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.

提出了转弯弧算法的扩展，用于模拟二维球体上具有与局部变化的Schoenberg序列相关的二阶依赖结构的随机场。特别地，作为随机度的勒让德波的加权和而获得的模拟随机场的相关范围以及分形指数在球面上可能随位置而变化。所提出的算法通过数值示例进行说明，其副产品是球上两个新的相关函数（指数贝塞尔模型和超几何模型）及其各自的Schoenberg序列的闭式表达式。我们的发现的适用性也通过对三维多重分形星形随机集的仿真来描述。