An algorithm for generating spatially correlated random fields using Cholesky decomposition and ordinary kriging

Abstract

Spatially correlated random field realizations are often required in geotechnical applications. Examples include (1) modeling soil inherent variability and (2) representing earthquake ground motion demands on a spatially distributed system. These random fields must often be densely sampled to accurately model the problem at hand, posing a challenge to algorithms commonly used to compute random field realizations. Spacing of sampling points is often small compared with the scale of fluctuation of the random field, presenting the possibility for computational efficiency by combining traditional realization techniques with interpolation techniques. This paper presents a Python package in which Cholesky decomposition of the covariance matrix is utilized to generate a random field realization for a subset of sampling points that is adequately densely spaced, while ordinary kriging is used to interpolate the random field at the remaining sampling points. The algorithm exhibits linear computational complexity whereas Cholesky decomposition exhibits cubic complexity. Nodes sampled for Cholesky decomposition must have at least 4 sampling points per effective wavelength of the random field to maintain the desired covariance between interpolated sampling points.