Multivariate random fields allow to simultaneously model multiple spatially indexed variables, playing a fundamental role in geophysical, environmental, and climate disciplines. This paper introduces the concept of cross‐dimple for bivariate isotropic random fields on spheres and proposes an approach to build parametric models that possess this attribute. Our findings are based on the spectral representation of the matrix‐valued covariance function. We show that our construction is compatible with both the negative binomial and circular‐Matérn bivariate families of covariance functions. We illustrate through simulation experiments that the models proposed in this work allow to achieve improvements in terms of predictive performance when a dimple‐like intrinsic structure is present.

中文翻译：

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球面上二元各向同性随机场的互协方差函数中的交叉凹坑

多元随机字段允许同时对多个空间索引变量进行建模，从而在地球物理，环境和气候学科中发挥重要作用。本文介绍了球面上双变量各向同性随机场的交叉凹坑的概念，并提出了一种建立具有此属性的参数模型的方法。我们的发现基于矩阵值协方差函数的频谱表示。我们证明我们的构造与负二项式和圆马特恩二元协方差函数族兼容。我们通过仿真实验说明，当存在酒窝状的内在结构时，本文中提出的模型可以改善预测性能。