation for gravity gradients and their variance-covariance in order to guarantee consistency well-known from problems in using Fourier transformations. We use the variance-covariance function of type (i) isotropic, (ii) homogeneous and (iii) potential as prior information for fitting the discrete data of variances and covariances estimated from observations. Keywords Stochastic process Gravity gradient Covariance function Taylor–Kármán structured tensor" />