Abstract

This paper focuses on vector random fields defined on Sd \times Rk, d ≥ 2 and k ≥ 1, with covariance functions that depend on the geodesic distance in Sd and on the separation vector in Rk. First, we propose parametric families of nonseparable covariance functions with closed-form expressions and explicit spectral representations. Then, we derive an algorithm for fast simulation of such random fields, which combines spectral simulation methods in Sd and Rk previously introduced in the literature and relies on importance sampling techniques. We provide computer codes and practical guidelines and describe the advantages of our proposal in comparison to other methods.