[formula omitted]-symmetric vector random fields.

This paper studies the properties of ℓ 1 -symmetric vector random fields in R d , whose direct/cross covariances are functions of ℓ 1 -norm. The spectral representation and a turning bands expression of the covariance matrix function are derived for an ℓ 1 -symmetric vector random field that is mean square continuous. We also establish an integral relationship between an ℓ 1 -symmetric covariance matrix function and an isotropic one. In addition, a simple but efficient approach is proposed to construct the ℓ 1 -symmetric random field in R d , whose univariate marginal distributions may be taken as arbitrary infinitely divisible distribution with finite variance. [ABSTRACT FROM AUTHOR]