Statistics

Geotechnical engineering

Hydrogeology

Gaussian random field

Physics

Geology

Random field

Pure mathematics

Mathematics

Quantum mechanics

Computer science

Gaussian process

Statistical physics

Gaussian

Field (mathematics)

Environmental science

Computational Geosciences

Gaussian (normal) distribution is a basic continuous probability distribution in statistics, it plays a substantial role in scientific and engineering problems that related to stochastic phenomena. This paper aims to review state-of-the-art of Gaussian random field generation methods, their applications in scientific and engineering issues of interest, and open-source software/packages for Gaussian random field generation. To this end, first, we briefly introduce basic mathematical concepts and theories in the Gaussian random field, then seven commonly used Gaussian random field generation methods are systematically presented. The basic idea, mathematical framework of each generation method are introduced in detail and comparisons of these methods are summarized. Then, representative applications of the Gaussian random field in various areas, especially of engineering interest in recent two decades, are reviewed. For readers’ convenience, four representative example codes are provided, and several relevant up-to-date open-source software and packages that freely available from the Internet are introduced.

Advances in Gaussian random field generation: a review