Simulation of Gaussian random field in a ball

TL;DR

This paper introduces a flexible statistical method for simulating Gaussian random fields within a 3D sphere, validated by numerical comparisons and applicable to planetary spatial heterogeneity analysis.

Contribution

It presents a novel numerical procedure for generating Gaussian random fields in a sphere with adjustable covariance functions, enhancing modeling of 3D spatial heterogeneity.

Findings

Numerical validation shows high accuracy of covariance function estimation.

Method effectively models spatial heterogeneity in planetary contexts.

Flexible covariance assumptions improve simulation realism.

Abstract

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.