A spectral algorithm to simulate nonstationary random fields on spheres and multifractal star-shaped random sets

Abstract

An extension of the turning arcs algorithm is proposed for simulating a random field on the two-dimensional sphere with a second-order dependency structure associated with a locally varying Schoenberg sequence. In particular, the correlation range as well as the fractal index of the simulated random field, obtained as a weighted sum of Legendre waves with random degrees, may vary from place to place on the spherical surface. The proposed algorithm is illustrated with numerical examples, a by-product of which is a closed-form expression for two new correlation functions (exponential-Bessel and hypergeometric models) on the sphere, together with their respective Schoenberg sequences. The applicability of our findings is also described via the emulation of three-dimensional multifractal star-shaped random sets.