The presented paper is devoted to statistical modeling of Gaussian scalar real random fields inside a three-dimensional sphere (ball). We propose a statistical model describing the spatial heterogeneity in a unit ball and a numerical procedure for generating an ensemble of corresponding random realizations. The accuracy of the presented approach is corroborated by the numerical comparison of the estimated and analytical covariance functions. Our approach is flexible with respect to the assumed radial and angular covariance function. We illustrate the effect of the covariance model parameters based on numerical examples of random field realizations. The presented statistical simulation technique can be applied, for example, to the inference of the 3D spatial heterogeneity in the Earth and other planets.
翻译:介绍的论文专门论述高森星标在三维领域(球)内实际随机字段的统计模型;我们提议了一个统计模型,说明单球的空间异质性,并提议一个数字程序,以产生相应的随机实现的共性;对估计和分析共变函数进行数字比较,可以证实所介绍方法的准确性;我们对假定的辐射和三角共变函数采取灵活的办法;我们根据随机地实现的数值实例说明共变模型参数的影响;例如,提出的统计模拟技术可以适用于地球和其他行星3D空间异性推断。