Modeling the spatial correlation structure of coregionalized data is a frequent task in numerous fields of the natural sciences. Even in the isotropic case, experimental covariances may exhibit complex features, such as a maximum cross-correlation attained at non-collocated locations (dimple or hole effect). Current construction principles for multivariate covariance models on Euclidean spaces do not allow accounting for such a property. We propose a spectral approach to modify cross-covariancefunctions of the isotropic bivariate Matérn model in order to obtain a cross-dimple. Our model admits analytic expressions in terms of special functions. Our findings are illustrated through applications to data sets from the fields of mining and geochemistry.

在自然科学的许多领域中，共同分区数据的空间相关性结构建模是一项常见的任务。即使在各向同性的情况下，实验协方差也可能表现出复杂的特征，例如在非并列位置获得的最大互相关（凹痕或空穴效应）。当前在欧几里得空间上的多元协方差模型的构造原理不允许考虑这种性质。我们提出了一种频谱方法来修改各向同性二元Matérn模型的交叉协方差函数，以获得交叉凹坑。我们的模型接受特殊函数形式的解析表达式。通过将其应用于采矿和地球化学领域的数据集，可以说明我们的发现。